diff --git a/.gitignore b/.gitignore
index 9f1082e..8bb7693 100644
--- a/.gitignore
+++ b/.gitignore
@@ -18,9 +18,17 @@ build/
 *.db
 *.sqlite
 *.sqlite3
+*.log
+.superpowers/
 tmp/
 temp/
 .cache/
 
 # Local git worktrees used for parallel AI development.
 .worktrees/
+
+# WeChat Mini Program — API key config (do not commit)
+wx-miniprogram/config.js
+
+# WeChat Mini Program — generated data bundle (rebuilt from content/)
+wx-miniprogram/data/all-chapters.js
diff --git a/app/fonts.css b/app/fonts.css
new file mode 100644
index 0000000..3afa196
--- /dev/null
+++ b/app/fonts.css
@@ -0,0 +1,218 @@
+/* 自托管字体 —— 由 scripts/fetch-fonts.mjs 生成，请勿手改。
+   中文走本地宋体/思源回退（见 globals.css 字体栈）。 */
+
+@font-face {
+  font-family: 'Spectral';
+  font-style: italic;
+  font-weight: 400;
+  font-display: swap;
+  src: url('/fonts/spectral-400-italic-latin-ext.woff2') format('woff2');
+  unicode-range: U+0100-02BA, U+02BD-02C5, U+02C7-02CC, U+02CE-02D7, U+02DD-02FF, U+0304, U+0308, U+0329, U+1D00-1DBF, U+1E00-1E9F, U+1EF2-1EFF, U+2020, U+20A0-20AB, U+20AD-20C0, U+2113, U+2C60-2C7F, U+A720-A7FF;
+}
+
+@font-face {
+  font-family: 'Spectral';
+  font-style: italic;
+  font-weight: 400;
+  font-display: swap;
+  src: url('/fonts/spectral-400-italic-latin.woff2') format('woff2');
+  unicode-range: U+0000-00FF, U+0131, U+0152-0153, U+02BB-02BC, U+02C6, U+02DA, U+02DC, U+0304, U+0308, U+0329, U+2000-206F, U+20AC, U+2122, U+2191, U+2193, U+2212, U+2215, U+FEFF, U+FFFD;
+}
+
+@font-face {
+  font-family: 'Spectral';
+  font-style: italic;
+  font-weight: 500;
+  font-display: swap;
+  src: url('/fonts/spectral-500-italic-latin-ext.woff2') format('woff2');
+  unicode-range: U+0100-02BA, U+02BD-02C5, U+02C7-02CC, U+02CE-02D7, U+02DD-02FF, U+0304, U+0308, U+0329, U+1D00-1DBF, U+1E00-1E9F, U+1EF2-1EFF, U+2020, U+20A0-20AB, U+20AD-20C0, U+2113, U+2C60-2C7F, U+A720-A7FF;
+}
+
+@font-face {
+  font-family: 'Spectral';
+  font-style: italic;
+  font-weight: 500;
+  font-display: swap;
+  src: url('/fonts/spectral-500-italic-latin.woff2') format('woff2');
+  unicode-range: U+0000-00FF, U+0131, U+0152-0153, U+02BB-02BC, U+02C6, U+02DA, U+02DC, U+0304, U+0308, U+0329, U+2000-206F, U+20AC, U+2122, U+2191, U+2193, U+2212, U+2215, U+FEFF, U+FFFD;
+}
+
+@font-face {
+  font-family: 'Spectral';
+  font-style: normal;
+  font-weight: 400;
+  font-display: swap;
+  src: url('/fonts/spectral-400-normal-latin-ext.woff2') format('woff2');
+  unicode-range: U+0100-02BA, U+02BD-02C5, U+02C7-02CC, U+02CE-02D7, U+02DD-02FF, U+0304, U+0308, U+0329, U+1D00-1DBF, U+1E00-1E9F, U+1EF2-1EFF, U+2020, U+20A0-20AB, U+20AD-20C0, U+2113, U+2C60-2C7F, U+A720-A7FF;
+}
+
+@font-face {
+  font-family: 'Spectral';
+  font-style: normal;
+  font-weight: 400;
+  font-display: swap;
+  src: url('/fonts/spectral-400-normal-latin.woff2') format('woff2');
+  unicode-range: U+0000-00FF, U+0131, U+0152-0153, U+02BB-02BC, U+02C6, U+02DA, U+02DC, U+0304, U+0308, U+0329, U+2000-206F, U+20AC, U+2122, U+2191, U+2193, U+2212, U+2215, U+FEFF, U+FFFD;
+}
+
+@font-face {
+  font-family: 'Spectral';
+  font-style: normal;
+  font-weight: 500;
+  font-display: swap;
+  src: url('/fonts/spectral-500-normal-latin-ext.woff2') format('woff2');
+  unicode-range: U+0100-02BA, U+02BD-02C5, U+02C7-02CC, U+02CE-02D7, U+02DD-02FF, U+0304, U+0308, U+0329, U+1D00-1DBF, U+1E00-1E9F, U+1EF2-1EFF, U+2020, U+20A0-20AB, U+20AD-20C0, U+2113, U+2C60-2C7F, U+A720-A7FF;
+}
+
+@font-face {
+  font-family: 'Spectral';
+  font-style: normal;
+  font-weight: 500;
+  font-display: swap;
+  src: url('/fonts/spectral-500-normal-latin.woff2') format('woff2');
+  unicode-range: U+0000-00FF, U+0131, U+0152-0153, U+02BB-02BC, U+02C6, U+02DA, U+02DC, U+0304, U+0308, U+0329, U+2000-206F, U+20AC, U+2122, U+2191, U+2193, U+2212, U+2215, U+FEFF, U+FFFD;
+}
+
+@font-face {
+  font-family: 'Spectral';
+  font-style: normal;
+  font-weight: 600;
+  font-display: swap;
+  src: url('/fonts/spectral-600-normal-latin-ext.woff2') format('woff2');
+  unicode-range: U+0100-02BA, U+02BD-02C5, U+02C7-02CC, U+02CE-02D7, U+02DD-02FF, U+0304, U+0308, U+0329, U+1D00-1DBF, U+1E00-1E9F, U+1EF2-1EFF, U+2020, U+20A0-20AB, U+20AD-20C0, U+2113, U+2C60-2C7F, U+A720-A7FF;
+}
+
+@font-face {
+  font-family: 'Spectral';
+  font-style: normal;
+  font-weight: 600;
+  font-display: swap;
+  src: url('/fonts/spectral-600-normal-latin.woff2') format('woff2');
+  unicode-range: U+0000-00FF, U+0131, U+0152-0153, U+02BB-02BC, U+02C6, U+02DA, U+02DC, U+0304, U+0308, U+0329, U+2000-206F, U+20AC, U+2122, U+2191, U+2193, U+2212, U+2215, U+FEFF, U+FFFD;
+}
+
+@font-face {
+  font-family: 'Spectral';
+  font-style: normal;
+  font-weight: 700;
+  font-display: swap;
+  src: url('/fonts/spectral-700-normal-latin-ext.woff2') format('woff2');
+  unicode-range: U+0100-02BA, U+02BD-02C5, U+02C7-02CC, U+02CE-02D7, U+02DD-02FF, U+0304, U+0308, U+0329, U+1D00-1DBF, U+1E00-1E9F, U+1EF2-1EFF, U+2020, U+20A0-20AB, U+20AD-20C0, U+2113, U+2C60-2C7F, U+A720-A7FF;
+}
+
+@font-face {
+  font-family: 'Spectral';
+  font-style: normal;
+  font-weight: 700;
+  font-display: swap;
+  src: url('/fonts/spectral-700-normal-latin.woff2') format('woff2');
+  unicode-range: U+0000-00FF, U+0131, U+0152-0153, U+02BB-02BC, U+02C6, U+02DA, U+02DC, U+0304, U+0308, U+0329, U+2000-206F, U+20AC, U+2122, U+2191, U+2193, U+2212, U+2215, U+FEFF, U+FFFD;
+}
+
+@font-face {
+  font-family: 'Source Serif 4';
+  font-style: italic;
+  font-weight: 400;
+  font-display: swap;
+  src: url('/fonts/source-serif-4-400-italic-latin-ext.woff2') format('woff2');
+  unicode-range: U+0100-02BA, U+02BD-02C5, U+02C7-02CC, U+02CE-02D7, U+02DD-02FF, U+0304, U+0308, U+0329, U+1D00-1DBF, U+1E00-1E9F, U+1EF2-1EFF, U+2020, U+20A0-20AB, U+20AD-20C0, U+2113, U+2C60-2C7F, U+A720-A7FF;
+}
+
+@font-face {
+  font-family: 'Source Serif 4';
+  font-style: italic;
+  font-weight: 400;
+  font-display: swap;
+  src: url('/fonts/source-serif-4-400-italic-latin.woff2') format('woff2');
+  unicode-range: U+0000-00FF, U+0131, U+0152-0153, U+02BB-02BC, U+02C6, U+02DA, U+02DC, U+0304, U+0308, U+0329, U+2000-206F, U+20AC, U+2122, U+2191, U+2193, U+2212, U+2215, U+FEFF, U+FFFD;
+}
+
+@font-face {
+  font-family: 'Source Serif 4';
+  font-style: normal;
+  font-weight: 400;
+  font-display: swap;
+  src: url('/fonts/source-serif-4-400-normal-latin-ext.woff2') format('woff2');
+  unicode-range: U+0100-02BA, U+02BD-02C5, U+02C7-02CC, U+02CE-02D7, U+02DD-02FF, U+0304, U+0308, U+0329, U+1D00-1DBF, U+1E00-1E9F, U+1EF2-1EFF, U+2020, U+20A0-20AB, U+20AD-20C0, U+2113, U+2C60-2C7F, U+A720-A7FF;
+}
+
+@font-face {
+  font-family: 'Source Serif 4';
+  font-style: normal;
+  font-weight: 400;
+  font-display: swap;
+  src: url('/fonts/source-serif-4-400-normal-latin.woff2') format('woff2');
+  unicode-range: U+0000-00FF, U+0131, U+0152-0153, U+02BB-02BC, U+02C6, U+02DA, U+02DC, U+0304, U+0308, U+0329, U+2000-206F, U+20AC, U+2122, U+2191, U+2193, U+2212, U+2215, U+FEFF, U+FFFD;
+}
+
+@font-face {
+  font-family: 'Source Serif 4';
+  font-style: normal;
+  font-weight: 500;
+  font-display: swap;
+  src: url('/fonts/source-serif-4-500-normal-latin-ext.woff2') format('woff2');
+  unicode-range: U+0100-02BA, U+02BD-02C5, U+02C7-02CC, U+02CE-02D7, U+02DD-02FF, U+0304, U+0308, U+0329, U+1D00-1DBF, U+1E00-1E9F, U+1EF2-1EFF, U+2020, U+20A0-20AB, U+20AD-20C0, U+2113, U+2C60-2C7F, U+A720-A7FF;
+}
+
+@font-face {
+  font-family: 'Source Serif 4';
+  font-style: normal;
+  font-weight: 500;
+  font-display: swap;
+  src: url('/fonts/source-serif-4-500-normal-latin.woff2') format('woff2');
+  unicode-range: U+0000-00FF, U+0131, U+0152-0153, U+02BB-02BC, U+02C6, U+02DA, U+02DC, U+0304, U+0308, U+0329, U+2000-206F, U+20AC, U+2122, U+2191, U+2193, U+2212, U+2215, U+FEFF, U+FFFD;
+}
+
+@font-face {
+  font-family: 'Source Serif 4';
+  font-style: normal;
+  font-weight: 600;
+  font-display: swap;
+  src: url('/fonts/source-serif-4-600-normal-latin-ext.woff2') format('woff2');
+  unicode-range: U+0100-02BA, U+02BD-02C5, U+02C7-02CC, U+02CE-02D7, U+02DD-02FF, U+0304, U+0308, U+0329, U+1D00-1DBF, U+1E00-1E9F, U+1EF2-1EFF, U+2020, U+20A0-20AB, U+20AD-20C0, U+2113, U+2C60-2C7F, U+A720-A7FF;
+}
+
+@font-face {
+  font-family: 'Source Serif 4';
+  font-style: normal;
+  font-weight: 600;
+  font-display: swap;
+  src: url('/fonts/source-serif-4-600-normal-latin.woff2') format('woff2');
+  unicode-range: U+0000-00FF, U+0131, U+0152-0153, U+02BB-02BC, U+02C6, U+02DA, U+02DC, U+0304, U+0308, U+0329, U+2000-206F, U+20AC, U+2122, U+2191, U+2193, U+2212, U+2215, U+FEFF, U+FFFD;
+}
+
+@font-face {
+  font-family: 'IBM Plex Mono';
+  font-style: normal;
+  font-weight: 400;
+  font-display: swap;
+  src: url('/fonts/ibm-plex-mono-400-normal-latin-ext.woff2') format('woff2');
+  unicode-range: U+0100-02BA, U+02BD-02C5, U+02C7-02CC, U+02CE-02D7, U+02DD-02FF, U+0304, U+0308, U+0329, U+1D00-1DBF, U+1E00-1E9F, U+1EF2-1EFF, U+2020, U+20A0-20AB, U+20AD-20C0, U+2113, U+2C60-2C7F, U+A720-A7FF;
+}
+
+@font-face {
+  font-family: 'IBM Plex Mono';
+  font-style: normal;
+  font-weight: 400;
+  font-display: swap;
+  src: url('/fonts/ibm-plex-mono-400-normal-latin.woff2') format('woff2');
+  unicode-range: U+0000-00FF, U+0131, U+0152-0153, U+02BB-02BC, U+02C6, U+02DA, U+02DC, U+0304, U+0308, U+0329, U+2000-206F, U+20AC, U+2122, U+2191, U+2193, U+2212, U+2215, U+FEFF, U+FFFD;
+}
+
+@font-face {
+  font-family: 'IBM Plex Mono';
+  font-style: normal;
+  font-weight: 500;
+  font-display: swap;
+  src: url('/fonts/ibm-plex-mono-500-normal-latin-ext.woff2') format('woff2');
+  unicode-range: U+0100-02BA, U+02BD-02C5, U+02C7-02CC, U+02CE-02D7, U+02DD-02FF, U+0304, U+0308, U+0329, U+1D00-1DBF, U+1E00-1E9F, U+1EF2-1EFF, U+2020, U+20A0-20AB, U+20AD-20C0, U+2113, U+2C60-2C7F, U+A720-A7FF;
+}
+
+@font-face {
+  font-family: 'IBM Plex Mono';
+  font-style: normal;
+  font-weight: 500;
+  font-display: swap;
+  src: url('/fonts/ibm-plex-mono-500-normal-latin.woff2') format('woff2');
+  unicode-range: U+0000-00FF, U+0131, U+0152-0153, U+02BB-02BC, U+02C6, U+02DA, U+02DC, U+0304, U+0308, U+0329, U+2000-206F, U+20AC, U+2122, U+2191, U+2193, U+2212, U+2215, U+FEFF, U+FFFD;
+}
diff --git a/app/globals.css b/app/globals.css
index 678944d..d37b7d2 100644
--- a/app/globals.css
+++ b/app/globals.css
@@ -462,7 +462,9 @@ a {
 /* 教学图示卡：像贴在书页上的插图 */
 .diagram-grid {
   display: grid;
-  gap: 16px;
+  grid-template-columns: repeat(auto-fit, minmax(320px, 1fr));
+  gap: 16px 18px;
+  counter-reset: fig;
 }
 
 .diagram-card {
@@ -487,6 +489,14 @@ a {
   color: var(--ink);
 }
 
+/* 教科书式图号：图 1 / 图 2 … */
+.diagram-card figcaption strong::before {
+  counter-increment: fig;
+  content: "图 " counter(fig) "　";
+  color: var(--gold);
+  font-variant-numeric: lining-nums tabular-nums;
+}
+
 .diagram-card svg {
   width: 100%;
   height: auto;
@@ -502,6 +512,50 @@ a {
   font-style: italic;
 }
 
+.diagram-card--concept {
+  background: var(--paper-page);
+  border-left: 3px solid var(--gold);
+  border-radius: 0 var(--radius) var(--radius) 0;
+}
+
+.diagram-card--concept .diagram-prompt {
+  margin-top: 14px;
+}
+
+.diagram-svg {
+  max-width: 560px;
+}
+
+.diagram-table-wrap {
+  margin-top: 12px;
+  overflow-x: auto;
+}
+
+.diagram-table {
+  width: 100%;
+  border-collapse: collapse;
+  font-family: var(--serif-body);
+  font-size: 14px;
+  color: var(--ink);
+}
+
+.diagram-table th,
+.diagram-table td {
+  padding: 7px 12px;
+  border: 1px solid var(--rule);
+  text-align: left;
+}
+
+.diagram-table thead th {
+  background: var(--accent-wash);
+  color: var(--accent-deep);
+  font-weight: 600;
+}
+
+.diagram-table tbody tr:nth-child(even) td {
+  background: color-mix(in srgb, var(--paper-page) 70%, transparent);
+}
+
 /* ----------------------------------------------------------------
    练习区
 ----------------------------------------------------------------- */
@@ -558,6 +612,19 @@ button:disabled {
   cursor: progress;
 }
 
+button.is-primary {
+  background: var(--accent);
+  border-color: var(--accent-deep);
+  color: white;
+  font-weight: 600;
+}
+
+button.is-primary:hover:not(:disabled) {
+  background: var(--accent-deep);
+  border-color: var(--accent-deep);
+  color: white;
+}
+
 textarea {
   width: 100%;
   min-height: 150px;
@@ -669,6 +736,20 @@ select:focus {
   flex-wrap: wrap;
   gap: 10px;
   margin: 16px 0;
+  align-items: center;
+  padding: 12px 0;
+  border-top: 1px solid var(--rule);
+  border-bottom: 1px solid var(--rule);
+}
+
+.exercise-action-label {
+  width: 100%;
+  font-family: var(--serif-display);
+  font-size: 11.5px;
+  font-weight: 600;
+  letter-spacing: 0.14em;
+  text-transform: uppercase;
+  color: var(--ink-faint);
 }
 
 .grading-error {
@@ -748,6 +829,28 @@ select:focus {
   color: var(--gold);
 }
 
+.mistake-list {
+  margin: 0;
+  padding: 0;
+  list-style: none;
+}
+
+.mistake-list li {
+  position: relative;
+  margin: 8px 0;
+  padding-left: 20px;
+  line-height: 1.65;
+}
+
+.mistake-list li::before {
+  content: "✕";
+  position: absolute;
+  left: 0;
+  color: var(--accent);
+  font-size: 11px;
+  top: 4px;
+}
+
 details {
   margin-top: 14px;
   border-top: 1px solid var(--rule);
@@ -995,7 +1098,7 @@ details summary {
   min-width: 0;
   display: flex;
   flex-direction: column;
-  gap: 4px;
+  gap: 5px;
 }
 
 .exercise-card-preview {
@@ -1008,6 +1111,18 @@ details summary {
   white-space: nowrap;
 }
 
+.exercise-card-title {
+  margin: 0;
+  font-size: 14px;
+  line-height: 1.45;
+  color: var(--ink);
+  font-weight: 500;
+  overflow: hidden;
+  text-overflow: ellipsis;
+  white-space: nowrap;
+  font-family: var(--serif-body);
+}
+
 .difficulty-pill {
   align-self: flex-start;
   padding: 2px 8px;
@@ -1042,6 +1157,54 @@ details summary {
   border-top: 1px solid var(--rule);
 }
 
+.problem-statement {
+  margin: 0 0 20px;
+  padding: 18px 20px 16px;
+  background: var(--paper-page);
+  border: 1px solid var(--rule);
+  border-left: 3px solid var(--accent);
+  border-radius: 0 var(--radius) var(--radius) 0;
+  box-shadow: var(--shadow-page);
+}
+
+.problem-title {
+  margin: 0 0 10px;
+  font-family: var(--serif-display);
+  font-size: 13px;
+  font-weight: 600;
+  letter-spacing: 0.08em;
+  text-transform: uppercase;
+  color: var(--accent-deep);
+  opacity: 0.8;
+}
+
+.problem-body {
+  font-family: var(--serif-body);
+  font-size: 16px;
+  line-height: 1.85;
+  color: var(--ink);
+}
+
+.answer-label {
+  margin: 0 0 8px;
+  font-family: var(--serif-display);
+  font-size: 12px;
+  font-weight: 600;
+  letter-spacing: 0.16em;
+  text-transform: uppercase;
+  color: var(--ink-faint);
+}
+
+.exercise-num-label {
+  margin: 0 0 12px;
+  font-size: 11.5px;
+  letter-spacing: 0.14em;
+  text-transform: uppercase;
+  color: var(--accent);
+  font-family: var(--serif-display);
+  font-weight: 600;
+}
+
 details summary:hover {
   color: var(--accent-deep);
 }
@@ -1112,7 +1275,10 @@ details ul {
   margin: 0 0 10px;
 }
 
-.chapter-header-kp-count {
+.chapter-header-stats {
+  display: flex;
+  flex-wrap: wrap;
+  gap: 8px;
   font-size: 12px;
   color: var(--ink-faint);
   margin: 0;
@@ -1120,6 +1286,21 @@ details ul {
   letter-spacing: 0.06em;
 }
 
+.chapter-header-stats span {
+  display: inline-flex;
+  align-items: center;
+  gap: 6px;
+}
+
+.chapter-header-stats span::before {
+  content: "";
+  width: 5px;
+  height: 5px;
+  border-radius: 50%;
+  background: var(--gold);
+  opacity: 0.8;
+}
+
 /* ----------------------------------------------------------------
    KP 导航：前后箭头
 ----------------------------------------------------------------- */
@@ -1193,6 +1374,13 @@ details ul {
   margin: 0;
 }
 
+.tutor-context {
+  margin: 5px 0 0;
+  color: var(--ink-soft);
+  font-size: 13.5px;
+  line-height: 1.45;
+}
+
 .settings-toggle {
   font-size: 12.5px;
   padding: 5px 11px;
diff --git a/app/layout.tsx b/app/layout.tsx
index 96bdf9a..af09fbc 100644
--- a/app/layout.tsx
+++ b/app/layout.tsx
@@ -1,5 +1,6 @@
 import type { Metadata } from "next";
 import "katex/dist/katex.min.css";
+import "./fonts.css";
 import "./globals.css";
 
 export const metadata: Metadata = {
@@ -10,14 +11,6 @@ export const metadata: Metadata = {
 export default function RootLayout({ children }: { children: React.ReactNode }) {
   return (
     <html lang="zh-CN">
-      <head>
-        <link rel="preconnect" href="https://fonts.googleapis.com" />
-        <link rel="preconnect" href="https://fonts.gstatic.com" crossOrigin="anonymous" />
-        <link
-          rel="stylesheet"
-          href="https://fonts.googleapis.com/css2?family=Spectral:ital,wght@0,400;0,500;0,600;0,700;1,400;1,500&family=Source+Serif+4:ital,opsz,wght@0,8..60,400;0,8..60,500;0,8..60,600;1,8..60,400&family=Noto+Serif+SC:wght@400;500;600;700&family=IBM+Plex+Mono:wght@400;500&display=swap"
-        />
-      </head>
       <body>
         <div className="page-frame">
           <header className="masthead">
diff --git a/components/course/ChapterHeader.tsx b/components/course/ChapterHeader.tsx
index 203d46d..e0688c4 100644
--- a/components/course/ChapterHeader.tsx
+++ b/components/course/ChapterHeader.tsx
@@ -1,3 +1,4 @@
+import { MathText } from "@/components/math/MathText";
 import type { ChapterContent } from "@/lib/course/types";
 
 const statusLabel: Record<string, string> = {
@@ -7,6 +8,9 @@ const statusLabel: Record<string, string> = {
 };
 
 export function ChapterHeader({ chapter }: { chapter: ChapterContent }) {
+  const diagramCount = new Set(chapter.knowledgePoints.flatMap((kp) => kp.diagramIds)).size;
+  const exerciseCount = new Set(chapter.knowledgePoints.flatMap((kp) => kp.exerciseIds)).size;
+
   return (
     <header className="chapter-header">
       <div className="chapter-header-meta">
@@ -14,10 +18,12 @@ export function ChapterHeader({ chapter }: { chapter: ChapterContent }) {
         <span className={`chapter-status-badge ${chapter.status}`}>{statusLabel[chapter.status] ?? chapter.status}</span>
       </div>
       <h1 className="chapter-header-title">{chapter.title}</h1>
-      {chapter.overview && <p className="chapter-header-overview">{chapter.overview}</p>}
-      <p className="chapter-header-kp-count">
-        {chapter.knowledgePoints.length} 个知识点
-      </p>
+      {chapter.overview && <p className="chapter-header-overview"><MathText text={chapter.overview} /></p>}
+      <div className="chapter-header-stats" aria-label="章节学习资源">
+        <span>{chapter.knowledgePoints.length} 个知识点</span>
+        {diagramCount > 0 && <span>{diagramCount} 张教学图示</span>}
+        {exerciseCount > 0 && <span>{exerciseCount} 道练习</span>}
+      </div>
     </header>
   );
 }
diff --git a/components/course/ExercisePanel.tsx b/components/course/ExercisePanel.tsx
index 0574698..e8ff9c1 100644
--- a/components/course/ExercisePanel.tsx
+++ b/components/course/ExercisePanel.tsx
@@ -33,13 +33,14 @@ function difficultyClass(d: string) {
   return d === "basic" ? "basic" : d === "medium" ? "medium" : "advanced";
 }
 
-function previewText(text: string, max = 72): string {
-  const stripped = text
-    .replace(/\$\$[\s\S]*?\$\$/g, "[式]")
-    .replace(/\$[^$\n]+\$/g, "[式]")
+function cardLabel(exercise: Exercise): string {
+  if (exercise.title) return exercise.title;
+  const stripped = exercise.prompt
+    .replace(/\$\$[\s\S]*?\$\$/g, "")
+    .replace(/\$[^$\n]+\$/g, "")
     .replace(/\n+/g, " ")
     .trim();
-  return stripped.length > max ? stripped.slice(0, max) + "…" : stripped;
+  return stripped.slice(0, 64) + (stripped.length > 64 ? "…" : "");
 }
 
 export function ExercisePanel({
@@ -66,6 +67,7 @@ export function ExercisePanel({
   const [gradeResult, setGradeResult] = useState<TutorGradeResponse | null>(null);
   const [masteryState, setMasteryState] = useState<MasteryState>("not_started");
   const attachmentsRef = useRef<AnswerImage[]>([]);
+  const rubricRef = useRef<HTMLDetailsElement>(null);
   const activeExercise = selectedIndex != null ? exercises[selectedIndex] : undefined;
 
   const visibleHints = useMemo(() => {
@@ -77,6 +79,13 @@ export function ExercisePanel({
     attachmentsRef.current = attachments;
   }, [attachments]);
 
+  useEffect(() => {
+    setSelectedIndex(exercises.length > 0 ? 0 : null);
+    resetAnswerState();
+    // Reset when the learning context changes; resetAnswerState is a local helper.
+    // eslint-disable-next-line react-hooks/exhaustive-deps
+  }, [knowledgePoint.id, exercises.length]);
+
   useEffect(() => {
     const progress = loadCourseProgress(courseId, volumeId);
     const record = getKnowledgePointProgress(progress, knowledgePoint.id);
@@ -193,7 +202,7 @@ export function ExercisePanel({
           <p className="eyebrow">练习</p>
           <strong className="exercise-count">{exercises.length > 0 ? `${exercises.length} 题` : "暂无练习"}</strong>
         </div>
-        <span className={`mastery-summary ${masteryState}`}>{getMasteryLabel(masteryState)}</span>
+        <span className={`mastery-summary ${masteryState}`}>当前掌握状态 · {getMasteryLabel(masteryState)}</span>
       </div>
 
       {exercises.length === 0 ? (
@@ -212,21 +221,28 @@ export function ExercisePanel({
             >
               <span className="exercise-card-num">{index + 1}</span>
               <div className="exercise-card-meta">
+                <p className="exercise-card-title">{cardLabel(exercise)}</p>
                 <span className={`difficulty-pill ${difficultyClass(exercise.difficulty)}`}>
                   {difficultyLabel(exercise.difficulty)}
                 </span>
-                <p className="exercise-card-preview">{previewText(exercise.prompt)}</p>
               </div>
             </button>
           ))}
         </div>
       )}
 
-      {activeExercise && (
+      {activeExercise && selectedIndex != null && (
         <div className="exercise-workspace">
-          <h3>
-            <MathText text={activeExercise.prompt} />
-          </h3>
+          <p className="exercise-num-label">第 {selectedIndex + 1} 题 · 共 {exercises.length} 题</p>
+          <div className="problem-statement">
+            {activeExercise.title && (
+              <p className="problem-title">{activeExercise.title}</p>
+            )}
+            <div className="problem-body">
+              <MathText text={activeExercise.prompt} />
+            </div>
+          </div>
+          <p className="answer-label">解答</p>
           <textarea
             aria-label="输入你的解答"
             onChange={(event) => setAnswer(event.target.value)}
@@ -266,13 +282,18 @@ export function ExercisePanel({
             </div>
           )}
           <div className="exercise-actions">
-            <button onClick={() => setHintLevel((value) => Math.min(value + 1, activeExercise.hints.length))} type="button">
-              获取提示
+            <span className="exercise-action-label">当前题操作</span>
+            <button
+              disabled={hintLevel >= activeExercise.hints.length}
+              onClick={() => setHintLevel((value) => Math.min(value + 1, activeExercise.hints.length))}
+              type="button"
+            >
+              {hintLevel === 0 ? "获取提示" : hintLevel < activeExercise.hints.length ? `再来一个提示 (${hintLevel}/${activeExercise.hints.length})` : `已显示全部提示`}
             </button>
-            <button disabled={gradingStatus === "submitting"} onClick={submitForAiGrading} type="button">
-              {gradingStatus === "submitting" ? "批改中..." : "提交给 AI 批改"}
+            <button className="is-primary" disabled={gradingStatus === "submitting"} onClick={submitForAiGrading} type="button">
+              {gradingStatus === "submitting" ? "批改中…" : "提交给 AI 批改"}
             </button>
-            <button type="button">对照评分要点</button>
+            <button onClick={() => { if (rubricRef.current) { rubricRef.current.open = true; rubricRef.current.scrollIntoView({ behavior: "smooth", block: "nearest" }); } }} type="button">对照评分要点</button>
           </div>
           {gradingError && <p className="grading-error">{gradingError}</p>}
           {gradeResult && (
@@ -281,9 +302,9 @@ export function ExercisePanel({
                 <strong>AI 批改结果</strong>
                 <span>{gradeResult.score} 分</span>
               </div>
-              <p>
+              <div className="grade-feedback">
                 <MathText text={gradeResult.feedback} />
-              </p>
+              </div>
               {gradeResult.missingKeyPoints.length > 0 && (
                 <div>
                   <strong>还缺这些要点</strong>
@@ -307,7 +328,7 @@ export function ExercisePanel({
               ))}
             </ul>
           )}
-          <details>
+          <details ref={rubricRef}>
             <summary>评分要点</summary>
             <ul>
               {activeExercise.gradingRubric.map((item) => (
diff --git a/components/course/LearningStepPanel.tsx b/components/course/LearningStepPanel.tsx
index 9b69ab1..548215b 100644
--- a/components/course/LearningStepPanel.tsx
+++ b/components/course/LearningStepPanel.tsx
@@ -61,7 +61,7 @@ export function LearningStepPanel({
       </div>
 
       {diagrams.length > 0 && (
-        <CollapsibleSection title="教学图示">
+        <CollapsibleSection defaultOpen title="教学图示">
           <div className="diagram-grid">
             {diagrams.map((diagram) => (
               <DiagramRenderer diagram={diagram} key={diagram.id} />
@@ -81,6 +81,18 @@ export function LearningStepPanel({
           </ol>
         </CollapsibleSection>
       )}
+
+      {knowledgePoint.commonMistakes.length > 0 && (
+        <CollapsibleSection title="易错提醒">
+          <ul className="mistake-list">
+            {knowledgePoint.commonMistakes.map((mistake) => (
+              <li key={mistake}>
+                <MathText text={mistake} />
+              </li>
+            ))}
+          </ul>
+        </CollapsibleSection>
+      )}
     </article>
   );
 }
diff --git a/components/course/TutorPanel.tsx b/components/course/TutorPanel.tsx
index 9bb5f73..96d0916 100644
--- a/components/course/TutorPanel.tsx
+++ b/components/course/TutorPanel.tsx
@@ -96,7 +96,10 @@ export function TutorPanel({ knowledgePoint }: { knowledgePoint: KnowledgePoint
   return (
     <aside className="tutor-panel">
       <div className="tutor-header">
-        <p className="eyebrow">AI 老师</p>
+        <div>
+          <p className="eyebrow">AI 老师</p>
+          <p className="tutor-context">正在围绕：{knowledgePoint.title}</p>
+        </div>
         <button
           aria-expanded={settingsOpen}
           className={`settings-toggle ${settingsOpen ? "is-active" : ""}`}
diff --git a/components/diagrams/CartesianDiagrams.tsx b/components/diagrams/CartesianDiagrams.tsx
new file mode 100644
index 0000000..0704a25
--- /dev/null
+++ b/components/diagrams/CartesianDiagrams.tsx
@@ -0,0 +1,306 @@
+import type { ReactNode } from "react";
+import type { DiagramSpec } from "@/lib/course/types";
+import {
+  PALETTE, CURVE_COLORS, compile, makeScales, plotPath, autoYRange,
+  asNum, asStr, asArr, asObj, type Frame, type Box,
+} from "@/lib/diagrams/engine";
+import { Figure, CartesianAxes, Lab, Dot, OpenDot } from "./Figure";
+
+const BOX: Box = { x0: 46, y0: 18, w: 402, h: 236 };
+
+/* ================================================================
+   函数曲线：multi-curve-plot / function-plot / area-under-curve
+================================================================ */
+export function FunctionPlotDiagram({ diagram }: { diagram: DiagramSpec }) {
+  const p = diagram.parameters;
+  const domain = asObj(p.domain);
+  const xRange = asArr(p.xRange);
+  const xMin = xRange.length === 2 ? asNum(xRange[0]) : asNum(domain.from, -1);
+  const xMax = xRange.length === 2 ? asNum(xRange[1]) : asNum(domain.to, 1);
+
+  // 收集曲线：curves[] 或单个 expr
+  const rawCurves = asArr(p.curves);
+  const curves = rawCurves.length
+    ? rawCurves.map((c) => ({ expr: asStr(asObj(c).expr), label: asStr(asObj(c).label) }))
+    : asStr(p.expr) ? [{ expr: asStr(p.expr), label: asStr(p.label) }] : [];
+
+  const fns = curves.map((c) => compile(c.expr));
+
+  // y 取景：合并所有曲线范围，并保证含 0
+  let yMin = Infinity, yMax = -Infinity;
+  for (const fn of fns) {
+    const [lo, hi] = autoYRange(fn, xMin, xMax);
+    yMin = Math.min(yMin, lo); yMax = Math.max(yMax, hi);
+  }
+  if (!isFinite(yMin)) { yMin = -1; yMax = 1; }
+  yMin = Math.min(yMin, 0); yMax = Math.max(yMax, 0);
+  const frame: Frame = { xMin, xMax, yMin, yMax };
+  const { sx, sy } = makeScales(frame, BOX);
+
+  // 定积分面积填充
+  const fillFrom = p.fillFrom !== undefined ? asNum(p.fillFrom) : null;
+  const fillTo = p.fillTo !== undefined ? asNum(p.fillTo) : null;
+  let areaPath = "";
+  if (fillFrom !== null && fillTo !== null && fns[0]) {
+    const N = 80;
+    const pts: string[] = [];
+    for (let i = 0; i <= N; i++) {
+      const x = fillFrom + (i / N) * (fillTo - fillFrom);
+      pts.push(`${sx(x).toFixed(1)} ${sy(fns[0](x)).toFixed(1)}`);
+    }
+    areaPath = `M${sx(fillFrom).toFixed(1)} ${sy(0).toFixed(1)} L` + pts.join(" L") + ` L${sx(fillTo).toFixed(1)} ${sy(0).toFixed(1)} Z`;
+  }
+
+  const marks = asArr(p.marks);
+
+  return (
+    <Figure diagram={diagram}>
+      <CartesianAxes frame={frame} box={BOX} />
+      {areaPath ? <path d={areaPath} fill={PALETTE.accent} opacity={0.14} /> : null}
+      {fns.map((fn, i) => (
+        <path key={i} d={plotPath(fn, frame, BOX)} fill="none" stroke={CURVE_COLORS[i % CURVE_COLORS.length]} strokeWidth={2.2} strokeLinecap="round" strokeLinejoin="round" />
+      ))}
+      {marks.map((m, i) => {
+        const mo = asObj(m);
+        const mx = asNum(mo.x);
+        const fy = fns[0] ? fns[0](mx) : 0;
+        return (
+          <g key={`mk${i}`}>
+            <Dot x={sx(mx)} y={sy(fy)} />
+            {asStr(mo.label) ? <Lab x={sx(mx)} y={sy(fy) - 8} italic size={12}>{asStr(mo.label)}</Lab> : null}
+          </g>
+        );
+      })}
+      {/* 图例 */}
+      {curves.length > 1 ? (
+        <g>
+          {curves.map((c, i) => (
+            <g key={`lg${i}`} transform={`translate(${BOX.x0 + 8}, ${BOX.y0 + 12 + i * 18})`}>
+              <line x1={0} y1={0} x2={20} y2={0} stroke={CURVE_COLORS[i % CURVE_COLORS.length]} strokeWidth={2.4} />
+              <Lab x={26} y={4} anchor="start" size={12} color={PALETTE.inkSoft}>{c.label || c.expr}</Lab>
+            </g>
+          ))}
+        </g>
+      ) : null}
+    </Figure>
+  );
+}
+
+/* ================================================================
+   ε-δ 几何定义：cartesian-epsilon-delta
+================================================================ */
+export function EpsilonDeltaDiagram({ diagram }: { diagram: DiagramSpec }) {
+  const p = diagram.parameters;
+  const x0 = asNum(asObj(p.limitPointX).x, 2);
+  const A = asNum(asObj(p.limitValueY).y, 3);
+  const band = asObj(p.epsilonBand);
+  const eps = asNum(band.value, 0.5);
+  const interval = asObj(p.deltaInterval);
+  const delta = asNum(interval.value, 0.4);
+
+  const frame: Frame = { xMin: x0 - 1.7, xMax: x0 + 1.7, yMin: A - 1.3, yMax: A + 1.3 };
+  const { sx, sy } = makeScales(frame, BOX);
+  // 代表性单调曲线，斜率取 ε/δ 使其恰好充满色带，过 (x0, A) 并在该处挖空
+  const slope = eps / delta;
+  const fn = (x: number) => A + slope * (x - x0) * 0.8;
+
+  return (
+    <Figure diagram={diagram}>
+      {/* 取景边框 */}
+      <rect x={BOX.x0} y={BOX.y0} width={BOX.w} height={BOX.h} fill="none" stroke={PALETTE.inkFaint} strokeWidth={0.8} opacity={0.6} />
+      {/* ε 水平带 */}
+      <rect x={BOX.x0} y={sy(A + eps)} width={BOX.w} height={sy(A - eps) - sy(A + eps)} fill={PALETTE.gold} opacity={0.13} />
+      {/* δ 竖直带 */}
+      <rect x={sx(x0 - delta)} y={BOX.y0} width={sx(x0 + delta) - sx(x0 - delta)} height={BOX.h} fill={PALETTE.curve} opacity={0.12} />
+      {/* 曲线 */}
+      <path d={plotPath(fn, frame, BOX)} fill="none" stroke={PALETTE.curve} strokeWidth={2.2} />
+      {/* 投影虚线 */}
+      <line x1={sx(x0)} y1={sy(A)} x2={sx(x0)} y2={sy(frame.yMin)} stroke={PALETTE.accent} strokeWidth={1} strokeDasharray="4 3" opacity={0.7} />
+      <line x1={sx(x0)} y1={sy(A)} x2={sx(frame.xMin)} y2={sy(A)} stroke={PALETTE.accent} strokeWidth={1} strokeDasharray="4 3" opacity={0.7} />
+      {/* 关键点（去心） */}
+      <OpenDot x={sx(x0)} y={sy(A)} />
+      {/* y 轴标注 */}
+      <Lab x={BOX.x0 - 4} y={sy(A) + 4} anchor="end" italic size={12}>{asStr(asObj(p.limitValueY).symbol, "A")}</Lab>
+      <Lab x={BOX.x0 - 4} y={sy(A + eps) + 4} anchor="end" size={11} color={PALETTE.gold}>{asStr(band.upperLabel, "A+ε")}</Lab>
+      <Lab x={BOX.x0 - 4} y={sy(A - eps) + 4} anchor="end" size={11} color={PALETTE.gold}>{asStr(band.lowerLabel, "A-ε")}</Lab>
+      {/* x 轴标注 */}
+      <Lab x={sx(x0)} y={BOX.y0 + BOX.h + 16} italic size={12}>{asStr(asObj(p.limitPointX).symbol, "x_0")}</Lab>
+      <Lab x={sx(x0 - delta)} y={BOX.y0 + BOX.h + 16} size={11} color={PALETTE.curve}>{asStr(interval.leftLabel, "x_0-δ")}</Lab>
+      <Lab x={sx(x0 + delta)} y={BOX.y0 + BOX.h + 16} size={11} color={PALETTE.curve}>{asStr(interval.rightLabel, "x_0+δ")}</Lab>
+    </Figure>
+  );
+}
+
+/* ================================================================
+   趋于水平渐近线：function-plot-asymptote
+================================================================ */
+export function AsymptoteDiagram({ diagram }: { diagram: DiagramSpec }) {
+  const p = diagram.parameters;
+  const A = asNum(asObj(p.asymptote).y, 1);
+  const eps = asNum(asObj(p.epsilonBand).value, 0.3);
+  const M = asNum(asObj(p.threshold).x, 5);
+
+  const xMax = M * 1.7;
+  const frame: Frame = { xMin: 0, xMax, yMin: Math.min(0, A - 1), yMax: A + 1.4 };
+  const { sx, sy } = makeScales(frame, BOX);
+  const fn = (x: number) => A + 1.3 / (x + 0.35); // 自上方单调贴近 y=A
+
+  return (
+    <Figure diagram={diagram}>
+      <CartesianAxes frame={frame} box={BOX} />
+      {/* ε 带 */}
+      <rect x={BOX.x0} y={sy(A + eps)} width={BOX.w} height={sy(A - eps) - sy(A + eps)} fill={PALETTE.gold} opacity={0.13} />
+      {/* 渐近线 */}
+      <line x1={BOX.x0} y1={sy(A)} x2={BOX.x0 + BOX.w} y2={sy(A)} stroke={PALETTE.gold} strokeWidth={1.4} strokeDasharray="6 4" />
+      <Lab x={BOX.x0 + BOX.w} y={sy(A) - 6} anchor="end" italic size={12} color={PALETTE.gold}>{`y=${asStr(asObj(p.asymptote).symbol, "A")}`}</Lab>
+      {/* 阈值 M */}
+      <line x1={sx(M)} y1={BOX.y0} x2={sx(M)} y2={sy(frame.yMin)} stroke={PALETTE.accent} strokeWidth={1} strokeDasharray="4 3" opacity={0.7} />
+      <Lab x={sx(M)} y={BOX.y0 + BOX.h + 16} italic size={12} color={PALETTE.accent}>{asStr(asObj(p.threshold).symbol, "M")}</Lab>
+      {/* 曲线 */}
+      <path d={plotPath(fn, frame, BOX)} fill="none" stroke={PALETTE.curve} strokeWidth={2.2} />
+    </Figure>
+  );
+}
+
+/* ================================================================
+   跳跃间断：piecewise-function-plot
+================================================================ */
+export function PiecewiseJumpDiagram({ diagram }: { diagram: DiagramSpec }) {
+  const p = diagram.parameters;
+  const x0 = asNum(asObj(p.breakPointX).x, 0);
+  const leftY = asNum(asObj(p.leftBranch).y, -1);
+  const rightY = asNum(asObj(p.rightBranch).y, 1);
+  const lo = Math.min(leftY, rightY), hi = Math.max(leftY, rightY);
+  const frame: Frame = { xMin: x0 - 2.6, xMax: x0 + 2.6, yMin: lo - 1.2, yMax: hi + 1.2 };
+  const { sx, sy } = makeScales(frame, BOX);
+
+  return (
+    <Figure diagram={diagram}>
+      <CartesianAxes frame={frame} box={BOX} />
+      {/* 左支：略向右上靠近 (x0, leftY) */}
+      <path d={`M${sx(x0 - 2.3)} ${sy(leftY - 0.35)} Q${sx(x0 - 0.8)} ${sy(leftY)} ${sx(x0)} ${sy(leftY)}`} fill="none" stroke={PALETTE.curve} strokeWidth={2.2} />
+      {/* 右支 */}
+      <path d={`M${sx(x0)} ${sy(rightY)} Q${sx(x0 + 0.8)} ${sy(rightY)} ${sx(x0 + 2.3)} ${sy(rightY + 0.35)}`} fill="none" stroke={PALETTE.curve} strokeWidth={2.2} />
+      {/* 跳跃量标注 */}
+      <line x1={sx(x0)} y1={sy(leftY)} x2={sx(x0)} y2={sy(rightY)} stroke={PALETTE.accent} strokeWidth={1} strokeDasharray="3 3" opacity={0.7} />
+      <OpenDot x={sx(x0)} y={sy(leftY)} color={PALETTE.curve} />
+      <OpenDot x={sx(x0)} y={sy(rightY)} color={PALETTE.curve} />
+      <Lab x={sx(x0) + 8} y={sy((leftY + rightY) / 2) + 4} anchor="start" size={11} color={PALETTE.accent}>跳跃</Lab>
+      <Lab x={sx(x0)} y={BOX.y0 + BOX.h + 16} italic size={12}>{asStr(asObj(p.breakPointX).symbol, "x_0")}</Lab>
+    </Figure>
+  );
+}
+
+/* ================================================================
+   二维区域：region-2d（为高数重积分等内容预备）
+================================================================ */
+export function Region2DDiagram({ diagram }: { diagram: DiagramSpec }) {
+  const p = diagram.parameters;
+  const xr = asArr(p.xRange), yr = asArr(p.yRange);
+  const frame: Frame = {
+    xMin: xr.length === 2 ? asNum(xr[0]) : -1, xMax: xr.length === 2 ? asNum(xr[1]) : 3,
+    yMin: yr.length === 2 ? asNum(yr[0]) : -1, yMax: yr.length === 2 ? asNum(yr[1]) : 3,
+  };
+  const { sx, sy } = makeScales(frame, BOX);
+  const boundaries = asArr(p.boundaries).map((b) => ({ expr: asStr(asObj(b).expr), label: asStr(asObj(b).label), fn: compile(asStr(asObj(b).expr)) }));
+
+  let fillPath = "";
+  if (boundaries.length >= 1) {
+    const a = Math.max(frame.xMin, 0), b = frame.xMax;
+    const N = 60;
+    const top = boundaries[0].fn;
+    const bottom = boundaries[1]?.fn ?? (() => 0);
+    const up: string[] = [], down: string[] = [];
+    for (let i = 0; i <= N; i++) {
+      const x = a + (i / N) * (b - a);
+      up.push(`${sx(x).toFixed(1)} ${sy(top(x)).toFixed(1)}`);
+      down.push(`${sx(x).toFixed(1)} ${sy(bottom(x)).toFixed(1)}`);
+    }
+    fillPath = `M${up.join(" L")} L${down.reverse().join(" L")} Z`;
+  }
+
+  return (
+    <Figure diagram={diagram}>
+      <CartesianAxes frame={frame} box={BOX} />
+      {fillPath ? <path d={fillPath} fill={PALETTE.curve} opacity={0.14} /> : null}
+      {boundaries.map((bd, i) => (
+        <g key={i}>
+          <path d={plotPath(bd.fn, frame, BOX)} fill="none" stroke={CURVE_COLORS[i % CURVE_COLORS.length]} strokeWidth={2} />
+          {bd.label ? <Lab x={BOX.x0 + BOX.w - 6} y={sy(bd.fn(frame.xMax)) - 6} anchor="end" italic size={12} color={CURVE_COLORS[i % CURVE_COLORS.length]}>{bd.label}</Lab> : null}
+        </g>
+      ))}
+    </Figure>
+  );
+}
+
+/* ================================================================
+   纯几何：geometric（向量 / 多边形 / 圆 / 点 / 线段）
+================================================================ */
+export function GeometricDiagram({ diagram }: { diagram: DiagramSpec }) {
+  const p = diagram.parameters;
+  const shapes = asArr(p.shapes).map(asObj);
+
+  // 自动取景：扫描所有坐标
+  let xMin = Infinity, xMax = -Infinity, yMin = Infinity, yMax = -Infinity;
+  const consider = (x: number, y: number) => { xMin = Math.min(xMin, x); xMax = Math.max(xMax, x); yMin = Math.min(yMin, y); yMax = Math.max(yMax, y); };
+  for (const s of shapes) {
+    for (const ptName of ["from", "to", "center"]) {
+      const pt = asObj(s[ptName]);
+      if (pt.x !== undefined) consider(asNum(pt.x), asNum(pt.y));
+    }
+    for (const pt of asArr(s.points)) { const o = asObj(pt); consider(asNum(o.x), asNum(o.y)); }
+    if (s.kind === "circle") { const c = asObj(s.center); const r = asNum(s.r, 1); consider(asNum(c.x) - r, asNum(c.y) - r); consider(asNum(c.x) + r, asNum(c.y) + r); }
+  }
+  if (!isFinite(xMin)) { xMin = -1; xMax = 3; yMin = -1; yMax = 3; }
+  const padX = (xMax - xMin) * 0.18 || 1, padY = (yMax - yMin) * 0.18 || 1;
+  const frame: Frame = { xMin: xMin - padX, xMax: xMax + padX, yMin: yMin - padY, yMax: yMax + padY };
+  const { sx, sy } = makeScales(frame, BOX);
+
+  const nodes: ReactNode[] = [];
+  shapes.forEach((s, i) => {
+    const color = asStr(s.color) || CURVE_COLORS[i % CURVE_COLORS.length];
+    const label = asStr(s.label);
+    if (s.kind === "vector") {
+      const f = asObj(s.from), t = asObj(s.to);
+      const x1 = sx(asNum(f.x)), y1 = sy(asNum(f.y)), x2 = sx(asNum(t.x)), y2 = sy(asNum(t.y));
+      const ang = Math.atan2(y2 - y1, x2 - x1);
+      nodes.push(
+        <g key={i}>
+          <line x1={x1} y1={y1} x2={x2} y2={y2} stroke={color} strokeWidth={2.2} />
+          <path d={`M${x2} ${y2} L${(x2 - 9 * Math.cos(ang - 0.4)).toFixed(1)} ${(y2 - 9 * Math.sin(ang - 0.4)).toFixed(1)} L${(x2 - 9 * Math.cos(ang + 0.4)).toFixed(1)} ${(y2 - 9 * Math.sin(ang + 0.4)).toFixed(1)} Z`} fill={color} />
+          {label ? <Lab x={(x1 + x2) / 2} y={(y1 + y2) / 2 - 6} italic size={12} color={color}>{label}</Lab> : null}
+        </g>,
+      );
+    } else if (s.kind === "circle") {
+      const c = asObj(s.center);
+      nodes.push(<circle key={i} cx={sx(asNum(c.x))} cy={sy(asNum(c.y))} r={Math.abs(sx(asNum(c.x) + asNum(s.r, 1)) - sx(asNum(c.x)))} fill="none" stroke={color} strokeWidth={2} />);
+    } else if (s.kind === "polygon") {
+      const pts = asArr(s.points).map(asObj).map((o) => `${sx(asNum(o.x)).toFixed(1)},${sy(asNum(o.y)).toFixed(1)}`).join(" ");
+      nodes.push(<polygon key={i} points={pts} fill={color} fillOpacity={0.1} stroke={color} strokeWidth={2} />);
+    } else if (s.kind === "line") {
+      const f = asObj(s.from), t = asObj(s.to);
+      const x1 = sx(asNum(f.x)), y1 = sy(asNum(f.y)), x2 = sx(asNum(t.x)), y2 = sy(asNum(t.y));
+      nodes.push(
+        <g key={i}>
+          <line x1={x1} y1={y1} x2={x2} y2={y2} stroke={color} strokeWidth={2} />
+          {label ? <Lab x={(x1 + x2) / 2 + asNum(s.labelDx)} y={(y1 + y2) / 2 + asNum(s.labelDy, -6)} italic size={12} color={color}>{label}</Lab> : null}
+        </g>,
+      );
+    } else if (s.kind === "point") {
+      const pt = asArr(s.points)[0] ? asObj(asArr(s.points)[0]) : s;
+      nodes.push(
+        <g key={i}>
+          <Dot x={sx(asNum(pt.x))} y={sy(asNum(pt.y))} color={color} />
+          {label ? <Lab x={sx(asNum(pt.x)) + 6} y={sy(asNum(pt.y)) - 6} anchor="start" italic size={12} color={color}>{label}</Lab> : null}
+        </g>,
+      );
+    }
+  });
+
+  return (
+    <Figure diagram={diagram}>
+      <CartesianAxes frame={frame} box={BOX} />
+      {nodes}
+    </Figure>
+  );
+}
diff --git a/components/diagrams/ConceptDiagram.tsx b/components/diagrams/ConceptDiagram.tsx
new file mode 100644
index 0000000..2d0e5bd
--- /dev/null
+++ b/components/diagrams/ConceptDiagram.tsx
@@ -0,0 +1,16 @@
+import { MathText } from "@/components/math/MathText";
+import type { DiagramSpec } from "@/lib/course/types";
+
+export function ConceptDiagram({ diagram }: { diagram: DiagramSpec }) {
+  return (
+    <figure className="diagram-card diagram-card--concept">
+      <figcaption>
+        <strong><MathText text={diagram.title} /></strong>
+        <MathText text={diagram.description} />
+      </figcaption>
+      <p className="diagram-prompt">
+        <MathText text={diagram.studentPrompt} />
+      </p>
+    </figure>
+  );
+}
diff --git a/components/diagrams/DiagramRenderer.tsx b/components/diagrams/DiagramRenderer.tsx
index 7ceb899..54f18d7 100644
--- a/components/diagrams/DiagramRenderer.tsx
+++ b/components/diagrams/DiagramRenderer.tsx
@@ -1,11 +1,44 @@
 import type { DiagramSpec } from "@/lib/course/types";
+import { ConceptDiagram } from "./ConceptDiagram";
 import { NumberLineDiagram } from "./NumberLineDiagram";
-import { SequencePlotDiagram } from "./SequencePlotDiagram";
+import { TableDiagram } from "./TableDiagram";
+import {
+  FunctionPlotDiagram,
+  EpsilonDeltaDiagram,
+  AsymptoteDiagram,
+  PiecewiseJumpDiagram,
+  Region2DDiagram,
+  GeometricDiagram,
+} from "./CartesianDiagrams";
+import {
+  SequenceOnNumberLine,
+  TwoPanelSequence,
+  BoundedStrip,
+  MonotoneSequence,
+  SubsequenceHighlight,
+} from "./SequenceDiagrams";
 
-export function DiagramRenderer({ diagram }: { diagram: DiagramSpec }) {
-  if (diagram.type === "number-line" || diagram.type === "sequence-on-number-line") {
-    return <NumberLineDiagram diagram={diagram} />;
-  }
+type Renderer = (props: { diagram: DiagramSpec }) => React.JSX.Element;
+
+const REGISTRY: Record<string, Renderer> = {
+  "number-line": NumberLineDiagram,
+  "cartesian-epsilon-delta": EpsilonDeltaDiagram,
+  "function-plot-asymptote": AsymptoteDiagram,
+  "piecewise-function-plot": PiecewiseJumpDiagram,
+  "multi-curve-plot": FunctionPlotDiagram,
+  "function-plot": FunctionPlotDiagram,
+  "area-under-curve": FunctionPlotDiagram,
+  "region-2d": Region2DDiagram,
+  "geometric": GeometricDiagram,
+  "sequence-on-number-line": SequenceOnNumberLine,
+  "two-panel-sequence-plot": TwoPanelSequence,
+  "bounded-strip": BoundedStrip,
+  "monotone-sequence-plot": MonotoneSequence,
+  "subsequence-highlight": SubsequenceHighlight,
+  "table": TableDiagram,
+};
 
-  return <SequencePlotDiagram diagram={diagram} />;
+export function DiagramRenderer({ diagram }: { diagram: DiagramSpec }) {
+  const Component = REGISTRY[diagram.type] ?? ConceptDiagram;
+  return <Component diagram={diagram} />;
 }
diff --git a/components/diagrams/Figure.tsx b/components/diagrams/Figure.tsx
new file mode 100644
index 0000000..a10f0e9
--- /dev/null
+++ b/components/diagrams/Figure.tsx
@@ -0,0 +1,106 @@
+import type { ReactNode } from "react";
+import { MathText } from "@/components/math/MathText";
+import type { DiagramSpec } from "@/lib/course/types";
+import { PALETTE, makeScales, texLabel, type Box, type Frame } from "@/lib/diagrams/engine";
+
+/** 统一的图示外壳：标题 + 描述 + SVG 画布 + 思考提示。 */
+export function Figure({
+  diagram,
+  viewBox = "0 0 480 300",
+  variant,
+  children,
+}: {
+  diagram: DiagramSpec;
+  viewBox?: string;
+  variant?: "concept";
+  children: ReactNode;
+}) {
+  return (
+    <figure className={`diagram-card${variant === "concept" ? " diagram-card--concept" : ""}`}>
+      <figcaption>
+        <strong><MathText text={diagram.title} /></strong>
+        <MathText text={diagram.description} />
+      </figcaption>
+      <svg className="diagram-svg" role="img" aria-label={diagram.title} viewBox={viewBox}>
+        {children}
+      </svg>
+      {diagram.studentPrompt ? (
+        <p className="diagram-prompt">
+          <MathText text={diagram.studentPrompt} />
+        </p>
+      ) : null}
+    </figure>
+  );
+}
+
+/** SVG 文本标注（衬线、可选斜体，自动把 LaTeX 转 Unicode）。 */
+export function Lab({
+  x, y, children, anchor = "middle", italic = false, size = 13, color = PALETTE.ink, dy,
+}: {
+  x: number; y: number; children: string; anchor?: "start" | "middle" | "end";
+  italic?: boolean; size?: number; color?: string; dy?: number;
+}) {
+  return (
+    <text
+      x={x} y={y} dy={dy} textAnchor={anchor} fill={color}
+      fontFamily='"Spectral", "Noto Serif SC", Georgia, serif'
+      fontStyle={italic ? "italic" : "normal"} fontSize={size}
+    >
+      {texLabel(children)}
+    </text>
+  );
+}
+
+/** 实心点（取到的值 / 数据点）。 */
+export function Dot({ x, y, r = 3.4, color = PALETTE.accent }: { x: number; y: number; r?: number; color?: string }) {
+  return <circle cx={x} cy={y} r={r} fill={color} />;
+}
+
+/** 空心点（去心 / 不取到的极限值）。 */
+export function OpenDot({ x, y, r = 3.6, color = PALETTE.accent }: { x: number; y: number; r?: number; color?: string }) {
+  return <circle cx={x} cy={y} r={r} fill={PALETTE.paperSunk} stroke={color} strokeWidth={1.6} />;
+}
+
+/**
+ * 直角坐标系：浅网格 + 坐标轴 + 箭头 + 轴标。
+ * 当 0 落在取景范围内时轴画在 0 处，否则贴边。
+ */
+export function CartesianAxes({
+  frame, box, xLabel = "x", yLabel = "y", grid = true,
+}: {
+  frame: Frame; box: Box; xLabel?: string; yLabel?: string; grid?: boolean;
+}) {
+  const { sx, sy } = makeScales(frame, box);
+  const xAxisY = frame.yMin <= 0 && frame.yMax >= 0 ? sy(0) : sy(frame.yMin);
+  const yAxisX = frame.xMin <= 0 && frame.xMax >= 0 ? sx(0) : sx(frame.xMin);
+
+  const gridLines: ReactNode[] = [];
+  if (grid) {
+    for (let gx = Math.ceil(frame.xMin); gx <= frame.xMax; gx++) {
+      const px = sx(gx);
+      gridLines.push(<line key={`gx${gx}`} x1={px} y1={box.y0} x2={px} y2={box.y0 + box.h} stroke={PALETTE.inkFaint} strokeWidth={0.5} opacity={0.45} />);
+    }
+    for (let gy = Math.ceil(frame.yMin); gy <= frame.yMax; gy++) {
+      const py = sy(gy);
+      gridLines.push(<line key={`gy${gy}`} x1={box.x0} y1={py} x2={box.x0 + box.w} y2={py} stroke={PALETTE.inkFaint} strokeWidth={0.5} opacity={0.45} />);
+    }
+  }
+
+  return (
+    <g>
+      {gridLines}
+      {/* x 轴 */}
+      <line x1={box.x0} y1={xAxisY} x2={box.x0 + box.w + 6} y2={xAxisY} stroke={PALETTE.ink} strokeWidth={1.3} />
+      <path d={`M${box.x0 + box.w + 6} ${xAxisY} l-7 -3.5 l0 7 z`} fill={PALETTE.ink} />
+      <Lab x={box.x0 + box.w + 12} y={xAxisY + 4} anchor="start" italic size={13}>{xLabel}</Lab>
+      {/* y 轴 */}
+      <line x1={yAxisX} y1={box.y0 + box.h} x2={yAxisX} y2={box.y0 - 6} stroke={PALETTE.ink} strokeWidth={1.3} />
+      <path d={`M${yAxisX} ${box.y0 - 6} l-3.5 7 l7 0 z`} fill={PALETTE.ink} />
+      <Lab x={yAxisX - 6} y={box.y0 - 2} anchor="end" italic size={13}>{yLabel}</Lab>
+      {/* 原点 */}
+      {frame.xMin <= 0 && frame.xMax >= 0 && frame.yMin <= 0 && frame.yMax >= 0 ? (
+        <Lab x={yAxisX - 5} y={xAxisY + 14} anchor="end" italic size={12} color={PALETTE.inkSoft}>O</Lab>
+      ) : null}
+    </g>
+  );
+}
diff --git a/components/diagrams/NumberLineDiagram.tsx b/components/diagrams/NumberLineDiagram.tsx
index ff6d13d..f7007f0 100644
--- a/components/diagrams/NumberLineDiagram.tsx
+++ b/components/diagrams/NumberLineDiagram.tsx
@@ -1,33 +1,67 @@
-import { MathText } from "@/components/math/MathText";
+import type { ReactNode } from "react";
 import type { DiagramSpec } from "@/lib/course/types";
+import { PALETTE, asNum, asStr, asArr, asObj } from "@/lib/diagrams/engine";
+import { Figure, Lab, Dot, OpenDot } from "./Figure";
 
+/**
+ * 数轴图：type = "number-line"。
+ * 读取 axisMin/axisMax、limitPoint、epsilon、highlightInterval、points、intervals，
+ * 真正按参数画出邻域、区间（开/闭端点）与标注。
+ */
 export function NumberLineDiagram({ diagram }: { diagram: DiagramSpec }) {
+  const p = diagram.parameters;
+  const axisMin = asNum(p.axisMin, -1.5);
+  const axisMax = asNum(p.axisMax, 1.5);
+  const X0 = 50, X1 = 440, baseY = 92;
+  const sx = (x: number) => X0 + ((x - axisMin) / (axisMax - axisMin)) * (X1 - X0);
+
+  const limit = asObj(p.limitPoint);
+  const hasLimit = limit.x !== undefined;
+  const eps = asObj(p.epsilon);
+  const epsVal = asNum(eps.value, NaN);
+
+  const hi = asObj(p.highlightInterval);
+  const intervals = asArr(p.intervals).map(asObj);
+  if (hi.from !== undefined) intervals.unshift(hi);
+  // 由 limit + epsilon 推出邻域区间
+  if (hasLimit && isFinite(epsVal) && intervals.length === 0) {
+    intervals.push({ from: asNum(limit.x) - epsVal, to: asNum(limit.x) + epsVal, label: "U(a;ε)", open: true });
+  }
+
+  const extraPoints = asArr(p.points).map(asObj);
+
+  const nodes: ReactNode[] = [];
+  intervals.forEach((iv, i) => {
+    const from = asNum(iv.from), to = asNum(iv.to);
+    const open = iv.open !== false;
+    nodes.push(<line key={`iv${i}`} x1={sx(from)} y1={baseY} x2={sx(to)} y2={baseY} stroke={PALETTE.curve} strokeWidth={9} opacity={0.28} strokeLinecap="round" />);
+    const EP = open ? OpenDot : Dot;
+    nodes.push(<EP key={`l${i}`} x={sx(from)} y={baseY} color={PALETTE.curve} />);
+    nodes.push(<EP key={`r${i}`} x={sx(to)} y={baseY} color={PALETTE.curve} />);
+    if (asStr(iv.leftEndpointLabel ?? iv.leftLabel)) nodes.push(<Lab key={`ll${i}`} x={sx(from)} y={baseY + 22} size={12}>{asStr(iv.leftEndpointLabel ?? iv.leftLabel)}</Lab>);
+    if (asStr(iv.rightEndpointLabel ?? iv.rightLabel)) nodes.push(<Lab key={`rl${i}`} x={sx(to)} y={baseY + 22} size={12}>{asStr(iv.rightEndpointLabel ?? iv.rightLabel)}</Lab>);
+    if (asStr(iv.label)) nodes.push(<Lab key={`il${i}`} x={(sx(from) + sx(to)) / 2} y={baseY - 16} size={12} italic color={PALETTE.curve}>{asStr(iv.label)}</Lab>);
+  });
+
   return (
-    <figure className="diagram-card">
-      <figcaption>
-        <strong>{diagram.title}</strong>
-        <MathText text={diagram.description} />
-      </figcaption>
-      <svg aria-label={diagram.title} role="img" viewBox="0 0 640 180">
-        <line stroke="currentColor" strokeWidth="2" x1="64" x2="576" y1="96" y2="96" />
-        <line opacity="0.28" stroke="#2f6f68" strokeLinecap="round" strokeWidth="12" x1="224" x2="416" y1="96" y2="96" />
-        <circle cx="320" cy="96" fill="#194d47" r="7" />
-        <text textAnchor="middle" x="320" y="58">
-          a
-        </text>
-        <text textAnchor="middle" x="224" y="130">
-          a-ε
-        </text>
-        <text textAnchor="middle" x="416" y="130">
-          a+ε
-        </text>
-        <text textAnchor="middle" x="320" y="156">
-          |xₙ-a| &lt; ε
-        </text>
-      </svg>
-      <p className="diagram-prompt">
-        <MathText text={diagram.studentPrompt} />
-      </p>
-    </figure>
+    <Figure diagram={diagram} viewBox="0 0 480 150">
+      {/* 轴线 + 双向箭头 */}
+      <line x1={X0 - 8} y1={baseY} x2={X1 + 8} y2={baseY} stroke={PALETTE.ink} strokeWidth={1.4} />
+      <path d={`M${X1 + 8} ${baseY} l-7 -3.5 l0 7 z`} fill={PALETTE.ink} />
+      <path d={`M${X0 - 8} ${baseY} l7 -3.5 l0 7 z`} fill={PALETTE.ink} />
+      {nodes}
+      {hasLimit ? (
+        <g>
+          <Dot x={sx(asNum(limit.x))} y={baseY} color={PALETTE.accent} r={3.8} />
+          <Lab x={sx(asNum(limit.x))} y={baseY - 16} italic size={14}>{asStr(limit.symbol, "a")}</Lab>
+        </g>
+      ) : null}
+      {extraPoints.map((pt, i) => (
+        <g key={`pt${i}`}>
+          <Dot x={sx(asNum(pt.x))} y={baseY} />
+          {asStr(pt.label) ? <Lab x={sx(asNum(pt.x))} y={baseY - 14} italic size={12}>{asStr(pt.label)}</Lab> : null}
+        </g>
+      ))}
+    </Figure>
   );
 }
diff --git a/components/diagrams/SequenceDiagrams.tsx b/components/diagrams/SequenceDiagrams.tsx
new file mode 100644
index 0000000..e734629
--- /dev/null
+++ b/components/diagrams/SequenceDiagrams.tsx
@@ -0,0 +1,188 @@
+import type { ReactNode } from "react";
+import type { DiagramSpec } from "@/lib/course/types";
+import { PALETTE, makeScales, asNum, asStr, asArr, asObj, type Frame, type Box } from "@/lib/diagrams/engine";
+import { Figure, CartesianAxes, Lab, Dot, OpenDot } from "./Figure";
+
+const BOX: Box = { x0: 46, y0: 18, w: 402, h: 236 };
+
+type Term = { n: number; y: number };
+const readTerms = (v: unknown): Term[] => asArr(v).map(asObj).map((o) => ({ n: asNum(o.n), y: asNum(o.y) }));
+
+function frameFor(termSets: Term[][], extraY: number[] = [], nDefault = 8): Frame {
+  let nMax = nDefault, yMin = Infinity, yMax = -Infinity;
+  for (const ts of termSets) for (const t of ts) { nMax = Math.max(nMax, t.n); yMin = Math.min(yMin, t.y); yMax = Math.max(yMax, t.y); }
+  for (const y of extraY) { yMin = Math.min(yMin, y); yMax = Math.max(yMax, y); }
+  if (!isFinite(yMin)) { yMin = -1; yMax = 1; }
+  yMin = Math.min(yMin, 0); yMax = Math.max(yMax, 0);
+  const pad = (yMax - yMin) * 0.12 || 0.5;
+  return { xMin: 0, xMax: nMax + 1, yMin: yMin - pad, yMax: yMax + pad };
+}
+
+function termDots(terms: Term[], sx: (n: number) => number, sy: (y: number) => number, color: string, connect = true): ReactNode {
+  const sorted = [...terms].sort((a, b) => a.n - b.n);
+  return (
+    <g>
+      {connect && sorted.length > 1 ? (
+        <polyline fill="none" stroke={color} strokeWidth={1} opacity={0.4} points={sorted.map((t) => `${sx(t.n)},${sy(t.y)}`).join(" ")} />
+      ) : null}
+      {sorted.map((t, i) => <Dot key={i} x={sx(t.n)} y={sy(t.y)} color={color} r={3} />)}
+    </g>
+  );
+}
+
+/* ================= sequence-on-number-line ================= */
+export function SequenceOnNumberLine({ diagram }: { diagram: DiagramSpec }) {
+  const p = diagram.parameters;
+  const a = asNum(asObj(p.limitPoint).x, 0);
+  const eps = asNum(asObj(p.epsilon).value, 0.35);
+  const thr = asNum(asObj(p.threshold).index, NaN);
+  const terms = asArr(p.terms).map(asObj).map((o) => ({ n: asNum(o.n), x: asNum(o.x), inside: o.inside === true }));
+  terms.sort((s, t) => s.n - t.n);
+
+  const X0 = 70, X1 = 440, baseY = 250;
+  const half = Math.max(Math.abs(a - eps), ...terms.map((t) => Math.abs(t.x - a))) + 0.2;
+  const xMin = a - half, xMax = a + half;
+  const sx = (x: number) => X0 + ((x - xMin) / (xMax - xMin)) * (X1 - X0);
+  const rowTop = 34, rowGap = (baseY - 50 - rowTop) / Math.max(1, terms.length);
+  const ty = (i: number) => rowTop + i * rowGap;
+
+  return (
+    <Figure diagram={diagram} viewBox="0 0 480 280">
+      {/* ε 邻域竖带 */}
+      <rect x={sx(a - eps)} y={20} width={sx(a + eps) - sx(a - eps)} height={baseY - 20} fill={PALETTE.curve} opacity={0.12} />
+      <Lab x={(sx(a - eps) + sx(a + eps)) / 2} y={16} size={11} color={PALETTE.curve}>U(a;ε)</Lab>
+      {/* 项：逐行向下，横向收敛进色带 */}
+      {terms.map((t, i) => (
+        <g key={i}>
+          {i > 0 ? <line x1={sx(terms[i - 1].x)} y1={ty(i - 1)} x2={sx(t.x)} y2={ty(i)} stroke={PALETTE.inkFaint} strokeWidth={0.8} opacity={0.6} /> : null}
+          <circle cx={sx(t.x)} cy={ty(i)} r={3.4} fill={t.inside ? PALETTE.accent : PALETTE.paperSunk} stroke={t.inside ? PALETTE.accent : PALETTE.inkSoft} strokeWidth={1.4} />
+          <Lab x={sx(t.x) + 7} y={ty(i) + 3} anchor="start" italic size={10} color={PALETTE.inkFaint}>{`x_${t.n}`}</Lab>
+        </g>
+      ))}
+      {/* 阈值线 */}
+      {isFinite(thr) && terms.some((t) => t.n === thr) ? (
+        <g>
+          {(() => { const idx = terms.findIndex((t) => t.n > thr); const yLine = ty(idx) - rowGap / 2; return (
+            <>
+              <line x1={X0} y1={yLine} x2={X1} y2={yLine} stroke={PALETTE.gold} strokeWidth={1} strokeDasharray="5 3" />
+              <Lab x={X1} y={yLine - 4} anchor="end" size={10} color={PALETTE.gold}>{`n>${asStr(asObj(p.threshold).symbol, "N")} 全部落入`}</Lab>
+            </>
+          ); })()}
+        </g>
+      ) : null}
+      {/* 数轴 */}
+      <line x1={X0 - 8} y1={baseY} x2={X1 + 8} y2={baseY} stroke={PALETTE.ink} strokeWidth={1.4} />
+      <path d={`M${X1 + 8} ${baseY} l-7 -3.5 l0 7 z`} fill={PALETTE.ink} />
+      <line x1={sx(a)} y1={baseY - 4} x2={sx(a)} y2={baseY + 4} stroke={PALETTE.accent} strokeWidth={1.6} />
+      <Lab x={sx(a)} y={baseY + 18} italic size={13} color={PALETTE.accent}>{asStr(asObj(p.limitPoint).symbol, "a")}</Lab>
+    </Figure>
+  );
+}
+
+/* ================= two-panel-sequence-plot ================= */
+export function TwoPanelSequence({ diagram }: { diagram: DiagramSpec }) {
+  const panels = asArr(diagram.parameters.panels).map(asObj).slice(0, 2);
+  const boxes: Box[] = [{ x0: 40, y0: 40, w: 168, h: 200 }, { x0: 272, y0: 40, w: 168, h: 200 }];
+
+  return (
+    <Figure diagram={diagram} viewBox="0 0 480 290">
+      {panels.map((panel, pi) => {
+        const box = boxes[pi];
+        const terms = readTerms(panel.terms);
+        const limitNum = Number(asStr(panel.limitLabel));
+        const hasLimit = isFinite(limitNum);
+        const frame = frameFor([terms], hasLimit ? [limitNum] : []);
+        const { sx, sy } = makeScales(frame, box);
+        return (
+          <g key={pi}>
+            <CartesianAxes frame={frame} box={box} xLabel="n" yLabel="" grid={false} />
+            {hasLimit ? <line x1={box.x0} y1={sy(limitNum)} x2={box.x0 + box.w} y2={sy(limitNum)} stroke={PALETTE.gold} strokeWidth={1.2} strokeDasharray="5 3" /> : null}
+            {termDots(terms, sx, sy, PALETTE.curve)}
+            <Lab x={box.x0 + box.w / 2} y={box.y0 - 14} size={12} color={PALETTE.ink}>{asStr(panel.title)}</Lab>
+            <Lab x={box.x0 + box.w / 2} y={box.y0 + box.h + 26} size={11} italic color={PALETTE.inkSoft}>{asStr(panel.limitLabel)}</Lab>
+          </g>
+        );
+      })}
+    </Figure>
+  );
+}
+
+/* ================= bounded-strip ================= */
+export function BoundedStrip({ diagram }: { diagram: DiagramSpec }) {
+  const p = diagram.parameters;
+  const prefix = readTerms(p.finitePrefix);
+  const tail = readTerms(p.tailTerms);
+  const nb = asObj(p.tailNeighborhood);
+  const lower = asNum(nb.lower, -1), upper = asNum(nb.upper, 1);
+  const M = Math.max(...prefix.map((t) => Math.abs(t.y)), ...tail.map((t) => Math.abs(t.y)), Math.abs(upper)) + 0.2;
+  const frame = frameFor([prefix, tail], [M, -M, lower, upper]);
+  const { sx, sy } = makeScales(frame, BOX);
+
+  return (
+    <Figure diagram={diagram}>
+      <CartesianAxes frame={frame} box={BOX} xLabel="n" grid={false} />
+      {/* 尾部邻域带 */}
+      <rect x={BOX.x0} y={sy(upper)} width={BOX.w} height={sy(lower) - sy(upper)} fill={PALETTE.curve} opacity={0.12} />
+      <Lab x={BOX.x0 + BOX.w - 4} y={sy(upper) - 4} anchor="end" size={11} color={PALETTE.curve}>{asStr(nb.label, "尾部邻域")}</Lab>
+      {/* 全局界 ±M */}
+      <line x1={BOX.x0} y1={sy(M)} x2={BOX.x0 + BOX.w} y2={sy(M)} stroke={PALETTE.accent} strokeWidth={1.1} strokeDasharray="6 4" />
+      <line x1={BOX.x0} y1={sy(-M)} x2={BOX.x0 + BOX.w} y2={sy(-M)} stroke={PALETTE.accent} strokeWidth={1.1} strokeDasharray="6 4" />
+      <Lab x={BOX.x0 + 4} y={sy(M) - 5} anchor="start" size={10} color={PALETTE.accent}>{asStr(p.globalBoundLabel, "±M")}</Lab>
+      {/* 前段（空心）与尾段（实心） */}
+      {prefix.map((t, i) => <OpenDot key={`p${i}`} x={sx(t.n)} y={sy(t.y)} color={PALETTE.inkSoft} />)}
+      {termDots(tail, sx, sy, PALETTE.curve)}
+    </Figure>
+  );
+}
+
+/* ================= monotone-sequence-plot ================= */
+export function MonotoneSequence({ diagram }: { diagram: DiagramSpec }) {
+  const p = diagram.parameters;
+  const terms = readTerms(p.terms);
+  const sup = asObj(p.supremum), ub = asObj(p.upperBound);
+  const supV = asNum(sup.value, 1), ubV = asNum(ub.value, 1.2);
+  const frame = frameFor([terms], [supV, ubV]);
+  const { sx, sy } = makeScales(frame, BOX);
+
+  return (
+    <Figure diagram={diagram}>
+      <CartesianAxes frame={frame} box={BOX} xLabel="n" grid={false} />
+      <line x1={BOX.x0} y1={sy(ubV)} x2={BOX.x0 + BOX.w} y2={sy(ubV)} stroke={PALETTE.inkSoft} strokeWidth={1.1} strokeDasharray="3 3" />
+      <Lab x={BOX.x0 + BOX.w - 4} y={sy(ubV) - 5} anchor="end" size={11} color={PALETTE.inkSoft}>{asStr(ub.label, "上界")}</Lab>
+      <line x1={BOX.x0} y1={sy(supV)} x2={BOX.x0 + BOX.w} y2={sy(supV)} stroke={PALETTE.accent} strokeWidth={1.3} strokeDasharray="6 4" />
+      <Lab x={BOX.x0 + BOX.w - 4} y={sy(supV) - 5} anchor="end" size={11} italic color={PALETTE.accent}>{asStr(sup.label, "sup")}</Lab>
+      {termDots(terms, sx, sy, PALETTE.curve)}
+    </Figure>
+  );
+}
+
+/* ================= subsequence-highlight ================= */
+export function SubsequenceHighlight({ diagram }: { diagram: DiagramSpec }) {
+  const p = diagram.parameters;
+  const orig = asArr(p.originalSequence).map(asObj).map((o) => ({ n: asNum(o.n), y: asNum(o.y), sub: asStr(o.subsequence) }));
+  const subs = asArr(p.subsequences).map(asObj);
+  const palette = [PALETTE.accent, PALETTE.curve];
+  const subColor: Record<string, string> = {};
+  orig.forEach((t) => { if (!(t.sub in subColor)) subColor[t.sub] = palette[Object.keys(subColor).length % palette.length]; });
+
+  const frame = frameFor([orig.map((t) => ({ n: t.n, y: t.y }))]);
+  const { sx, sy } = makeScales(frame, BOX);
+
+  return (
+    <Figure diagram={diagram}>
+      <CartesianAxes frame={frame} box={BOX} xLabel="n" grid={false} />
+      {/* 各子列极限线 */}
+      {subs.map((s, i) => {
+        const lim = Number(asStr(s.limit));
+        if (!isFinite(lim)) return null;
+        return (
+          <g key={`lim${i}`}>
+            <line x1={BOX.x0} y1={sy(lim)} x2={BOX.x0 + BOX.w} y2={sy(lim)} stroke={palette[i % palette.length]} strokeWidth={1.1} strokeDasharray="5 3" opacity={0.8} />
+            <Lab x={BOX.x0 + BOX.w - 4} y={sy(lim) - 5} anchor="end" size={11} color={palette[i % palette.length]}>{`${asStr(s.label)} → ${asStr(s.limit)}`}</Lab>
+          </g>
+        );
+      })}
+      {orig.map((t, i) => <Dot key={i} x={sx(t.n)} y={sy(t.y)} color={subColor[t.sub] ?? PALETTE.ink} r={3.4} />)}
+    </Figure>
+  );
+}
diff --git a/components/diagrams/SequencePlotDiagram.tsx b/components/diagrams/SequencePlotDiagram.tsx
deleted file mode 100644
index 21e9976..0000000
--- a/components/diagrams/SequencePlotDiagram.tsx
+++ /dev/null
@@ -1,38 +0,0 @@
-import { MathText } from "@/components/math/MathText";
-import type { DiagramSpec } from "@/lib/course/types";
-
-const points = [
-  [70, 120],
-  [130, 86],
-  [190, 68],
-  [250, 56],
-  [310, 48],
-  [370, 42],
-  [430, 38]
-];
-
-export function SequencePlotDiagram({ diagram }: { diagram: DiagramSpec }) {
-  return (
-    <figure className="diagram-card">
-      <figcaption>
-        <strong>{diagram.title}</strong>
-        <MathText text={diagram.description} />
-      </figcaption>
-      <svg aria-label={diagram.title} role="img" viewBox="0 0 520 190">
-        <line stroke="currentColor" strokeWidth="2" x1="48" x2="480" y1="150" y2="150" />
-        <line stroke="currentColor" strokeWidth="2" x1="48" x2="48" y1="24" y2="150" />
-        <line stroke="#c18a2d" strokeDasharray="6 6" strokeWidth="2" x1="48" x2="480" y1="36" y2="36" />
-        <text x="486" y="40">
-          limit
-        </text>
-        <polyline fill="none" points={points.map(([x, y]) => `${x},${y}`).join(" ")} stroke="#2f6f68" strokeWidth="3" />
-        {points.map(([x, y], index) => (
-          <circle cx={x} cy={y} fill="#194d47" key={`${x}-${y}-${index}`} r="5" />
-        ))}
-      </svg>
-      <p className="diagram-prompt">
-        <MathText text={diagram.studentPrompt} />
-      </p>
-    </figure>
-  );
-}
diff --git a/components/diagrams/TableDiagram.tsx b/components/diagrams/TableDiagram.tsx
new file mode 100644
index 0000000..2417478
--- /dev/null
+++ b/components/diagrams/TableDiagram.tsx
@@ -0,0 +1,35 @@
+import { MathText } from "@/components/math/MathText";
+import type { DiagramSpec } from "@/lib/course/types";
+import { asArr, asStr } from "@/lib/diagrams/engine";
+
+/** 表格图：type = "table"。columns + rows 渲染成对照表（支持单元格内 LaTeX）。 */
+export function TableDiagram({ diagram }: { diagram: DiagramSpec }) {
+  const columns = asArr(diagram.parameters.columns).map((c) => asStr(c));
+  const rows = asArr(diagram.parameters.rows).map((r) => asArr(r).map((c) => asStr(c)));
+
+  return (
+    <figure className="diagram-card">
+      <figcaption>
+        <strong><MathText text={diagram.title} /></strong>
+        <MathText text={diagram.description} />
+      </figcaption>
+      <div className="diagram-table-wrap">
+        <table className="diagram-table">
+          {columns.length ? (
+            <thead>
+              <tr>{columns.map((c, i) => <th key={i}><MathText text={c} /></th>)}</tr>
+            </thead>
+          ) : null}
+          <tbody>
+            {rows.map((row, ri) => (
+              <tr key={ri}>{row.map((cell, ci) => <td key={ci}><MathText text={cell} /></td>)}</tr>
+            ))}
+          </tbody>
+        </table>
+      </div>
+      {diagram.studentPrompt ? (
+        <p className="diagram-prompt"><MathText text={diagram.studentPrompt} /></p>
+      ) : null}
+    </figure>
+  );
+}
diff --git a/components/math/MathText.tsx b/components/math/MathText.tsx
index e7627f4..8bc0cc9 100644
--- a/components/math/MathText.tsx
+++ b/components/math/MathText.tsx
@@ -13,6 +13,15 @@ function renderLatex(latex: string, displayMode: boolean) {
   });
 }
 
+function parseMarkdownLine(line: string, key: string): ReactNode[] {
+  const parts = line.split(/(\*\*[^*\n]+\*\*|\*[^*\n]+\*)/g);
+  return parts.map((p, i) => {
+    if (p.startsWith("**") && p.endsWith("**")) return <strong key={`${key}-s${i}`}>{p.slice(2, -2)}</strong>;
+    if (p.startsWith("*") && p.endsWith("*")) return <em key={`${key}-e${i}`}>{p.slice(1, -1)}</em>;
+    return p;
+  });
+}
+
 function renderInlineParts(text: string, keyPrefix: string): ReactNode[] {
   const parts = text.split(/(\$\$[\s\S]+?\$\$|\$[^$\n]+\$)/g).filter((p) => p.length > 0);
   return parts.map((part, index) => {
@@ -30,7 +39,7 @@ function renderInlineParts(text: string, keyPrefix: string): ReactNode[] {
     return (
       <span key={`${keyPrefix}-${index}`}>
         {part.split("\n").flatMap((line, li, arr) => {
-          const nodes: ReactNode[] = [line];
+          const nodes: ReactNode[] = parseMarkdownLine(line, `${keyPrefix}-${index}-l${li}`);
           if (li < arr.length - 1) nodes.push(<br key={`${keyPrefix}-${index}-br-${li}`} />);
           return nodes;
         })}
@@ -47,12 +56,12 @@ export function MathText({ className, text }: { className?: string; text: string
   }
 
   return (
-    <span className={className}>
+    <div className={className}>
       {paragraphs.map((para, i) => (
         <p key={i}>
           {renderInlineParts(para.trim(), `p${i}`)}
         </p>
       ))}
-    </span>
+    </div>
   );
 }
diff --git a/content/courses/gaodeng-shuxue/chapters/.gitkeep b/content/courses/gaodeng-shuxue/chapters/.gitkeep
new file mode 100644
index 0000000..e69de29
diff --git a/content/courses/gaodeng-shuxue/chapters/gd-definite-integral.json b/content/courses/gaodeng-shuxue/chapters/gd-definite-integral.json
new file mode 100644
index 0000000..8312c43
--- /dev/null
+++ b/content/courses/gaodeng-shuxue/chapters/gd-definite-integral.json
@@ -0,0 +1 @@
+{"id":"ch-gd-definite-integral","courseId":"gaodeng-shuxue","volumeId":"gaodeng-shuxue-volume-1","number":5,"title":"定积分及其应用","status":"planned","overview":"","knowledgePoints":[]}
diff --git a/content/courses/gaodeng-shuxue/chapters/gd-derivative.json b/content/courses/gaodeng-shuxue/chapters/gd-derivative.json
new file mode 100644
index 0000000..c3812b2
--- /dev/null
+++ b/content/courses/gaodeng-shuxue/chapters/gd-derivative.json
@@ -0,0 +1 @@
+{"id":"ch-gd-derivative","courseId":"gaodeng-shuxue","volumeId":"gaodeng-shuxue-volume-1","number":2,"title":"导数与微分","status":"planned","overview":"","knowledgePoints":[]}
diff --git a/content/courses/gaodeng-shuxue/chapters/gd-function-limit.json b/content/courses/gaodeng-shuxue/chapters/gd-function-limit.json
new file mode 100644
index 0000000..524888e
--- /dev/null
+++ b/content/courses/gaodeng-shuxue/chapters/gd-function-limit.json
@@ -0,0 +1,396 @@
+{
+  "id": "ch-gd-function-limit",
+  "courseId": "gaodeng-shuxue",
+  "volumeId": "gaodeng-shuxue-volume-1",
+  "number": 1,
+  "title": "函数、极限与连续",
+  "status": "sample-ready",
+  "overview": "本章是工科高等数学的入口：先掌握函数与基本初等函数，再用计算型方法处理数列极限与函数极限，熟练运用两个重要极限与无穷小替换，最后建立连续性与间断点分类，为导数与积分打基础。讲义侧重会算、会用，证明只给思路。",
+  "knowledgePoints": [
+    {
+      "id": "gd-function-elementary",
+      "title": "函数概念与基本初等函数",
+      "learningGoals": [
+        "能写出函数的定义域、值域，并判断奇偶性、单调性、周期性。",
+        "熟悉幂函数、指数函数、对数函数、三角函数与反三角函数的基本图像与运算性质。",
+        "会把分段函数、复合函数与初等函数变形联系起来，为后续极限与导数计算做准备。"
+      ],
+      "coreExplanation": "工科高数里，函数是描述变量依赖关系的基本语言。给定对应法则 $f$，每个允许输入的自变量 $x$ 唯一确定一个输出 $f(x)$；所有允许的 $x$ 构成**定义域**，所有可能的 $f(x)$ 构成**值域**。实际计算中，第一件事永远是写定义域：根式要求被开方数 $\\\\geq 0$，对数要求真数 $>0$，分式要求分母 $\\\\ne 0$。\n\n**基本初等函数**包括幂函数 $x^\\\\alpha$、指数函数 $a^x$（$a>0,a\\\\ne 1$）、对数函数 $\\\\log_a x$、三角函数与反三角函数。它们的图像与性质要熟：$y=x^2$ 在 $[0,+\\\\infty)$ 递增；$y=a^x$ 恒正且过点 $(0,1)$；$y=\\\\ln x$ 只在 $x>0$ 定义；$y=\\\\sin x$ 有界且周期为 $2\\\\pi$。工科建模里，指数函数常描述增长/衰减，对数函数常处理数量级压缩，三角函数描述周期振动。\n\n**算例**：求 $f(x)=\\\\sqrt{4-x^2}+\\\\ln(x+1)$ 的定义域。由 $4-x^2\\\\geq 0$ 得 $-2\\\\leq x\\\\leq 2$；由 $x+1>0$ 得 $x>-1$；取交集得 $(-1,2]$。再求 $f(-1)=\\\\sqrt{3}+0=\\\\sqrt{3}$，$f(0)=2+0=2$。分段函数要先看自变量落在哪个区间，例如 $g(x)=\\\\begin{cases}x^2,&x\\\\leq 0\\\\\\\\2^x,&x>0\\\\end{cases}$ 在 $x=0$ 处取第一支，$g(0)=0$，在 $x=1$ 处取第二支，$g(1)=2$。",
+      "textbookRefs": [
+        "高等数学（同济第八版）上册 第一章 §1–§2"
+      ],
+      "keyDefinitions": [
+        {
+          "name": "函数",
+          "statement": "设 $D$ 为非空实数集，若对每个 $x\\\\in D$，按法则 $f$ 唯一确定实数 $y=f(x)$，则称 $f$ 为定义在 $D$ 上的函数，$D$ 为定义域。"
+        },
+        {
+          "name": "基本初等函数",
+          "statement": "由常数、幂函数、指数函数、对数函数、三角函数、反三角函数经过有限次四则运算与复合得到的函数，称为初等函数。"
+        }
+      ],
+      "keyTheorems": [],
+      "proofIdeas": [
+        "写定义域的标准流程：逐个限制条件列不等式，再取交集。",
+        "判断分段函数在某点的取值：先定位区间，再代入对应解析式。"
+      ],
+      "socraticQuestions": [
+        "$y=\\\\ln(x-1)+\\\\sqrt{5-x}$ 的定义域如何求？",
+        "指数函数 $y=2^{x-1}+1$ 与 $y=2^x$ 的图像有什么关系？",
+        "分段函数在分界点处，函数值与后面要学的极限值一定相同吗？"
+      ],
+      "commonMistakes": [
+        "只求部分限制条件，忘记取交集。",
+        "对数真数含参数时不讨论参数范围。",
+        "分段函数在分界点直接代入错误分支。"
+      ],
+      "exampleIds": ["gd-fl-ex-001", "gd-fl-ex-002"],
+      "exerciseIds": ["gd-fl-ex-001", "gd-fl-ex-002", "gd-fl-ex-003"],
+      "diagramIds": ["gd-fl-elementary-functions"],
+      "masteryCriteria": [
+        "能独立求常见初等函数的定义域。",
+        "能识别并计算分段函数在指定点的函数值。",
+        "能说出五类基本初等函数的核心性质。"
+      ]
+    },
+    {
+      "id": "gd-sequence-limit-calc",
+      "title": "数列极限的计算",
+      "learningGoals": [
+        "理解数列极限的直观含义，会把通项前几项写出来判断趋势。",
+        "掌握 $\\\\infty/\\\\infty$ 型有理数列极限的「抓最高次幂」法。",
+        "会对根式差、指数型数列使用有理化与重要极限思想。"
+      ],
+      "coreExplanation": "数列 $\\\\{a_n\\\\}$ 的极限描述的是：当 $n$ 越来越大时，项 $a_n$ 是否稳定靠近某个常数 $A$。工科课程不强调 $\\\\varepsilon$-$N$ 证明，但计算套路必须熟练。最典型的是有理式 $\\\\lim\\\\frac{P(n)}{Q(n)}$：若分子分母最高次相同，极限等于最高次系数之比；若分母次数更高，极限为 $0$；若分子次数更高，极限为 $\\\\infty$。\n\n**算例 1**：$\\\\lim_{n\\\\to\\\\infty}\\\\frac{3n^2-n+1}{2n^2+5}$。分子分母同除以 $n^2$，得 $\\\\lim\\\\frac{3-1/n+1/n^2}{2+5/n^2}=\\\\frac32$。\n\n**算例 2**：$\\\\lim_{n\\\\to\\\\infty}(\\\\sqrt{n^2+n}-n)$。有理化：$\\\\sqrt{n^2+n}-n=\\\\frac{n}{\\\\sqrt{n^2+n}+n}=\\\\frac{1}{\\\\sqrt{1+1/n}+1}\\\\to\\\\frac12$。这类「$\\\\infty-\\\\infty$」必须先变形，不可直接相减。\n\n**算例 3**：$\\\\lim_{n\\\\to\\\\infty}(1+\\\\frac{2}{n})^{3n}$。改写为 $\\\\left[(1+\\\\frac{2}{n})^n\\\\right]^3\\\\to e^3$？注意：应凑 $\\\\left(1+\\\\frac{2}{n}\\\\right)^n\\\\to e^2$ 的结构，更标准写法是令 $m=n/2$，得 $\\\\left(1+\\\\frac{1}{m}\\\\right)^{6m}\\\\to e^6$。重要极限 $\\\\lim(1+1/n)^n=e$ 在复利、人口增长、RC 电路等模型中反复出现。",
+      "textbookRefs": [
+        "高等数学（同济第八版）上册 第一章 §2–§3"
+      ],
+      "keyDefinitions": [
+        {
+          "name": "数列极限（直观）",
+          "statement": "若当 $n$ 无限增大时，数列 $\\\\{a_n\\\\}$ 的项 $a_n$ 无限接近常数 $A$，则称 $A$ 为数列极限，记 $\\\\lim_{n\\\\to\\\\infty}a_n=A$。"
+        }
+      ],
+      "keyTheorems": [
+        {
+          "name": "重要极限（数列形式）",
+          "statement": "$\\\\lim_{n\\\\to\\\\infty}(1+\\\\frac{1}{n})^n=e$。",
+          "proofSketch": "可用单调有界或二项式展开给出存在性；工科使用以计算为主。"
+        }
+      ],
+      "proofIdeas": [
+        "有理数列极限：同除最高次幂。",
+        "根式差：分子有理化化为 $0/0$ 型再处理。",
+        "指数底型：凑 $(1+1/n)^n$ 或 $(1+1/m)^m$ 的结构。"
+      ],
+      "socraticQuestions": [
+        "$a_n=(-1)^n$ 为什么发散？",
+        "为什么 $\\\\sqrt{n^2+n}$ 不能写成 $n+\\\\sqrt{n}$？",
+        "$(1+2/n)^{3n}$ 与 $(1+1/n)^{3n}$ 的极限有何不同？"
+      ],
+      "commonMistakes": [
+        "把 $\\\\infty-\\\\infty$ 直接当作 $0$。",
+        "有理化时符号写错。",
+        "重要极限中指数与底数系数不配平。"
+      ],
+      "exampleIds": ["gd-fl-ex-004"],
+      "exerciseIds": ["gd-fl-ex-004", "gd-fl-ex-005", "gd-fl-ex-006"],
+      "diagramIds": ["gd-fl-limit-neighborhood"],
+      "masteryCriteria": [
+        "能熟练计算有理数列极限。",
+        "会对根式差型数列有理化。",
+        "能识别并计算简单的重要极限型数列。"
+      ]
+    },
+    {
+      "id": "gd-function-limit-calc",
+      "title": "函数极限与基本计算",
+      "learningGoals": [
+        "理解 $x\\\\to x_0$ 与 $x\\\\to\\\\infty$ 时函数极限的直观含义。",
+        "掌握因式分解、有理化、约分等化简技巧处理 $0/0$ 型极限。",
+        "会求单侧极限，并判断双侧极限是否存在。"
+      ],
+      "coreExplanation": "函数极限关心：当 $x$ 按某种方式靠近 $x_0$（或 $\\\\infty$）时，$f(x)$ 是否靠近某个常数。工科教学强调**会算**：先代入看类型，若是 $0/0$，就因式分解或有理化；若是 $\\\\infty/\\\\infty$，就抓最高次幂；若是 $\\\\infty-\\\\infty$，先通分或有理化。\n\n**算例 1**：$\\\\lim_{x\\\\to 2}\\\\frac{x^2-4}{x-2}$。代入得 $0/0$，因式分解 $\\\\frac{(x-2)(x+2)}{x-2}=x+2$（$x\\\\ne 2$），极限为 $4$。注意 $f(2)$ 可以无定义，但极限仍可为 $4$。\n\n**算例 2**：$\\\\lim_{x\\\\to 0}\\\\frac{\\\\sqrt{1+x}-\\\\sqrt{1-x}}{x}$。分子有理化后得 $\\\\frac{2}{\\\\sqrt{1+x}+\\\\sqrt{1-x}}\\\\to 1$。\n\n**单侧极限**：$f(x)=|x|/x$ 在 $x>0$ 时为 $1$，$x<0$ 时为 $-1$，故 $f(0^+)=1$、$f(0^-)=-1$，双侧极限不存在。分段函数在分界点必须先分侧计算。",
+      "textbookRefs": [
+        "高等数学（同济第八版）上册 第一章 §3–§4"
+      ],
+      "keyDefinitions": [
+        {
+          "name": "函数极限（直观）",
+          "statement": "当 $x$ 无限趋近 $x_0$（或 $\\\\infty$）时，$f(x)$ 无限趋近常数 $A$，则称 $A$ 为函数极限，记 $\\\\lim_{x\\\\to x_0}f(x)=A$。"
+        },
+        {
+          "name": "左极限与右极限",
+          "statement": "只让 $x$ 从左侧趋近 $x_0$ 得到的极限为左极限 $f(x_0^-)$；只从右侧趋近得到右极限 $f(x_0^+)$。双侧极限存在当且仅当左右极限存在且相等。"
+        }
+      ],
+      "keyTheorems": [],
+      "proofIdeas": [
+        "见极限就代入；出现 $0/0$ 先化简。",
+        "根式差优先有理化。",
+        "分段点、绝对值点先分侧。"
+      ],
+      "socraticQuestions": [
+        "为什么 $\\\\lim_{x\\\\to 1}\\\\frac{x^2-1}{x-1}$ 与 $f(1)$ 可以不同？",
+        "什么时候必须分左右极限？",
+        "$x\\\\to\\\\infty$ 时，$\\\\frac{2x^3+1}{5x^3-x}$ 的极限如何一眼看出？"
+      ],
+      "commonMistakes": [
+        "遇到 $0/0$ 就说极限不存在。",
+        "有理化共轭乘错。",
+        "只算一侧极限就下结论。"
+      ],
+      "exampleIds": ["gd-fl-ex-007", "gd-fl-ex-008"],
+      "exerciseIds": ["gd-fl-ex-007", "gd-fl-ex-008", "gd-fl-ex-009"],
+      "diagramIds": ["gd-fl-limit-neighborhood"],
+      "masteryCriteria": [
+        "能处理常见 $0/0$ 型函数极限。",
+        "会求单侧极限并判断双侧极限。",
+        "能区分极限值与函数值。"
+      ]
+    },
+    {
+      "id": "gd-infinitesimal-infinite",
+      "title": "无穷小与无穷大",
+      "learningGoals": [
+        "掌握无穷小、无穷大的定义及其与极限的关系。",
+        "会在极限计算中把无穷小量提出来简化表达式。",
+        "理解无穷大与无界、竖直渐近线的联系。"
+      ],
+      "coreExplanation": "若 $\\\\lim f(x)=0$，则 $f(x)$ 是 $x\\\\to x_0$（或 $x\\\\to\\\\infty$）时的**无穷小量**；若 $\\\\lim|f(x)|=+\\\\infty$，则称 $f(x)$ 为**无穷大量**。无穷小与有限常数、无穷大一起构成极限计算的基本语言。例如 $3x^2$ 在 $x\\\\to 0$ 时是无穷小，$1/x$ 在 $x\\\\to 0^+$ 时是无穷大。\n\n**算例 1**：$\\\\lim_{x\\\\to\\\\infty}\\\\frac{2x^3-x+1}{5x^3+4x}$。分子分母同除以 $x^3$，低次项消失，极限 $2/5$。这是 $\\\\infty/\\\\infty$ 型抓主项。\n\n**算例 2**：说明 $\\\\lim_{x\\\\to 0^+}\\\\ln x=-\\\\infty$。当 $x$ 从右侧趋近 $0$，$\\\\ln x$ 取越来越大的负值，因此是无穷大而非无穷小。此时 $x=0$ 是 $y=\\\\ln x$ 的竖直渐近线。工科电路中，某些参数趋近零时电流或功率可出现无穷大理想模型，实际中意味着模型失效，需要分段讨论。",
+      "textbookRefs": [
+        "高等数学（同济第八版）上册 第一章 §4"
+      ],
+      "keyDefinitions": [
+        {
+          "name": "无穷小量",
+          "statement": "若 $\\\\lim f(x)=0$，则称 $f(x)$ 为该趋近过程中的无穷小量。"
+        },
+        {
+          "name": "无穷大量",
+          "statement": "若 $\\\\lim|f(x)|=+\\\\infty$，则称 $f(x)$ 为该趋近过程中的无穷大量。"
+        }
+      ],
+      "keyTheorems": [
+        {
+          "name": "无穷小与极限的关系",
+          "statement": "$\\\\lim f(x)=A$ 当且仅当 $f(x)-A$ 是无穷小量。",
+          "proofSketch": "直接把极限定义改写成差趋于零。"
+        }
+      ],
+      "proofIdeas": [
+        "判断无穷小：算极限是否为 $0$。",
+        "判断无穷大：看绝对值是否无限增大。",
+        "$\\\\infty/\\\\infty$：同除最高次幂。"
+      ],
+      "socraticQuestions": [
+        "无穷小量是不是「很小的数」？",
+        "无界数列是否一定是无穷大？",
+        "为什么讨论 $\\\\ln x$ 在 $0$ 附近必须限定 $x\\\\to 0^+$？"
+      ],
+      "commonMistakes": [
+        "把趋于非零常数也称作无穷小。",
+        "混淆无界与无穷大。",
+        "对数函数在 $x\\\\leq 0$ 上讨论极限。"
+      ],
+      "exampleIds": ["gd-fl-ex-010"],
+      "exerciseIds": ["gd-fl-ex-010", "gd-fl-ex-011", "gd-fl-ex-012"],
+      "diagramIds": [],
+      "masteryCriteria": [
+        "能判断给定函数是否为无穷小或无穷大。",
+        "会用主项法计算 $\\\\infty/\\\\infty$ 型极限。",
+        "能写出简单函数的竖直渐近线。"
+      ]
+    },
+    {
+      "id": "gd-limit-arithmetic",
+      "title": "极限运算法则",
+      "learningGoals": [
+        "熟练运用和、差、积、商的极限法则。",
+        "知道极限不存在时不能盲目拆算式。",
+        "会把复杂极限拆成若干简单极限的组合。"
+      ],
+      "coreExplanation": "若 $\\\\lim f(x)=A$、$\\\\lim g(x)=B$ 都存在，则：$\\\\lim[f(x)\\\\pm g(x)]=A\\\\pm B$，$\\\\lim[f(x)g(x)]=AB$，当 $B\\\\ne 0$ 时 $\\\\lim\\\\frac{f(x)}{g(x)}=\\\\frac{A}{B}$。这些法则把复杂极限拆成简单极限，是工科计算的主线。但要注意前提：拆之前必须确认各部分的极限存在，且商法则要求分母极限非零。\n\n**算例 1**：已知 $\\\\lim_{x\\\\to 1}f(x)=2$、$\\\\lim_{x\\\\to 1}g(x)=-1$，则 $\\\\lim_{x\\\\to 1}[3f(x)-2g(x)]=3\\\\cdot 2-2\\\\cdot(-1)=8$。\n\n**算例 2**：$\\\\lim_{x\\\\to 2}\\\\frac{x^2-3x+2}{x^2-4}$。先识别 $0/0$，分子 $(x-1)(x-2)$，分母 $(x-2)(x+2)$，约去 $x-2$ 得 $\\\\frac{x-1}{x+2}\\\\to\\\\frac14$。\n\n**算例 3**：$\\\\lim_{x\\\\to 0}\\\\frac{\\\\sin 3x}{\\\\tan 2x}$。写成 $\\\\frac{\\\\sin 3x}{3x}\\\\cdot\\\\frac{2x}{\\\\tan 2x}\\\\cdot\\\\frac{3}{2}\\\\to 1\\\\cdot 1\\\\cdot\\\\frac32=\\\\frac32$。乘除结构下可把已知极限因子拆开，这是后续等价无穷小替换的理论依据。",
+      "textbookRefs": [
+        "高等数学（同济第八版）上册 第一章 §4"
+      ],
+      "keyDefinitions": [],
+      "keyTheorems": [
+        {
+          "name": "极限四则运算法则",
+          "statement": "设 $\\\\lim f(x)=A$、$\\\\lim g(x)=B$，则和差积极限分别为 $A\\\\pm B$、$AB$；若 $B\\\\ne 0$，则商极限为 $A/B$。"
+        }
+      ],
+      "proofIdeas": [
+        "先判断能否直接代入。",
+        "不能代入则先化简到可用法则的形式。",
+        "乘除型可拆因子，加减型一般要先通分或有理化。"
+      ],
+      "socraticQuestions": [
+        "为什么商法则要求分母极限不为零？",
+        "两个函数极限都不存在，它们的和极限一定不存在吗？",
+        "什么时候可以把 $\\\\lim(f+g)$ 拆成 $\\\\lim f+\\\\lim g$？"
+      ],
+      "commonMistakes": [
+        "对 $0/0$ 型直接套用商法则。",
+        "拆极限时忽略某一项极限不存在。",
+        "符号计算错误导致线性组合结果错。"
+      ],
+      "exampleIds": ["gd-fl-ex-013", "gd-fl-ex-014"],
+      "exerciseIds": ["gd-fl-ex-013", "gd-fl-ex-014", "gd-fl-ex-015"],
+      "diagramIds": [],
+      "masteryCriteria": [
+        "能正确运用四则法则计算极限。",
+        "会在乘除结构中拆分已知极限因子。",
+        "能识别不能盲目拆极限的情形。"
+      ]
+    },
+    {
+      "id": "gd-important-limits",
+      "title": "两个重要极限",
+      "learningGoals": [
+        "熟记并会变形使用 $\\\\lim_{x\\\\to 0}\\\\frac{\\\\sin x}{x}=1$。",
+        "熟记并会变形使用 $\\\\lim_{x\\\\to\\\\infty}(1+\\\\frac{1}{x})^x=e$。",
+        "能把三角、指数型极限凑成重要极限的标准形。"
+      ],
+      "coreExplanation": "工科高数最重要的两个极限：\n$$\\\\lim_{x\\\\to 0}\\\\frac{\\\\sin x}{x}=1,\\\\qquad \\\\lim_{x\\\\to\\\\infty}\\\\left(1+\\\\frac{1}{x}\\\\right)^x=e.$$\n第一个来自小角度近似 $\\\\sin x\\\\approx x$，在振动、交流电路相位分析中极常见；第二个是连续复利模型的核心，描述「以无穷细分方式增长」的极限。\n\n**算例 1**：$\\\\lim_{x\\\\to 0}\\\\frac{\\\\sin 5x}{x}=5\\\\cdot\\\\frac{\\\\sin 5x}{5x}\\\\to 5$。\n\n**算例 2**：$\\\\lim_{x\\\\to 0}\\\\frac{1-\\\\cos x}{x^2}$。用 $1-\\\\cos x=2\\\\sin^2(x/2)$，得 $\\\\frac{2\\\\sin^2(x/2)}{x^2}=\\\\frac12\\\\left(\\\\frac{\\\\sin(x/2)}{x/2}\\\\right)^2\\\\to\\\\frac12$。\n\n**算例 3**：$\\\\lim_{x\\\\to\\\\infty}(1+\\\\frac{3}{x})^{2x}$。改写为 $\\\\left[(1+\\\\frac{3}{x})^{x/3}\\\\right]^6\\\\to e^6$。凑形口诀：底数写成 $1+$（无穷小），指数写成倒数关系，再配平剩余系数。",
+      "textbookRefs": [
+        "高等数学（同济第八版）上册 第一章 §4"
+      ],
+      "keyDefinitions": [],
+      "keyTheorems": [
+        {
+          "name": "第一个重要极限",
+          "statement": "$\\\\lim_{x\\\\to 0}\\\\frac{\\\\sin x}{x}=1$，等价地 $\\\\sin x\\\\sim x\\\\ (x\\\\to 0)$。"
+        },
+        {
+          "name": "第二个重要极限",
+          "statement": "$\\\\lim_{x\\\\to\\\\infty}(1+\\\\frac{1}{x})^x=e$，等价地 $\\\\lim_{t\\\\to 0}(1+t)^{1/t}=e$。"
+        }
+      ],
+      "proofIdeas": [
+        "三角极限：把分子分母凑成 $\\\\sin u/u$。",
+        "指数极限：把底数写成 $1+1/t$，指数写成 $t$ 的倍数。",
+        "变形时保持乘除结构，避免对加减直接替换。"
+      ],
+      "socraticQuestions": [
+        "为什么 $\\\\lim_{x\\\\to 0}\\\\frac{\\\\tan x}{x}$ 也等于 $1$？",
+        "$(1+2/x)^x$ 的极限为什么是 $e^2$ 而不是 $e$？",
+        "$1-\\\\cos x$ 为什么与 $x^2/2$ 等价，而不是与 $x$ 等价？"
+      ],
+      "commonMistakes": [
+        "三角极限中分子分母角度不配平。",
+        "第二个重要极限指数配平错误。",
+        "在加减结构里直接替换 $\\\\sin x\\\\sim x$ 导致错误。"
+      ],
+      "exampleIds": ["gd-fl-ex-016", "gd-fl-ex-017"],
+      "exerciseIds": ["gd-fl-ex-016", "gd-fl-ex-017", "gd-fl-ex-018"],
+      "diagramIds": ["gd-fl-sinx-over-x"],
+      "masteryCriteria": [
+        "能独立使用两个重要极限计算常见题。",
+        "会把一般极限凑成标准形。",
+        "知道小角度近似与第一个重要极限的关系。"
+      ]
+    },
+    {
+      "id": "gd-infinitesimal-comparison",
+      "title": "无穷小的比较与等价替换",
+      "learningGoals": [
+        "掌握无穷小阶、等价无穷小的定义。",
+        "熟记常用等价：$\\\\sin x\\\\sim x$、$\\\\tan x\\\\sim x$、$1-\\\\cos x\\\\sim x^2/2$、$\\\\ln(1+x)\\\\sim x$、$e^x-1\\\\sim x$。",
+        "会在乘除极限中安全使用等价替换，并知道加减中为何不能乱用。"
+      ],
+      "coreExplanation": "设 $\\\\alpha,\\\\beta\\\\to 0$，若 $\\\\lim\\\\frac{\\\\alpha}{\\\\beta}=1$，则称 $\\\\alpha$ 与 $\\\\beta$ **等价无穷小**，记 $\\\\alpha\\\\sim\\\\beta$。若 $\\\\lim\\\\frac{\\\\alpha}{\\\\beta}=0$，则 $\\\\alpha$ 是比 $\\\\beta$ 更高阶的无穷小。等价替换的原则：**只在乘除结构中使用**。例如 $\\\\lim_{x\\\\to 0}\\\\frac{\\\\sin 3x}{\\\\tan 2x}=\\\\frac{3x}{2x}=\\\\frac32$ 正确；但在 $\\\\lim_{x\\\\to 0}\\\\frac{\\\\tan x-\\\\sin x}{x^3}$ 中，不能写 $\\\\tan x-\\\\sin x\\\\approx x-x=0$，必须化为 $\\\\sin x(\\\\frac1{\\\\cos x}-1)$ 再处理。\n\n**算例 1**：$\\\\lim_{x\\\\to 0}\\\\frac{\\\\sin x}{x}=1$，故 $\\\\sin x\\\\sim x$。\n\n**算例 2**：$\\\\lim_{x\\\\to 0}\\\\frac{\\\\tan x-\\\\sin x}{x^3}=\\\\lim\\\\frac{\\\\sin x(1-\\\\cos x)}{x^3\\\\cos x}=\\\\lim\\\\frac{x\\\\cdot x^2/2}{x^3\\\\cdot 1}=\\\\frac12$。\n\n**算例 3**：$\\\\lim_{x\\\\to 0}\\\\frac{\\\\sqrt{1+x}-1-x/2}{x^2}$。展开到二阶：$\\\\sqrt{1+x}-1=\\\\frac x2-\\\\frac{x^2}{8}+o(x^2)$，分子为 $-\\\\frac{x^2}{8}+o(x^2)$，极限 $-1/8$。这说明加减结构里替换阶数不够会出错。",
+      "textbookRefs": [
+        "高等数学（同济第八版）上册 第一章 §4"
+      ],
+      "keyDefinitions": [
+        {
+          "name": "等价无穷小",
+          "statement": "若 $\\\\alpha\\\\to 0$、$\\\\beta\\\\to 0$ 且 $\\\\lim\\\\frac{\\\\alpha}{\\\\beta}=1$，则称 $\\\\alpha\\\\sim\\\\beta$。"
+        },
+        {
+          "name": "高阶无穷小",
+          "statement": "若 $\\\\lim\\\\frac{\\\\alpha}{\\\\beta}=0$，则称 $\\\\alpha$ 是比 $\\\\beta$ 更高阶的无穷小。"
+        }
+      ],
+      "keyTheorems": [],
+      "proofIdeas": [
+        "乘除极限：把因子替换成等价无穷小。",
+        "加减极限：先恒等变形，或展开到足够阶数。",
+        "拿不准时回到重要极限或泰勒一阶/二阶。"
+      ],
+      "socraticQuestions": [
+        "为什么 $x^2$ 是比 $x$ 更高阶的无穷小？",
+        "能否在 $\\\\lim\\\\frac{\\\\sin x-x}{x^3}$ 中直接写 $\\\\sin x\\\\sim x$ 得 $0$？",
+        "$1-\\\\cos x$ 与 $x^2/2$ 等价能用在哪些算式里？"
+      ],
+      "commonMistakes": [
+        "在加减结构里直接等价替换。",
+        "替换阶数不足导致分子被误判为 $0$。",
+        "把高阶无穷小与等价无穷小混为一谈。"
+      ],
+      "exampleIds": ["gd-fl-ex-019"],
+      "exerciseIds": ["gd-fl-ex-019", "gd-fl-ex-020", "gd-fl-ex-021"],
+      "diagramIds": ["gd-fl-infinitesimal-orders"],
+      "masteryCriteria": [
+        "能判断无穷小阶与等价关系。",
+        "能在乘除极限中正确使用等价替换。",
+        "能识别加减结构中的替换陷阱。"
+      ]
+    },
+    {
+      "id": "gd-continuity-discontinuity",
+      "title": "连续性与间断点",
+      "learningGoals": [
+        "掌握连续的定义：$\\\\lim_{x\\\\to x_0}f(x)=f(x_0)$。",
+        "会对初等函数、分段函数判断连续性与间断点类型。",
+        "了解闭区间上连续函数的零点定理与最值定理的应用场景。"
+      ],
+      "coreExplanation": "函数在 $x_0$ **连续**意味着三件事合一：$f(x_0)$ 有定义、$\\\\lim_{x\\\\to x_0}f(x)$ 存在、且二者相等。若不满足，则 $x_0$ 为**间断点**。常见分类：可去间断（极限存在但不等于函数值或无定义）、跳跃间断（左右极限存在但不等）、无穷间断（极限为无穷）。初等函数在其定义域内连续，因此实际计算常是「代入法」。\n\n**算例 1**：$f(x)=\\\\frac{x^2-1}{x-1}$ 在 $x=1$ 无定义，但化简后 $x+1$ 的极限为 $2$，属**可去间断**；补充 $f(1)=2$ 即可连续。\n\n**算例 2**：$g(x)=\\\\begin{cases}x+1,&x<0\\\\\\\\x^2,&0\\\\leq x\\\\leq 1\\\\\\\\2-x,&x>1\\\\end{cases}$。在 $x=0$：左极限 $1$、右极限 $0$，为**跳跃间断**；在 $x=1$：左极限 $1$、右极限 $1$、函数值 $1$，连续。\n\n**零点定理**：若 $f$ 在 $[a,b]$ 连续且 $f(a)f(b)<0$，则 $(a,b)$ 内至少有一个根。例如 $f(x)=x^3-4x+1$ 在 $[0,1]$ 上 $f(0)=1>0$、$f(1)=-2<0$，故必有实根。工程上用来判断方程有没有解，比硬算根更快捷。",
+      "textbookRefs": [
+        "高等数学（同济第八版）上册 第一章 §8–§10"
+      ],
+      "keyDefinitions": [
+        {
+          "name": "连续",
+          "statement": "若 $f(x_0)$ 有定义且 $\\\\lim_{x\\\\to x_0}f(x)=f(x_0)$，则称 $f$ 在 $x_0$ 连续。"
+        },
+        {
+          "name": "间断点",
+          "statement": "不满足连续定义的点称为间断点；若左右极限都存在但不等，为跳跃间断；若极限存在但不等于函数值，为可去间断。"
+        }
+      ],
+      "keyTheorems": [
+        {
+          "name": "零点定理",
+          "statement": "若 $f\\\\in C[a,b]$ 且 $f(a)f(b)<0$，则存在 $\\\\xi\\\\in(a,b)$ 使 $f(\\\\xi)=0$。",
+          "proofSketch": "用介值定理：连续函数不能从正值跳到负值而不经过 $0$。"
+        }
+      ],
+      "proofIdeas": [
+        "判连续：算极限，再与函数值比较。",
+        "判间断类型：先分左右极限，再看是否有限、是否相等。",
+        "证根存在：验证连续 + 端点异号。"
+      ],
+      "socraticQuestions": [
+        "可去间断与跳跃间断的本质区别是什么？",
+        "为什么初等函数在定义域内连续？",
+        "零点定理为什么不能用到不连续函数上？"
+      ],
+      "commonMistakes": [
+        "只检查极限存在就断言连续，忘记比较函数值。",
+        "把左右极限不等误判为可去间断。",
+        "零点定理未验证闭区间连续。"
+      ],
+      "exampleIds": ["gd-fl-ex-022"],
+      "exerciseIds": ["gd-fl-ex-022", "gd-fl-ex-023", "gd-fl-ex-024"],
+      "diagramIds": ["gd-fl-jump-vs-removable"],
+      "masteryCriteria": [
+        "能判断函数在指定点是否连续。",
+        "能对间断点正确分类。",
+        "会用零点定理证明方程有根。"
+      ]
+    }
+  ]
+}
diff --git a/content/courses/gaodeng-shuxue/chapters/gd-indefinite-integral.json b/content/courses/gaodeng-shuxue/chapters/gd-indefinite-integral.json
new file mode 100644
index 0000000..52fea30
--- /dev/null
+++ b/content/courses/gaodeng-shuxue/chapters/gd-indefinite-integral.json
@@ -0,0 +1 @@
+{"id":"ch-gd-indefinite-integral","courseId":"gaodeng-shuxue","volumeId":"gaodeng-shuxue-volume-1","number":4,"title":"不定积分","status":"planned","overview":"","knowledgePoints":[]}
diff --git a/content/courses/gaodeng-shuxue/chapters/gd-line-surface.json b/content/courses/gaodeng-shuxue/chapters/gd-line-surface.json
new file mode 100644
index 0000000..47c1dff
--- /dev/null
+++ b/content/courses/gaodeng-shuxue/chapters/gd-line-surface.json
@@ -0,0 +1 @@
+{"id":"ch-gd-line-surface","courseId":"gaodeng-shuxue","volumeId":"gaodeng-shuxue-volume-2","number":10,"title":"曲线积分与曲面积分","status":"planned","overview":"","knowledgePoints":[]}
diff --git a/content/courses/gaodeng-shuxue/chapters/gd-mean-value.json b/content/courses/gaodeng-shuxue/chapters/gd-mean-value.json
new file mode 100644
index 0000000..277fc5f
--- /dev/null
+++ b/content/courses/gaodeng-shuxue/chapters/gd-mean-value.json
@@ -0,0 +1 @@
+{"id":"ch-gd-mean-value","courseId":"gaodeng-shuxue","volumeId":"gaodeng-shuxue-volume-1","number":3,"title":"微分中值定理与导数应用","status":"planned","overview":"","knowledgePoints":[]}
diff --git a/content/courses/gaodeng-shuxue/chapters/gd-multiple-integrals.json b/content/courses/gaodeng-shuxue/chapters/gd-multiple-integrals.json
new file mode 100644
index 0000000..bbcd13e
--- /dev/null
+++ b/content/courses/gaodeng-shuxue/chapters/gd-multiple-integrals.json
@@ -0,0 +1 @@
+{"id":"ch-gd-multiple-integrals","courseId":"gaodeng-shuxue","volumeId":"gaodeng-shuxue-volume-2","number":9,"title":"重积分","status":"planned","overview":"","knowledgePoints":[]}
diff --git a/content/courses/gaodeng-shuxue/chapters/gd-multivariable-diff.json b/content/courses/gaodeng-shuxue/chapters/gd-multivariable-diff.json
new file mode 100644
index 0000000..d22800d
--- /dev/null
+++ b/content/courses/gaodeng-shuxue/chapters/gd-multivariable-diff.json
@@ -0,0 +1 @@
+{"id":"ch-gd-multivariable-diff","courseId":"gaodeng-shuxue","volumeId":"gaodeng-shuxue-volume-2","number":8,"title":"多元函数微分法及其应用","status":"planned","overview":"","knowledgePoints":[]}
diff --git a/content/courses/gaodeng-shuxue/chapters/gd-ode.json b/content/courses/gaodeng-shuxue/chapters/gd-ode.json
new file mode 100644
index 0000000..31c9791
--- /dev/null
+++ b/content/courses/gaodeng-shuxue/chapters/gd-ode.json
@@ -0,0 +1 @@
+{"id":"ch-gd-ode","courseId":"gaodeng-shuxue","volumeId":"gaodeng-shuxue-volume-1","number":6,"title":"微分方程","status":"planned","overview":"","knowledgePoints":[]}
diff --git a/content/courses/gaodeng-shuxue/chapters/gd-series.json b/content/courses/gaodeng-shuxue/chapters/gd-series.json
new file mode 100644
index 0000000..d677301
--- /dev/null
+++ b/content/courses/gaodeng-shuxue/chapters/gd-series.json
@@ -0,0 +1 @@
+{"id":"ch-gd-series","courseId":"gaodeng-shuxue","volumeId":"gaodeng-shuxue-volume-2","number":11,"title":"无穷级数","status":"planned","overview":"","knowledgePoints":[]}
diff --git a/content/courses/gaodeng-shuxue/chapters/gd-vectors.json b/content/courses/gaodeng-shuxue/chapters/gd-vectors.json
new file mode 100644
index 0000000..0fceb35
--- /dev/null
+++ b/content/courses/gaodeng-shuxue/chapters/gd-vectors.json
@@ -0,0 +1 @@
+{"id":"ch-gd-vectors","courseId":"gaodeng-shuxue","volumeId":"gaodeng-shuxue-volume-2","number":7,"title":"向量代数与空间解析几何","status":"planned","overview":"","knowledgePoints":[]}
diff --git a/content/courses/gaodeng-shuxue/course.json b/content/courses/gaodeng-shuxue/course.json
new file mode 100644
index 0000000..d2e9553
--- /dev/null
+++ b/content/courses/gaodeng-shuxue/course.json
@@ -0,0 +1,14 @@
+{
+  "id": "gaodeng-shuxue",
+  "title": "高等数学",
+  "subtitle": "按同济第八版教材顺序学习概念、方法与习题",
+  "audience": "大学工科高等数学学习者",
+  "defaultVolumeId": "gaodeng-shuxue-volume-1",
+  "volumes": ["gaodeng-shuxue-volume-1", "gaodeng-shuxue-volume-2"],
+  "textbook": {
+    "title": "高等数学（第八版）上下册",
+    "note": "本课程依据同济版教材结构整理，原始 PDF 不进入仓库，前台仅展示整理后的课程结构、讲义与训练。"
+  },
+  "schemaVersion": 1,
+  "status": "draft"
+}
diff --git a/content/courses/gaodeng-shuxue/diagrams/.gitkeep b/content/courses/gaodeng-shuxue/diagrams/.gitkeep
new file mode 100644
index 0000000..e69de29
diff --git a/content/courses/gaodeng-shuxue/diagrams/gd-definite-integral.json b/content/courses/gaodeng-shuxue/diagrams/gd-definite-integral.json
new file mode 100644
index 0000000..0382be7
--- /dev/null
+++ b/content/courses/gaodeng-shuxue/diagrams/gd-definite-integral.json
@@ -0,0 +1 @@
+{"courseId":"gaodeng-shuxue","volumeId":"gaodeng-shuxue-volume-1","chapterId":"ch-gd-definite-integral","schemaVersion":1,"diagrams":[]}
diff --git a/content/courses/gaodeng-shuxue/diagrams/gd-derivative.json b/content/courses/gaodeng-shuxue/diagrams/gd-derivative.json
new file mode 100644
index 0000000..e6638e8
--- /dev/null
+++ b/content/courses/gaodeng-shuxue/diagrams/gd-derivative.json
@@ -0,0 +1 @@
+{"courseId":"gaodeng-shuxue","volumeId":"gaodeng-shuxue-volume-1","chapterId":"ch-gd-derivative","schemaVersion":1,"diagrams":[]}
diff --git a/content/courses/gaodeng-shuxue/diagrams/gd-function-limit.json b/content/courses/gaodeng-shuxue/diagrams/gd-function-limit.json
new file mode 100644
index 0000000..8f3bcf3
--- /dev/null
+++ b/content/courses/gaodeng-shuxue/diagrams/gd-function-limit.json
@@ -0,0 +1,113 @@
+{
+  "courseId": "gaodeng-shuxue",
+  "volumeId": "gaodeng-shuxue-volume-1",
+  "chapterId": "ch-gd-function-limit",
+  "schemaVersion": 1,
+  "renderingPolicy": {
+    "preferredRenderer": "programmatic-svg",
+    "reason": "工科高数图示强调可计算、可复核的几何直观。",
+    "formulaRenderer": "KaTeX"
+  },
+  "diagrams": [
+    {
+      "id": "gd-fl-elementary-functions",
+      "title": "基本初等函数图像对照",
+      "type": "multi-curve-plot",
+      "knowledgePointIds": ["gd-function-elementary"],
+      "description": "在同一坐标系中对比幂函数、指数函数与对数函数在 $x>0$ 上的增长趋势。",
+      "parameters": {
+        "xRange": [0.1, 3],
+        "curves": [
+          { "expr": "x^2", "label": "y=x^2", "style": "solid" },
+          { "expr": "2^x", "label": "y=2^x", "style": "dashed" },
+          { "expr": "log(x)", "label": "y=ln x", "style": "dotted" }
+        ]
+      },
+      "teacherNotes": [
+        "强调定义域：$y=\\\\ln x$ 只在 $x>0$ 有意义。",
+        "工科应用中常先判断函数类型再选化简或近似方法。"
+      ],
+      "studentPrompt": "在 $x=2$ 附近，哪条曲线增长最快？为什么工程里指数模型常用来描述快速增长过程？"
+    },
+    {
+      "id": "gd-fl-limit-neighborhood",
+      "title": "数轴上的极限邻域",
+      "type": "number-line",
+      "knowledgePointIds": ["gd-function-limit-calc", "gd-sequence-limit-calc"],
+      "description": "用数轴区间展示「$x$ 趋近 $a$」时自变量落在 $(a-\\\\delta,a+\\\\delta)$ 去心邻域内的含义。",
+      "parameters": {
+        "axisMin": -1,
+        "axisMax": 5,
+        "points": [{ "x": 2, "label": "a=2" }],
+        "intervals": [
+          { "from": 1.3, "to": 2.7, "label": "\\\\delta 邻域", "open": true }
+        ]
+      },
+      "teacherNotes": [
+        "工科教学可弱化 $\\\\varepsilon$-$\\\\delta$ 证明，但邻域语言有助于理解单侧极限。",
+        "去心邻域意味着极限关心趋近过程，不必等于端点取值。"
+      ],
+      "studentPrompt": "若极限为 $2$，图中哪一段表示「$x$ 足够靠近 $2$ 但不必等于 $2$」？"
+    },
+    {
+      "id": "gd-fl-sinx-over-x",
+      "title": "重要极限 $\\\\sin x/x$ 在 $x\\\\to 0$ 的图像",
+      "type": "function-plot",
+      "knowledgePointIds": ["gd-important-limits"],
+      "description": "观察 $y=\\\\sin x/x$ 在 $x\\\\to 0$ 附近如何趋近 $1$，并对比 $y=\\\\cos x$ 辅助理解。",
+      "parameters": {
+        "xRange": [-3.5, 3.5],
+        "expr": "sin(x)/x",
+        "marks": [{ "x": 0, "label": "极限=1" }],
+        "asymptotes": []
+      },
+      "teacherNotes": [
+        "强调 $x=0$ 处无定义，但极限存在且为 $1$。",
+        "此极限是三角函数化简、振动系统小角度近似的核心工具。"
+      ],
+      "studentPrompt": "当 $|x|$ 越来越小时，$\\\\sin x/x$ 的函数值靠近哪个数？这与小角度近似 $\\\\sin x\\\\approx x$ 有何关系？"
+    },
+    {
+      "id": "gd-fl-jump-vs-removable",
+      "title": "跳跃间断与可去间断对比",
+      "type": "multi-curve-plot",
+      "knowledgePointIds": ["gd-continuity-discontinuity"],
+      "description": "对比分段函数在分界点处的左右极限关系，区分跳跃间断与可去间断。",
+      "parameters": {
+        "xRange": [-2, 2],
+        "curves": [
+          { "expr": "x+1", "label": "左支 x<0", "style": "solid" },
+          { "expr": "x+2", "label": "右支 x>0", "style": "dashed" },
+          { "expr": "(x^2-1)/(x-1)", "label": "可去型 x≠1", "style": "dotted" }
+        ]
+      },
+      "teacherNotes": [
+        "跳跃间断：左右极限都存在但不相等。",
+        "可去间断：极限存在但不等于函数值，或函数在该点无定义。"
+      ],
+      "studentPrompt": "哪条曲线在「看起来断掉」的点附近，左右极限其实相等？补一个点后能否连续？"
+    },
+    {
+      "id": "gd-fl-infinitesimal-orders",
+      "title": "无穷小阶对照表",
+      "type": "table",
+      "knowledgePointIds": ["gd-infinitesimal-comparison"],
+      "description": "当 $x\\\\to 0$ 时，常见无穷小量与 $x$、$x^2$、$\\\\sin x$ 的阶比较。",
+      "parameters": {
+        "columns": ["无穷小", "与 x 的阶关系", "x→0 时比值极限"],
+        "rows": [
+          ["x", "同阶", "1"],
+          ["x^2", "高阶", "0"],
+          ["sin x", "等价", "1"],
+          ["1-cos x", "高阶", "0"],
+          ["tan x - x", "高阶", "0"]
+        ]
+      },
+      "teacherNotes": [
+        "等价无穷小替换只在乘除结构中使用，加减一般不可直接替换。",
+        "记忆口诀：$\\\\sin x\\\\sim x$，$\\\\tan x\\\\sim x$，$1-\\\\cos x\\\\sim x^2/2$。"
+      ],
+      "studentPrompt": "为什么 $\\\\sin x$ 与 $x$ 是等价无穷小，而 $x^2$ 是比 $x$ 更高阶的无穷小？"
+    }
+  ]
+}
diff --git a/content/courses/gaodeng-shuxue/diagrams/gd-indefinite-integral.json b/content/courses/gaodeng-shuxue/diagrams/gd-indefinite-integral.json
new file mode 100644
index 0000000..ecd6056
--- /dev/null
+++ b/content/courses/gaodeng-shuxue/diagrams/gd-indefinite-integral.json
@@ -0,0 +1 @@
+{"courseId":"gaodeng-shuxue","volumeId":"gaodeng-shuxue-volume-1","chapterId":"ch-gd-indefinite-integral","schemaVersion":1,"diagrams":[]}
diff --git a/content/courses/gaodeng-shuxue/diagrams/gd-line-surface.json b/content/courses/gaodeng-shuxue/diagrams/gd-line-surface.json
new file mode 100644
index 0000000..fc2f0b0
--- /dev/null
+++ b/content/courses/gaodeng-shuxue/diagrams/gd-line-surface.json
@@ -0,0 +1 @@
+{"courseId":"gaodeng-shuxue","volumeId":"gaodeng-shuxue-volume-2","chapterId":"ch-gd-line-surface","schemaVersion":1,"diagrams":[]}
diff --git a/content/courses/gaodeng-shuxue/diagrams/gd-mean-value.json b/content/courses/gaodeng-shuxue/diagrams/gd-mean-value.json
new file mode 100644
index 0000000..0680f38
--- /dev/null
+++ b/content/courses/gaodeng-shuxue/diagrams/gd-mean-value.json
@@ -0,0 +1 @@
+{"courseId":"gaodeng-shuxue","volumeId":"gaodeng-shuxue-volume-1","chapterId":"ch-gd-mean-value","schemaVersion":1,"diagrams":[]}
diff --git a/content/courses/gaodeng-shuxue/diagrams/gd-multiple-integrals.json b/content/courses/gaodeng-shuxue/diagrams/gd-multiple-integrals.json
new file mode 100644
index 0000000..9cc8831
--- /dev/null
+++ b/content/courses/gaodeng-shuxue/diagrams/gd-multiple-integrals.json
@@ -0,0 +1 @@
+{"courseId":"gaodeng-shuxue","volumeId":"gaodeng-shuxue-volume-2","chapterId":"ch-gd-multiple-integrals","schemaVersion":1,"diagrams":[]}
diff --git a/content/courses/gaodeng-shuxue/diagrams/gd-multivariable-diff.json b/content/courses/gaodeng-shuxue/diagrams/gd-multivariable-diff.json
new file mode 100644
index 0000000..6360c43
--- /dev/null
+++ b/content/courses/gaodeng-shuxue/diagrams/gd-multivariable-diff.json
@@ -0,0 +1 @@
+{"courseId":"gaodeng-shuxue","volumeId":"gaodeng-shuxue-volume-2","chapterId":"ch-gd-multivariable-diff","schemaVersion":1,"diagrams":[]}
diff --git a/content/courses/gaodeng-shuxue/diagrams/gd-ode.json b/content/courses/gaodeng-shuxue/diagrams/gd-ode.json
new file mode 100644
index 0000000..984b4f1
--- /dev/null
+++ b/content/courses/gaodeng-shuxue/diagrams/gd-ode.json
@@ -0,0 +1 @@
+{"courseId":"gaodeng-shuxue","volumeId":"gaodeng-shuxue-volume-1","chapterId":"ch-gd-ode","schemaVersion":1,"diagrams":[]}
diff --git a/content/courses/gaodeng-shuxue/diagrams/gd-series.json b/content/courses/gaodeng-shuxue/diagrams/gd-series.json
new file mode 100644
index 0000000..5d3be67
--- /dev/null
+++ b/content/courses/gaodeng-shuxue/diagrams/gd-series.json
@@ -0,0 +1 @@
+{"courseId":"gaodeng-shuxue","volumeId":"gaodeng-shuxue-volume-2","chapterId":"ch-gd-series","schemaVersion":1,"diagrams":[]}
diff --git a/content/courses/gaodeng-shuxue/diagrams/gd-vectors.json b/content/courses/gaodeng-shuxue/diagrams/gd-vectors.json
new file mode 100644
index 0000000..9034232
--- /dev/null
+++ b/content/courses/gaodeng-shuxue/diagrams/gd-vectors.json
@@ -0,0 +1 @@
+{"courseId":"gaodeng-shuxue","volumeId":"gaodeng-shuxue-volume-2","chapterId":"ch-gd-vectors","schemaVersion":1,"diagrams":[]}
diff --git a/content/courses/gaodeng-shuxue/exercises/.gitkeep b/content/courses/gaodeng-shuxue/exercises/.gitkeep
new file mode 100644
index 0000000..e69de29
diff --git a/content/courses/gaodeng-shuxue/exercises/gd-definite-integral.json b/content/courses/gaodeng-shuxue/exercises/gd-definite-integral.json
new file mode 100644
index 0000000..dcc427f
--- /dev/null
+++ b/content/courses/gaodeng-shuxue/exercises/gd-definite-integral.json
@@ -0,0 +1 @@
+{"chapterId":"ch-gd-definite-integral","courseId":"gaodeng-shuxue","volumeId":"gaodeng-shuxue-volume-1","exercises":[]}
diff --git a/content/courses/gaodeng-shuxue/exercises/gd-derivative.json b/content/courses/gaodeng-shuxue/exercises/gd-derivative.json
new file mode 100644
index 0000000..cc3749c
--- /dev/null
+++ b/content/courses/gaodeng-shuxue/exercises/gd-derivative.json
@@ -0,0 +1 @@
+{"chapterId":"ch-gd-derivative","courseId":"gaodeng-shuxue","volumeId":"gaodeng-shuxue-volume-1","exercises":[]}
diff --git a/content/courses/gaodeng-shuxue/exercises/gd-function-limit.json b/content/courses/gaodeng-shuxue/exercises/gd-function-limit.json
new file mode 100644
index 0000000..704666b
--- /dev/null
+++ b/content/courses/gaodeng-shuxue/exercises/gd-function-limit.json
@@ -0,0 +1,567 @@
+{
+  "chapterId": "ch-gd-function-limit",
+  "courseId": "gaodeng-shuxue",
+  "volumeId": "gaodeng-shuxue-volume-1",
+  "sourceTypeLegend": {
+    "textbook-example": "教材例题",
+    "textbook-exercise": "教材课后习题",
+    "adapted": "由教材题改编",
+    "bridging": "自编过渡题，仅用于衔接，不作为正式题"
+  },
+  "intakeNote": "sourceRef 为「待核对题源」表示题面已录入但题号尚未与教材核对。",
+  "exercises": [
+    {
+      "id": "gd-fl-ex-001",
+      "sourceType": "adapted",
+      "sourceRef": "待核对题源（第一章 函数）",
+      "knowledgePointIds": ["gd-function-elementary"],
+      "difficulty": "basic",
+      "type": "computation",
+      "recommendedTiming": "after-lecture",
+      "prompt": "求函数 $f(x)=\\\\sqrt{4-x^2}+\\\\ln(x+1)$ 的定义域。",
+      "gradingRubric": [
+        "由 $4-x^2\\\\geq 0$ 得 $-2\\\\leq x\\\\leq 2$",
+        "由 $x+1>0$ 得 $x>-1$",
+        "取交集得定义域 $(-1,2]$"
+      ],
+      "hints": [
+        "根式要求被开方数非负。",
+        "对数要求真数大于零。",
+        "最后写区间交集。"
+      ],
+      "commonMistakes": [
+        "只写根式条件，忽略对数条件",
+        "把开闭区间端点写错"
+      ]
+    },
+    {
+      "id": "gd-fl-ex-002",
+      "sourceType": "adapted",
+      "sourceRef": "待核对题源（第一章 函数）",
+      "knowledgePointIds": ["gd-function-elementary"],
+      "difficulty": "medium",
+      "type": "computation",
+      "recommendedTiming": "after-lecture",
+      "prompt": "已知 $f(x)=\\\\begin{cases}x^2,&x\\\\leq 0\\\\\\\\2^x,&x>0\\\\end{cases}$，求 $f(-1)$、$f(0)$、$f(1)$。",
+      "gradingRubric": [
+        "$f(-1)=(-1)^2=1$",
+        "$f(0)=0^2=0$",
+        "$f(1)=2^1=2$"
+      ],
+      "hints": [
+        "先看自变量落在哪个区间。",
+        "分界点 $x=0$ 属于 $x\\\\leq 0$ 分支。"
+      ],
+      "commonMistakes": [
+        "在 $x=0$ 误用指数分支",
+        "分段函数未先分类讨论"
+      ]
+    },
+    {
+      "id": "gd-fl-ex-003",
+      "sourceType": "bridging",
+      "sourceRef": "待核对题源（第一章 函数）",
+      "knowledgePointIds": ["gd-function-elementary"],
+      "difficulty": "medium",
+      "type": "analysis",
+      "recommendedTiming": "after-lecture",
+      "prompt": "说明函数 $y=2^{x-1}+1$ 可由 $y=2^x$ 经过怎样的平移与伸缩得到，并写出其水平渐近线。",
+      "gradingRubric": [
+        "识别为指数函数平移：向右平移 1 个单位，向上平移 1 个单位",
+        "写出 $y=2^{x-1}+1$",
+        "当 $x\\\\to-\\\\infty$ 时 $y\\\\to 1$，水平渐近线为 $y=1$"
+      ],
+      "hints": [
+        "把指数部分写成 $2^{x-1}$。",
+        "平移规律：$x\\\\to x-1$ 右移，$+1$ 上移。"
+      ],
+      "commonMistakes": [
+        "把平移方向搞反",
+        "忽略 $+1$ 导致的渐近线上移"
+      ]
+    },
+    {
+      "id": "gd-fl-ex-004",
+      "sourceType": "adapted",
+      "sourceRef": "待核对题源（第一章 数列极限）",
+      "knowledgePointIds": ["gd-sequence-limit-calc"],
+      "difficulty": "basic",
+      "type": "computation",
+      "recommendedTiming": "after-lecture",
+      "prompt": "求极限 $\\\\lim_{n\\\\to\\\\infty}\\\\frac{3n^2-n+1}{2n^2+5}$。",
+      "gradingRubric": [
+        "分子分母同除以 $n^2$",
+        "利用 $\\\\lim 1/n=0$、$\\\\lim 1/n^2=0$",
+        "得极限 $3/2$"
+      ],
+      "hints": [
+        "观察分子分母最高次幂。",
+        "同除以最高次项系数。"
+      ],
+      "commonMistakes": [
+        "直接代入 $n=\\\\infty$",
+        "只除 $n$ 而不是 $n^2$"
+      ]
+    },
+    {
+      "id": "gd-fl-ex-005",
+      "sourceType": "adapted",
+      "sourceRef": "待核对题源（第一章 数列极限）",
+      "knowledgePointIds": ["gd-sequence-limit-calc"],
+      "difficulty": "medium",
+      "type": "computation",
+      "recommendedTiming": "after-lecture",
+      "prompt": "求极限 $\\\\lim_{n\\\\to\\\\infty}(\\\\sqrt{n^2+n}-n)$。",
+      "gradingRubric": [
+        "分子有理化：$\\\\frac{n}{\\\\sqrt{n^2+n}+n}$",
+        "分母同除以 $n$",
+        "得极限 $1/2$"
+      ],
+      "hints": [
+        "根式差型常用有理化。",
+        "注意 $\\\\sqrt{n^2+n}=n\\\\sqrt{1+1/n}$。"
+      ],
+      "commonMistakes": [
+        "有理化后忘记化简分母",
+        "把 $\\\\sqrt{n^2+n}$ 误写成 $n+\\\\sqrt{n}$"
+      ]
+    },
+    {
+      "id": "gd-fl-ex-006",
+      "sourceType": "adapted",
+      "sourceRef": "待核对题源（第一章 数列极限）",
+      "knowledgePointIds": ["gd-sequence-limit-calc"],
+      "difficulty": "advanced",
+      "type": "computation",
+      "recommendedTiming": "after-lecture",
+      "prompt": "求极限 $\\\\lim_{n\\\\to\\\\infty}\\\\left(1+\\\\frac{2}{n}\\\\right)^{3n}$。",
+      "gradingRubric": [
+        "改写为 $\\\\left[\\\\left(1+\\\\frac{2}{n}\\\\right)^n\\\\right]^6$ 或令 $m=n/2$",
+        "利用 $\\\\lim(1+1/m)^m=e$",
+        "得 $e^6$"
+      ],
+      "hints": [
+        "凑重要极限 $\\\\lim(1+1/n)^n=e$ 的结构。",
+        "注意指数与底数中系数要匹配。"
+      ],
+      "commonMistakes": [
+        "直接把极限写成 $1^\\\\infty$ 而乱写结果",
+        "指数换算错误"
+      ]
+    },
+    {
+      "id": "gd-fl-ex-007",
+      "sourceType": "adapted",
+      "sourceRef": "待核对题源（第一章 函数极限）",
+      "knowledgePointIds": ["gd-function-limit-calc"],
+      "difficulty": "basic",
+      "type": "computation",
+      "recommendedTiming": "after-lecture",
+      "prompt": "求极限 $\\\\lim_{x\\\\to 2}\\\\frac{x^2-4}{x-2}$。",
+      "gradingRubric": [
+        "分子因式分解 $(x-2)(x+2)$",
+        "约去公因子 $x-2$（$x\\\\ne 2$）",
+        "代入得 $4$"
+      ],
+      "hints": [
+        "先判断是否为 $0/0$ 型。",
+        "因式分解后约分再代入。"
+      ],
+      "commonMistakes": [
+        "直接代入 $x=2$ 得 $0/0$ 后放弃",
+        "约分后忘记极限与函数值可不同"
+      ]
+    },
+    {
+      "id": "gd-fl-ex-008",
+      "sourceType": "adapted",
+      "sourceRef": "待核对题源（第一章 函数极限）",
+      "knowledgePointIds": ["gd-function-limit-calc"],
+      "difficulty": "medium",
+      "type": "computation",
+      "recommendedTiming": "after-lecture",
+      "prompt": "求极限 $\\\\lim_{x\\\\to 0}\\\\frac{\\\\sqrt{1+x}-\\\\sqrt{1-x}}{x}$。",
+      "gradingRubric": [
+        "分子有理化",
+        "化简得 $\\\\frac{2}{\\\\sqrt{1+x}+\\\\sqrt{1-x}}$",
+        "代入 $x=0$ 得 $1$"
+      ],
+      "hints": [
+        "根式差用共轭有理化。",
+        "化简后再令 $x\\\\to 0$。"
+      ],
+      "commonMistakes": [
+        "有理化时符号错误",
+        "未化简就代入"
+      ]
+    },
+    {
+      "id": "gd-fl-ex-009",
+      "sourceType": "adapted",
+      "sourceRef": "待核对题源（第一章 单侧极限）",
+      "knowledgePointIds": ["gd-function-limit-calc"],
+      "difficulty": "medium",
+      "type": "analysis",
+      "recommendedTiming": "after-lecture",
+      "prompt": "讨论 $f(x)=\\\\frac{|x|}{x}$（$x\\\\ne 0$）在 $x=0$ 处的左、右极限，并判断双侧极限是否存在。",
+      "gradingRubric": [
+        "$x>0$ 时 $f(x)=1$，故 $f(0^+)=1$",
+        "$x<0$ 时 $f(x)=-1$，故 $f(0^-)=-1$",
+        "左右极限不等，双侧极限不存在"
+      ],
+      "hints": [
+        "按绝对值定义分 $x>0$ 与 $x<0$。",
+        "比较 $f(0^+)$ 与 $f(0^-)$。"
+      ],
+      "commonMistakes": [
+        "只算一侧就下结论",
+        "把 $f(0)$ 的值当作极限"
+      ]
+    },
+    {
+      "id": "gd-fl-ex-010",
+      "sourceType": "adapted",
+      "sourceRef": "待核对题源（第一章 无穷小）",
+      "knowledgePointIds": ["gd-infinitesimal-infinite"],
+      "difficulty": "basic",
+      "type": "computation",
+      "recommendedTiming": "after-lecture",
+      "prompt": "当 $x\\\\to 0$ 时，判断 $3x^2$、$\\\\sin 5x$、$\\\\frac{1}{x}$ 中哪些是无穷小，哪些是无穷大。",
+      "gradingRubric": [
+        "$3x^2\\\\to 0$，是无穷小",
+        "$\\\\sin 5x\\\\to 0$，是无穷小",
+        "$1/x\\\\to \\\\infty$，是无穷大"
+      ],
+      "hints": [
+        "无穷小：极限为 $0$。",
+        "无穷大：绝对值无限增大。"
+      ],
+      "commonMistakes": [
+        "把趋于常数也当成无穷小",
+        "混淆无穷大与无界"
+      ]
+    },
+    {
+      "id": "gd-fl-ex-011",
+      "sourceType": "adapted",
+      "sourceRef": "待核对题源（第一章 无穷小）",
+      "knowledgePointIds": ["gd-infinitesimal-infinite"],
+      "difficulty": "medium",
+      "type": "computation",
+      "recommendedTiming": "after-lecture",
+      "prompt": "求极限 $\\\\lim_{x\\\\to \\\\infty}\\\\frac{2x^3-x+1}{5x^3+4x}$。",
+      "gradingRubric": [
+        "分子分母同除以 $x^3$",
+        "低次项趋于 $0$",
+        "得极限 $2/5$"
+      ],
+      "hints": [
+        "这是 $x\\\\to\\\\infty$ 时的有理函数极限。",
+        "看最高次幂系数之比。"
+      ],
+      "commonMistakes": [
+        "只除 $x$ 而不是 $x^3$",
+        "把 $\\\\infty/\\\\infty$ 直接当作 $1$"
+      ]
+    },
+    {
+      "id": "gd-fl-ex-012",
+      "sourceType": "bridging",
+      "sourceRef": "待核对题源（第一章 无穷小）",
+      "knowledgePointIds": ["gd-infinitesimal-infinite"],
+      "difficulty": "advanced",
+      "type": "analysis",
+      "recommendedTiming": "after-lecture",
+      "prompt": "说明为何 $\\\\lim_{x\\\\to 0^+}\\\\ln x=-\\\\infty$，并写出 $y=\\\\ln x$ 在 $x\\\\to 0^+$ 时的竖直渐近线。",
+      "gradingRubric": [
+        "说明 $x\\\\to 0^+$ 时 $\\\\ln x$ 单调递减且无下界",
+        "因此极限为 $-\\\\infty$",
+        "竖直渐近线为 $x=0$"
+      ],
+      "hints": [
+        "对数函数只在 $x>0$ 有定义。",
+        "观察 $x$ 越靠近 $0$，$\\\\ln x$ 越负。"
+      ],
+      "commonMistakes": [
+        "写成 $x\\\\to 0$ 双侧讨论",
+        "把 $y=0$ 误作渐近线"
+      ]
+    },
+    {
+      "id": "gd-fl-ex-013",
+      "sourceType": "adapted",
+      "sourceRef": "待核对题源（第一章 极限运算法则）",
+      "knowledgePointIds": ["gd-limit-arithmetic"],
+      "difficulty": "basic",
+      "type": "computation",
+      "recommendedTiming": "after-lecture",
+      "prompt": "已知 $\\\\lim_{x\\\\to 1}f(x)=2$，$\\\\lim_{x\\\\to 1}g(x)=-1$，求 $\\\\lim_{x\\\\to 1}[3f(x)-2g(x)]$。",
+      "gradingRubric": [
+        "使用和差法则",
+        "计算 $3\\\\cdot 2-2\\\\cdot(-1)$",
+        "得 $8$"
+      ],
+      "hints": [
+        "极限存在时，线性组合可直接分配。",
+        "先代入已知极限值。"
+      ],
+      "commonMistakes": [
+        "把极限符号拆开时漏掉系数",
+        "符号计算错误"
+      ]
+    },
+    {
+      "id": "gd-fl-ex-014",
+      "sourceType": "adapted",
+      "sourceRef": "待核对题源（第一章 极限运算法则）",
+      "knowledgePointIds": ["gd-limit-arithmetic"],
+      "difficulty": "medium",
+      "type": "computation",
+      "recommendedTiming": "after-lecture",
+      "prompt": "求极限 $\\\\lim_{x\\\\to 2}\\\\frac{x^2-3x+2}{x^2-4}$。",
+      "gradingRubric": [
+        "分子分母因式分解",
+        "约去公因子 $x-2$",
+        "代入 $x=2$ 得 $1/4$"
+      ],
+      "hints": [
+        "先识别 $0/0$ 型。",
+        "分子 $x^2-3x+2=(x-1)(x-2)$。"
+      ],
+      "commonMistakes": [
+        "分母为零后直接写极限不存在",
+        "约分前未先因式分解"
+      ]
+    },
+    {
+      "id": "gd-fl-ex-015",
+      "sourceType": "adapted",
+      "sourceRef": "待核对题源（第一章 极限运算法则）",
+      "knowledgePointIds": ["gd-limit-arithmetic"],
+      "difficulty": "advanced",
+      "type": "computation",
+      "recommendedTiming": "after-lecture",
+      "prompt": "求极限 $\\\\lim_{x\\\\to 0}\\\\frac{\\\\sin 3x}{\\\\tan 2x}$。",
+      "gradingRubric": [
+        "写成 $\\\\frac{\\\\sin 3x}{3x}\\\\cdot\\\\frac{2x}{\\\\tan 2x}\\\\cdot\\\\frac{3}{2}$",
+        "利用 $\\\\sin u/u\\\\to 1$、$\\\\tan u/u\\\\to 1$",
+        "得 $3/2$"
+      ],
+      "hints": [
+        "凑 $\\\\sin u/u$ 与 $\\\\tan u/u$ 的标准形。",
+        "保持乘除结构以便用重要极限。"
+      ],
+      "commonMistakes": [
+        "在加减结构里直接替换等价无穷小",
+        "系数配比错误"
+      ]
+    },
+    {
+      "id": "gd-fl-ex-016",
+      "sourceType": "adapted",
+      "sourceRef": "待核对题源（第一章 两个重要极限）",
+      "knowledgePointIds": ["gd-important-limits"],
+      "difficulty": "basic",
+      "type": "computation",
+      "recommendedTiming": "after-lecture",
+      "prompt": "求极限 $\\\\lim_{x\\\\to 0}\\\\frac{\\\\sin 5x}{x}$。",
+      "gradingRubric": [
+        "改写为 $5\\\\cdot\\\\frac{\\\\sin 5x}{5x}$",
+        "利用 $\\\\lim_{u\\\\to 0}\\\\sin u/u=1$",
+        "得 $5$"
+      ],
+      "hints": [
+        "分子分母同乘 $5$。",
+        "识别第一个重要极限。"
+      ],
+      "commonMistakes": [
+        "直接得 $\\\\sin 5x\\\\sim 5x$ 但漏乘系数",
+        "把 $x$ 与 $5x$ 混淆"
+      ]
+    },
+    {
+      "id": "gd-fl-ex-017",
+      "sourceType": "adapted",
+      "sourceRef": "待核对题源（第一章 两个重要极限）",
+      "knowledgePointIds": ["gd-important-limits"],
+      "difficulty": "medium",
+      "type": "computation",
+      "recommendedTiming": "after-lecture",
+      "prompt": "求极限 $\\\\lim_{x\\\\to \\\\infty}\\\\left(1+\\\\frac{3}{x}\\\\right)^{2x}$。",
+      "gradingRubric": [
+        "改写为 $\\\\left[\\\\left(1+\\\\frac{3}{x}\\\\right)^{x/3}\\\\right]^6$",
+        "利用第二个重要极限",
+        "得 $e^6$"
+      ],
+      "hints": [
+        "令底数凑成 $1+1/t$ 形式。",
+        "指数与底数要同步变形。"
+      ],
+      "commonMistakes": [
+        "把结果写成 $e^2$ 或 $e^3$",
+        "未把指数完全配平"
+      ]
+    },
+    {
+      "id": "gd-fl-ex-018",
+      "sourceType": "adapted",
+      "sourceRef": "待核对题源（第一章 两个重要极限）",
+      "knowledgePointIds": ["gd-important-limits"],
+      "difficulty": "advanced",
+      "type": "computation",
+      "recommendedTiming": "after-lecture",
+      "prompt": "求极限 $\\\\lim_{x\\\\to 0}\\\\frac{1-\\\\cos x}{x^2}$。",
+      "gradingRubric": [
+        "利用 $1-\\\\cos x\\\\sim x^2/2$ 或恒等变形",
+        "化为 $\\\\frac{1-\\\\cos x}{x^2}\\\\to 1/2$",
+        "结论 $1/2$"
+      ],
+      "hints": [
+        "可用等价无穷小 $1-\\\\cos x\\\\sim x^2/2$。",
+        "也可用 $1-\\\\cos x=2\\\\sin^2(x/2)$。"
+      ],
+      "commonMistakes": [
+        "误用 $1-\\\\cos x\\\\sim x$",
+        "在加减结构里粗暴替换"
+      ]
+    },
+    {
+      "id": "gd-fl-ex-019",
+      "sourceType": "adapted",
+      "sourceRef": "待核对题源（第一章 无穷小比较）",
+      "knowledgePointIds": ["gd-infinitesimal-comparison"],
+      "difficulty": "basic",
+      "type": "computation",
+      "recommendedTiming": "after-lecture",
+      "prompt": "当 $x\\\\to 0$ 时，比较 $x$、$x^2$、$\\\\sin x$ 的阶，并求 $\\\\lim_{x\\\\to 0}\\\\frac{\\\\sin x}{x}$。",
+      "gradingRubric": [
+        "说明 $x^2$ 是比 $x$ 更高阶的无穷小",
+        "$\\\\sin x$ 与 $x$ 等价",
+        "比值极限为 $1$"
+      ],
+      "hints": [
+        "比较阶看比值极限是否为有限非零常数。",
+        "第一个重要极限直接给出 $\\\\sin x/x$。"
+      ],
+      "commonMistakes": [
+        "把高阶与等价概念混用",
+        "认为 $\\\\sin x$ 比 $x$ 高阶"
+      ]
+    },
+    {
+      "id": "gd-fl-ex-020",
+      "sourceType": "adapted",
+      "sourceRef": "待核对题源（第一章 无穷小比较）",
+      "knowledgePointIds": ["gd-infinitesimal-comparison"],
+      "difficulty": "medium",
+      "type": "computation",
+      "recommendedTiming": "after-lecture",
+      "prompt": "求极限 $\\\\lim_{x\\\\to 0}\\\\frac{\\\\tan x-\\\\sin x}{x^3}$。",
+      "gradingRubric": [
+        "化为 $\\\\frac{\\\\sin x}{x}\\\\cdot\\\\frac{1-\\\\cos x}{x^2}\\\\cdot\\\\frac{1}{\\\\cos x}$",
+        "利用等价无穷小或已知极限",
+        "得 $1/2$"
+      ],
+      "hints": [
+        "先提取 $\\\\sin x$。",
+        "再用 $1-\\\\cos x\\\\sim x^2/2$。"
+      ],
+      "commonMistakes": [
+        "直接对差式用 $\\\\tan x\\\\sim x$、$\\\\sin x\\\\sim x$ 相减得 $0$",
+        "忽略 $\\\\cos x\\\\to 1$"
+      ]
+    },
+    {
+      "id": "gd-fl-ex-021",
+      "sourceType": "adapted",
+      "sourceRef": "待核对题源（第一章 无穷小比较）",
+      "knowledgePointIds": ["gd-infinitesimal-comparison"],
+      "difficulty": "advanced",
+      "type": "computation",
+      "recommendedTiming": "after-lecture",
+      "prompt": "求极限 $\\\\lim_{x\\\\to 0}\\\\frac{\\\\sqrt{1+x}-1-\\\\frac{x}{2}}{x^2}$。",
+      "gradingRubric": [
+        "用泰勒或等价变形到二阶",
+        "分子主部为 $-x^2/8+o(x^2)$",
+        "得极限 $-1/8$"
+      ],
+      "hints": [
+        "这是检验等价替换阶数是否足够的典型题。",
+        "展开到 $x^2$ 项。"
+      ],
+      "commonMistakes": [
+        "只展开到一阶导致分子误判为 $0$",
+        "把 $\\\\sqrt{1+x}-1$ 直接替换成 $x/2$ 后不再保留高阶项"
+      ]
+    },
+    {
+      "id": "gd-fl-ex-022",
+      "sourceType": "adapted",
+      "sourceRef": "待核对题源（第一章 连续性）",
+      "knowledgePointIds": ["gd-continuity-discontinuity"],
+      "difficulty": "basic",
+      "type": "computation",
+      "recommendedTiming": "after-lecture",
+      "prompt": "讨论 $f(x)=\\\\frac{x^2-1}{x-1}$ 在 $x=1$ 处的连续性；若间断，指出类型。",
+      "gradingRubric": [
+        "化简得 $f(x)=x+1$（$x\\\\ne 1$）",
+        "$\\\\lim_{x\\\\to 1}f(x)=2$ 存在",
+        "因 $x=1$ 无定义，为可去间断点"
+      ],
+      "hints": [
+        "先化简函数。",
+        "比较极限值与函数值。"
+      ],
+      "commonMistakes": [
+        "看到分母为零就断言第二型间断",
+        "未说明可去间断可通过补定义修复"
+      ]
+    },
+    {
+      "id": "gd-fl-ex-023",
+      "sourceType": "adapted",
+      "sourceRef": "待核对题源（第一章 连续性）",
+      "knowledgePointIds": ["gd-continuity-discontinuity"],
+      "difficulty": "medium",
+      "type": "analysis",
+      "recommendedTiming": "after-lecture",
+      "prompt": "设 $f(x)=\\\\begin{cases}x+1,&x<0\\\\\\\\x^2,&0\\\\leq x\\\\leq 1\\\\\\\\2-x,&x>1\\\\end{cases}$，求所有间断点并分类。",
+      "gradingRubric": [
+        "在 $x=0$：左极限 $1$，右极限 $0$，跳跃间断",
+        "在 $x=1$：左极限 $1$，右极限 $1$，且 $f(1)=1$，连续",
+        "正确列出间断点 $x=0$"
+      ],
+      "hints": [
+        "分段点 $x=0$、$x=1$ 必查。",
+        "分别算左右极限。"
+      ],
+      "commonMistakes": [
+        "只查定义域端点，不查分段点",
+        "把左右极限存在但不等误判为可去间断"
+      ]
+    },
+    {
+      "id": "gd-fl-ex-024",
+      "sourceType": "adapted",
+      "sourceRef": "待核对题源（第一章 闭区间连续函数）",
+      "knowledgePointIds": ["gd-continuity-discontinuity"],
+      "difficulty": "advanced",
+      "type": "proof",
+      "recommendedTiming": "after-lecture",
+      "prompt": "证明方程 $x^3-4x+1=0$ 在区间 $[0,1]$ 上至少有一个实根。",
+      "gradingRubric": [
+        "令 $f(x)=x^3-4x+1$，验证在 $[0,1]$ 连续",
+        "计算 $f(0)=1>0$、$f(1)=-2<0$",
+        "由零点定理得至少一个根"
+      ],
+      "hints": [
+        "多项式在闭区间上连续。",
+        "检查端点函数值异号。"
+      ],
+      "commonMistakes": [
+        "把零点定理错用到不连续函数",
+        "只说明有根但不说明使用的定理"
+      ]
+    }
+  ]
+}
diff --git a/content/courses/gaodeng-shuxue/exercises/gd-indefinite-integral.json b/content/courses/gaodeng-shuxue/exercises/gd-indefinite-integral.json
new file mode 100644
index 0000000..91c4625
--- /dev/null
+++ b/content/courses/gaodeng-shuxue/exercises/gd-indefinite-integral.json
@@ -0,0 +1 @@
+{"chapterId":"ch-gd-indefinite-integral","courseId":"gaodeng-shuxue","volumeId":"gaodeng-shuxue-volume-1","exercises":[]}
diff --git a/content/courses/gaodeng-shuxue/exercises/gd-line-surface.json b/content/courses/gaodeng-shuxue/exercises/gd-line-surface.json
new file mode 100644
index 0000000..098cd1d
--- /dev/null
+++ b/content/courses/gaodeng-shuxue/exercises/gd-line-surface.json
@@ -0,0 +1 @@
+{"chapterId":"ch-gd-line-surface","courseId":"gaodeng-shuxue","volumeId":"gaodeng-shuxue-volume-2","exercises":[]}
diff --git a/content/courses/gaodeng-shuxue/exercises/gd-mean-value.json b/content/courses/gaodeng-shuxue/exercises/gd-mean-value.json
new file mode 100644
index 0000000..d4238ad
--- /dev/null
+++ b/content/courses/gaodeng-shuxue/exercises/gd-mean-value.json
@@ -0,0 +1 @@
+{"chapterId":"ch-gd-mean-value","courseId":"gaodeng-shuxue","volumeId":"gaodeng-shuxue-volume-1","exercises":[]}
diff --git a/content/courses/gaodeng-shuxue/exercises/gd-multiple-integrals.json b/content/courses/gaodeng-shuxue/exercises/gd-multiple-integrals.json
new file mode 100644
index 0000000..6e6487a
--- /dev/null
+++ b/content/courses/gaodeng-shuxue/exercises/gd-multiple-integrals.json
@@ -0,0 +1 @@
+{"chapterId":"ch-gd-multiple-integrals","courseId":"gaodeng-shuxue","volumeId":"gaodeng-shuxue-volume-2","exercises":[]}
diff --git a/content/courses/gaodeng-shuxue/exercises/gd-multivariable-diff.json b/content/courses/gaodeng-shuxue/exercises/gd-multivariable-diff.json
new file mode 100644
index 0000000..5835373
--- /dev/null
+++ b/content/courses/gaodeng-shuxue/exercises/gd-multivariable-diff.json
@@ -0,0 +1 @@
+{"chapterId":"ch-gd-multivariable-diff","courseId":"gaodeng-shuxue","volumeId":"gaodeng-shuxue-volume-2","exercises":[]}
diff --git a/content/courses/gaodeng-shuxue/exercises/gd-ode.json b/content/courses/gaodeng-shuxue/exercises/gd-ode.json
new file mode 100644
index 0000000..801662f
--- /dev/null
+++ b/content/courses/gaodeng-shuxue/exercises/gd-ode.json
@@ -0,0 +1 @@
+{"chapterId":"ch-gd-ode","courseId":"gaodeng-shuxue","volumeId":"gaodeng-shuxue-volume-1","exercises":[]}
diff --git a/content/courses/gaodeng-shuxue/exercises/gd-series.json b/content/courses/gaodeng-shuxue/exercises/gd-series.json
new file mode 100644
index 0000000..f82e3df
--- /dev/null
+++ b/content/courses/gaodeng-shuxue/exercises/gd-series.json
@@ -0,0 +1 @@
+{"chapterId":"ch-gd-series","courseId":"gaodeng-shuxue","volumeId":"gaodeng-shuxue-volume-2","exercises":[]}
diff --git a/content/courses/gaodeng-shuxue/exercises/gd-vectors.json b/content/courses/gaodeng-shuxue/exercises/gd-vectors.json
new file mode 100644
index 0000000..d3d8df5
--- /dev/null
+++ b/content/courses/gaodeng-shuxue/exercises/gd-vectors.json
@@ -0,0 +1 @@
+{"chapterId":"ch-gd-vectors","courseId":"gaodeng-shuxue","volumeId":"gaodeng-shuxue-volume-2","exercises":[]}
diff --git a/content/courses/gaodeng-shuxue/volume-1.json b/content/courses/gaodeng-shuxue/volume-1.json
new file mode 100644
index 0000000..5b39447
--- /dev/null
+++ b/content/courses/gaodeng-shuxue/volume-1.json
@@ -0,0 +1,72 @@
+{
+  "id": "gaodeng-shuxue-volume-1",
+  "courseId": "gaodeng-shuxue",
+  "title": "高等数学 上册",
+  "statusLegend": {
+    "planned": "已列入目录，尚未整理内容",
+    "sample-ready": "样板章节，已整理为可学习的结构化内容",
+    "draft": "正在整理，内容不完整"
+  },
+  "chapters": [
+    {
+      "id": "ch-gd-function-limit",
+      "number": 1,
+      "title": "函数、极限与连续",
+      "status": "draft",
+      "chapterFile": "chapters/gd-function-limit.json",
+      "exercisesFile": "exercises/gd-function-limit.json",
+      "diagramFile": "diagrams/gd-function-limit.json",
+      "sections": []
+    },
+    {
+      "id": "ch-gd-derivative",
+      "number": 2,
+      "title": "导数与微分",
+      "status": "draft",
+      "chapterFile": "chapters/gd-derivative.json",
+      "exercisesFile": "exercises/gd-derivative.json",
+      "diagramFile": "diagrams/gd-derivative.json",
+      "sections": []
+    },
+    {
+      "id": "ch-gd-mean-value",
+      "number": 3,
+      "title": "微分中值定理与导数应用",
+      "status": "draft",
+      "chapterFile": "chapters/gd-mean-value.json",
+      "exercisesFile": "exercises/gd-mean-value.json",
+      "diagramFile": "diagrams/gd-mean-value.json",
+      "sections": []
+    },
+    {
+      "id": "ch-gd-indefinite-integral",
+      "number": 4,
+      "title": "不定积分",
+      "status": "draft",
+      "chapterFile": "chapters/gd-indefinite-integral.json",
+      "exercisesFile": "exercises/gd-indefinite-integral.json",
+      "diagramFile": "diagrams/gd-indefinite-integral.json",
+      "sections": []
+    },
+    {
+      "id": "ch-gd-definite-integral",
+      "number": 5,
+      "title": "定积分及其应用",
+      "status": "draft",
+      "chapterFile": "chapters/gd-definite-integral.json",
+      "exercisesFile": "exercises/gd-definite-integral.json",
+      "diagramFile": "diagrams/gd-definite-integral.json",
+      "sections": []
+    },
+    {
+      "id": "ch-gd-ode",
+      "number": 6,
+      "title": "微分方程",
+      "status": "draft",
+      "chapterFile": "chapters/gd-ode.json",
+      "exercisesFile": "exercises/gd-ode.json",
+      "diagramFile": "diagrams/gd-ode.json",
+      "sections": []
+    }
+  ]
+}
diff --git a/content/courses/gaodeng-shuxue/volume-2.json b/content/courses/gaodeng-shuxue/volume-2.json
new file mode 100644
index 0000000..f13758f
--- /dev/null
+++ b/content/courses/gaodeng-shuxue/volume-2.json
@@ -0,0 +1,62 @@
+{
+  "id": "gaodeng-shuxue-volume-2",
+  "courseId": "gaodeng-shuxue",
+  "title": "高等数学 下册",
+  "statusLegend": {
+    "planned": "已列入目录，尚未整理内容",
+    "sample-ready": "样板章节，已整理为可学习的结构化内容",
+    "draft": "正在整理，内容不完整"
+  },
+  "chapters": [
+    {
+      "id": "ch-gd-vectors",
+      "number": 7,
+      "title": "向量代数与空间解析几何",
+      "status": "draft",
+      "chapterFile": "chapters/gd-vectors.json",
+      "exercisesFile": "exercises/gd-vectors.json",
+      "diagramFile": "diagrams/gd-vectors.json",
+      "sections": []
+    },
+    {
+      "id": "ch-gd-multivariable-diff",
+      "number": 8,
+      "title": "多元函数微分法及其应用",
+      "status": "draft",
+      "chapterFile": "chapters/gd-multivariable-diff.json",
+      "exercisesFile": "exercises/gd-multivariable-diff.json",
+      "diagramFile": "diagrams/gd-multivariable-diff.json",
+      "sections": []
+    },
+    {
+      "id": "ch-gd-multiple-integrals",
+      "number": 9,
+      "title": "重积分",
+      "status": "draft",
+      "chapterFile": "chapters/gd-multiple-integrals.json",
+      "exercisesFile": "exercises/gd-multiple-integrals.json",
+      "diagramFile": "diagrams/gd-multiple-integrals.json",
+      "sections": []
+    },
+    {
+      "id": "ch-gd-line-surface",
+      "number": 10,
+      "title": "曲线积分与曲面积分",
+      "status": "draft",
+      "chapterFile": "chapters/gd-line-surface.json",
+      "exercisesFile": "exercises/gd-line-surface.json",
+      "diagramFile": "diagrams/gd-line-surface.json",
+      "sections": []
+    },
+    {
+      "id": "ch-gd-series",
+      "number": 11,
+      "title": "无穷级数",
+      "status": "draft",
+      "chapterFile": "chapters/gd-series.json",
+      "exercisesFile": "exercises/gd-series.json",
+      "diagramFile": "diagrams/gd-series.json",
+      "sections": []
+    }
+  ]
+}
diff --git a/content/courses/math-analysis/chapters/definite-integral-applications.json b/content/courses/math-analysis/chapters/definite-integral-applications.json
index 4636872..3bf4cd4 100644
--- a/content/courses/math-analysis/chapters/definite-integral-applications.json
+++ b/content/courses/math-analysis/chapters/definite-integral-applications.json
@@ -14,7 +14,9 @@
         "掌握极坐标下平面图形（扇形元素）的面积公式"
       ],
       "coreExplanation": "**直角坐标下面积**：曲线 $y=f(x)$、$y=g(x)$（$f\\\\geq g$）在 $[a,b]$ 上围成图形的面积：\n$$A=\\\\int_a^b[f(x)-g(x)]\\\\,\\\\mathrm{d}x.$$\n若图形关于 $y$ 轴方向更自然（左右曲线 $x=\\\\varphi(y)$，$x=\\\\psi(y)$），用：$A=\\\\int_c^d[\\\\varphi(y)-\\\\psi(y)]\\\\,\\\\mathrm{d}y$。\n**参数方程下面积**：曲线 $x=\\\\varphi(t)$，$y=\\\\psi(t)$，$t\\\\in[\\\\alpha,\\\\beta]$（$\\\\varphi$ 单调，$\\\\varphi(\\\\alpha)=a$，$\\\\varphi(\\\\beta)=b$），与 $x$ 轴围成面积：\n$$A=\\\\int_\\\\alpha^\\\\beta|\\\\psi(t)|\\\\cdot|\\\\varphi'(t)|\\\\,\\\\mathrm{d}t.$$\n典型例子：椭圆 $x=a\\\\cos t$，$y=b\\\\sin t$ 的面积 $=4\\\\int_0^{\\\\pi/2}b\\\\sin t\\\\cdot a\\\\sin t\\,\\\\mathrm{d}t=\\\\pi ab$。\n**极坐标下面积**：曲线 $r=r(\\\\theta)$，$\\\\theta\\\\in[\\\\alpha,\\\\beta]$ 与极点围成的扇形面积微元为 $\\\\frac{1}{2}r^2\\\\,\\\\mathrm{d}\\\\theta$，故\n$$A=\\\\frac{1}{2}\\\\int_\\\\alpha^\\\\beta r^2(\\\\theta)\\\\,\\\\mathrm{d}\\\\theta.$$\n典型例子：心形线 $r=a(1+\\\\cos\\\\theta)$ 的面积 $=\\\\frac{1}{2}\\\\int_0^{2\\\\pi}a^2(1+\\\\cos\\\\theta)^2\\\\,\\\\mathrm{d}\\\\theta=\\\\frac{3\\\\pi a^2}{2}$。",
-      "textbookRefs": ["数学分析（第5版）上册 §10.1"],
+      "textbookRefs": [
+        "数学分析（第5版）上册 §10.1"
+      ],
       "keyDefinitions": [
         {
           "term": "面积微元",
@@ -41,8 +43,13 @@
         "确定直角坐标积分区间时忘记先求交点",
         "参数方程下面积方向问题：$\\\\varphi'(t)$ 与 $|\\\\varphi'(t)|$ 的选用"
       ],
-      "exerciseIds": ["app-ex-001", "app-ex-002"],
-      "diagramIds": ["area-calculation-diagram"],
+      "exerciseIds": [
+        "app-ex-001",
+        "app-ex-002"
+      ],
+      "diagramIds": [
+        "area-calculation-diagram"
+      ],
       "masteryCriteria": [
         "能计算由两条曲线围成的面积（包括需要分段讨论的情形）",
         "能计算极坐标曲线围成的面积"
@@ -59,7 +66,9 @@
         "掌握直角坐标、参数方程、极坐标下的弧长公式"
       ],
       "coreExplanation": "**旋转体体积（圆盘法/垫圈法）**：曲线 $y=f(x)\\\\geq 0$ 在 $[a,b]$ 上绕 $x$ 轴旋转一周所得体积：\n$$V=\\\\pi\\\\int_a^b[f(x)]^2\\\\,\\\\mathrm{d}x.$$\n若是两条曲线 $f\\\\geq g\\\\geq 0$ 之间绕 $x$ 轴的区域（垫圈法）：$V=\\\\pi\\\\int_a^b([f(x)]^2-[g(x)]^2)\\\\,\\\\mathrm{d}x$。\n**柱壳法（绕 $y$ 轴）**：$V=2\\\\pi\\\\int_a^b x f(x)\\,\\\\mathrm{d}x$（$f\\\\geq 0$，$0\\\\leq a<b$）。\n**平行截面法**：若垂直于某轴（设为 $x$ 轴）的截面面积为 $A(x)$，则体积 $V=\\\\int_a^b A(x)\\,\\\\mathrm{d}x$（圆盘法是其特例）。\n**弧长公式**：\n- 直角坐标：$L=\\\\int_a^b\\\\sqrt{1+[f'(x)]^2}\\\\,\\\\mathrm{d}x$\n- 参数方程 $x=\\\\varphi(t)$，$y=\\\\psi(t)$：$L=\\\\int_\\\\alpha^\\\\beta\\\\sqrt{[\\\\varphi'(t)]^2+[\\\\psi'(t)]^2}\\\\,\\\\mathrm{d}t$\n- 极坐标 $r=r(\\\\theta)$：$L=\\\\int_\\\\alpha^\\\\beta\\\\sqrt{r^2+(r')^2}\\\\,\\\\mathrm{d}\\\\theta$",
-      "textbookRefs": ["数学分析（第5版）上册 §10.2"],
+      "textbookRefs": [
+        "数学分析（第5版）上册 §10.2"
+      ],
       "keyDefinitions": [
         {
           "term": "体积微元（圆盘法）",
@@ -90,8 +99,14 @@
         "弧长公式中 $\\\\sqrt{1+(f')^2}$ 而非 $\\\\sqrt{1+f^2}$——是导数不是函数值",
         "参数方程弧长积分上下限需与参数 $t$ 对应，而非 $x$ 值"
       ],
-      "exerciseIds": ["app-ex-003", "app-ex-004", "app-ex-005"],
-      "diagramIds": ["volume-disk-diagram"],
+      "exerciseIds": [
+        "app-ex-003",
+        "app-ex-004",
+        "app-ex-005"
+      ],
+      "diagramIds": [
+        "volume-disk-diagram"
+      ],
       "masteryCriteria": [
         "能用圆盘法计算绕坐标轴旋转体的体积",
         "能用直角坐标和参数方程弧长公式计算典型曲线弧长"
@@ -108,7 +123,9 @@
         "了解质心（重心）坐标的积分公式"
       ],
       "coreExplanation": "**微元法思路**：将问题量（功、压力、质心）分割为无穷小元素，每个元素上物理量可用简单公式近似，求和取极限得积分。\n**变力做功**：沿 $x$ 轴从 $a$ 到 $b$，力 $F(x)$ 做功：\n$$W=\\\\int_a^b F(x)\\,\\\\mathrm{d}x.$$\n典型：弹簧从自然长度拉伸 $x$，$F=kx$（Hooke 定律），拉伸 $d$ 做功 $W=\\\\frac{1}{2}kd^2$。\n**液体静压力**：宽度为 $w(h)$、深度为 $h$ 处的压强为 $\\\\rho g h$（$\\\\rho$ 为液体密度），水平细长条的压力 $\\\\mathrm{d}F=\\\\rho g h\\\\cdot w(h)\\\\,\\\\mathrm{d}h$，总压力：\n$$F=\\\\rho g\\\\int_0^H h\\\\cdot w(h)\\,\\\\mathrm{d}h.$$\n**质心坐标**：均匀密度平面薄片（面积为 $A$，区域 $D$）的质心：\n$$\\\\bar{x}=\\\\frac{1}{A}\\\\iint_D x\\,\\\\mathrm{d}A,\\\\quad\\\\bar{y}=\\\\frac{1}{A}\\\\iint_D y\\,\\\\mathrm{d}A.$$\n对由曲线 $y=f(x)$ 和 $x$ 轴围成（$f\\\\geq 0$，$x\\\\in[a,b]$）：$\\\\bar{x}=\\\\frac{1}{A}\\\\int_a^b x f(x)\\,\\\\mathrm{d}x$，$\\\\bar{y}=\\\\frac{1}{A}\\\\int_a^b\\\\frac{[f(x)]^2}{2}\\,\\\\mathrm{d}x$。",
-      "textbookRefs": ["数学分析（第5版）上册 §10.3"],
+      "textbookRefs": [
+        "数学分析（第5版）上册 §10.3"
+      ],
       "keyDefinitions": [
         {
           "term": "微元法（元素法）",
@@ -132,12 +149,17 @@
         "压力计算中混淆深度（从水面向下）与坐标轴方向，导致积分上下限颠倒",
         "弹簧问题中使用 $F=kd$（终态力）代替积分，忽略力是变量"
       ],
-      "exerciseIds": ["app-ex-006", "app-ex-007", "app-ex-008"],
+      "exerciseIds": [
+        "app-ex-006",
+        "app-ex-007",
+        "app-ex-008"
+      ],
       "diagramIds": [],
       "masteryCriteria": [
         "能用微元法建立变力做功的积分表达式并计算",
         "能建立矩形或梯形截面水坝的压力积分"
       ]
     }
-  ]
+  ],
+  "overview": "用 Riemann 和的极限定义定积分，讨论可积条件与基本性质，最终以微积分基本定理（Newton-Leibniz 公式）将积分与微分统一起来。"
 }
diff --git a/content/courses/math-analysis/chapters/definite-integral.json b/content/courses/math-analysis/chapters/definite-integral.json
index 5440837..6e265e5 100644
--- a/content/courses/math-analysis/chapters/definite-integral.json
+++ b/content/courses/math-analysis/chapters/definite-integral.json
@@ -15,7 +15,9 @@
         "了解定积分与不定积分的本质区别"
       ],
       "coreExplanation": "设 $f$ 在 $[a,b]$ 上有界。对 $[a,b]$ 作分割 $P: a=x_0<x_1<\\\\cdots<x_n=b$，令 $\\\\Delta x_i=x_i-x_{i-1}$，在每个子区间任取 $\\\\xi_i\\\\in[x_{i-1},x_i]$，作 Riemann 和\n$$S(P,\\\\xi)=\\\\sum_{i=1}^{n}f(\\\\xi_i)\\\\Delta x_i.$$\n若对任意 $\\\\varepsilon>0$，存在 $\\\\delta>0$，使得当 $\\\\|P\\\\|=\\\\max_i\\\\Delta x_i<\\\\delta$ 时，对任意取样点 $\\\\xi_i$ 均有 $|S(P,\\\\xi)-I|<\\\\varepsilon$，则称 $f$ 在 $[a,b]$ 上 **Riemann 可积**，$I$ 称为 $f$ 在 $[a,b]$ 上的**定积分**，记作\n$$I=\\\\int_a^b f(x)\\\\,\\\\mathrm{d}x.$$\n**几何意义**：若 $f\\\\geq 0$，$\\\\int_a^b f\\\\,\\\\mathrm{d}x$ 等于曲线 $y=f(x)$、$x$ 轴和直线 $x=a,x=b$ 围成的面积；若 $f$ 变号，积分是**有向面积**（$x$ 轴上方取正，下方取负）。\n**约定**：$\\\\int_a^a f\\\\,\\\\mathrm{d}x=0$；$\\\\int_b^a f\\\\,\\\\mathrm{d}x=-\\\\int_a^b f\\\\,\\\\mathrm{d}x$（上下限互换变号）。",
-      "textbookRefs": ["数学分析（第5版）上册 §9.1"],
+      "textbookRefs": [
+        "数学分析（第5版）上册 §9.1"
+      ],
       "keyDefinitions": [
         {
           "term": "Riemann 和",
@@ -54,8 +56,13 @@
         "认为 $\\\\int_a^b f\\\\,\\\\mathrm{d}x$ 一定是面积——当 $f$ 变号时是有向面积，面积需加绝对值",
         "上下限互换时忘记变号"
       ],
-      "exerciseIds": ["defint-ex-001", "defint-ex-002"],
-      "diagramIds": ["riemann-sum-illustration"],
+      "exerciseIds": [
+        "defint-ex-001",
+        "defint-ex-002"
+      ],
+      "diagramIds": [
+        "riemann-sum-illustration"
+      ],
       "masteryCriteria": [
         "能写出 $\\\\int_0^1 x\\\\,\\\\mathrm{d}x$ 对应的 Riemann 和并求极限",
         "能判断给定函数是否满足可积必要条件"
@@ -72,7 +79,9 @@
         "了解 Riemann 可积的充要条件（振幅和趋于零）"
       ],
       "coreExplanation": "**Darboux 方法**：对分割 $P$ 定义上和 $\\\\overline{S}(P)=\\\\sum M_i\\\\Delta x_i$，下和 $\\\\underline{S}(P)=\\\\sum m_i\\\\Delta x_i$（$M_i,m_i$ 为第 $i$ 段上的上/下确界）。总有 $\\\\underline{S}(P)\\\\leq S(P,\\\\xi)\\\\leq\\\\overline{S}(P)$。\n**可积充要条件（Riemann）**：$f$ 可积 $\\\\Leftrightarrow$ $\\\\lim_{\\\\|P\\\\|\\\\to 0}(\\\\overline{S}(P)-\\\\underline{S}(P))=0$，即振幅和趋零：对任意 $\\\\varepsilon>0$，$\\\\exists\\\\delta>0$ 使 $\\\\|P\\\\|<\\\\delta$ 时 $\\\\sum_{i=1}^n\\\\omega_i\\\\Delta x_i<\\\\varepsilon$（$\\\\omega_i=M_i-m_i$）。\n**三大充分条件**：\n1. **$f$ 在 $[a,b]$ 上连续** $\\\\Rightarrow$ $f$ 可积（均匀连续保证振幅可任意小）\n2. **$f$ 在 $[a,b]$ 上有界且只有有限个不连续点** $\\\\Rightarrow$ $f$ 可积\n3. **$f$ 在 $[a,b]$ 上单调有界** $\\\\Rightarrow$ $f$ 可积（振幅和 $\\\\leq (f(b)-f(a))\\\\cdot\\\\|P\\\\|\\\\to 0$）",
-      "textbookRefs": ["数学分析（第5版）上册 §9.2"],
+      "textbookRefs": [
+        "数学分析（第5版）上册 §9.2"
+      ],
       "keyDefinitions": [
         {
           "term": "Darboux 上和、下和",
@@ -107,7 +116,9 @@
         "误认为\"有界 $\\\\Rightarrow$ 可积\"——狄利克雷函数有界但不可积",
         "混淆可积充要条件与充分条件"
       ],
-      "exerciseIds": ["defint-ex-003"],
+      "exerciseIds": [
+        "defint-ex-003"
+      ],
       "diagramIds": [],
       "masteryCriteria": [
         "能用振幅和判断单调函数可积",
@@ -125,7 +136,9 @@
         "能利用被积函数的奇偶性/周期性简化计算"
       ],
       "coreExplanation": "**基本性质**（设 $f,g$ 在 $[a,b]$ 可积）：\n1. **线性性**：$\\\\int_a^b(\\\\alpha f+\\\\beta g)\\\\,\\\\mathrm{d}x=\\\\alpha\\\\int_a^b f\\\\,\\\\mathrm{d}x+\\\\beta\\\\int_a^b g\\\\,\\\\mathrm{d}x$\n2. **区间可加性**：$\\\\int_a^b f=\\\\int_a^c f+\\\\int_c^b f$（对任意 $c\\\\in[a,b]$，甚至 $c\\\\notin[a,b]$ 也成立）\n3. **保号性**：若 $f\\\\geq 0$ 在 $[a,b]$ 上，则 $\\\\int_a^b f\\\\,\\\\mathrm{d}x\\\\geq 0$\n4. **单调性**：若 $f\\\\leq g$ 在 $[a,b]$ 上，则 $\\\\int_a^b f\\\\leq\\\\int_a^b g$\n5. **估值不等式**：$m(b-a)\\\\leq\\\\int_a^b f\\\\,\\\\mathrm{d}x\\\\leq M(b-a)$（$m,M$ 为最小、最大值）\n6. **绝对值不等式**：$\\\\left|\\\\int_a^b f\\\\,\\\\mathrm{d}x\\\\right|\\\\leq\\\\int_a^b|f|\\\\,\\\\mathrm{d}x$\n**积分中值定理**：若 $f$ 在 $[a,b]$ 连续，则 $\\\\exists\\\\xi\\\\in(a,b)$ 使 $\\\\int_a^b f(x)\\\\,\\\\mathrm{d}x=f(\\\\xi)(b-a)$（$f(\\\\xi)$ 称为 $f$ 在 $[a,b]$ 上的**积分平均值**）。\n**奇偶性**：若 $f$ 在 $[-a,a]$ 上连续，$f$ 为奇函数则 $\\\\int_{-a}^a f=0$；$f$ 为偶函数则 $\\\\int_{-a}^a f=2\\\\int_0^a f$。\n**周期性**：若 $f$ 以 $T$ 为周期，则 $\\\\int_a^{a+T}f=\\\\int_0^T f$（积分值与起点无关）。",
-      "textbookRefs": ["数学分析（第5版）上册 §9.3"],
+      "textbookRefs": [
+        "数学分析（第5版）上册 §9.3"
+      ],
       "keyDefinitions": [
         {
           "term": "积分平均值",
@@ -153,7 +166,10 @@
         "对非连续函数套用积分中值定理（该定理要求连续）",
         "奇偶性简化计算仅适用于关于原点对称的区间 $[-a,a]$"
       ],
-      "exerciseIds": ["defint-ex-004", "defint-ex-005"],
+      "exerciseIds": [
+        "defint-ex-004",
+        "defint-ex-005"
+      ],
       "diagramIds": [],
       "masteryCriteria": [
         "能用估值不等式估计定积分的大小",
@@ -172,7 +188,10 @@
         "掌握定积分的换元法和分部积分法"
       ],
       "coreExplanation": "**变上限积分**：设 $f$ 在 $[a,b]$ 可积，$x\\\\in[a,b]$，定义 $\\\\Phi(x)=\\\\int_a^x f(t)\\\\,\\\\mathrm{d}t$。\n**微积分基本定理（第一部分）**：若 $f\\\\in C[a,b]$，则 $\\\\Phi'(x)=f(x)$，即 $\\\\Phi$ 是 $f$ 的一个原函数。\n**Newton-Leibniz 公式**：若 $f\\\\in C[a,b]$，$F$ 为 $f$ 的任一原函数，则\n$$\\\\int_a^b f(x)\\\\,\\\\mathrm{d}x = F(b)-F(a)=[F(x)]_a^b.$$\n**定积分换元法**：设 $f\\\\in C[a,b]$，$x=\\\\varphi(t)$ 满足 $\\\\varphi(\\\\alpha)=a$，$\\\\varphi(\\\\beta)=b$，$\\\\varphi'$ 连续且不变号，则\n$$\\\\int_a^b f(x)\\\\,\\\\mathrm{d}x=\\\\int_\\\\alpha^\\\\beta f(\\\\varphi(t))\\\\varphi'(t)\\\\,\\\\mathrm{d}t.$$\n注意：**换元后上下限同步换**，不必换回。\n**定积分分部积分法**：$\\\\int_a^b u\\\\,\\\\mathrm{d}v=[uv]_a^b-\\\\int_a^b v\\\\,\\\\mathrm{d}u$。\n**Wallis 公式**（重要推论）：\n$$\\\\int_0^{\\\\pi/2}\\\\sin^n x\\\\,\\\\mathrm{d}x=\\\\int_0^{\\\\pi/2}\\\\cos^n x\\\\,\\\\mathrm{d}x=\\\\begin{cases}\\\\dfrac{(n-1)!!}{n!!}\\\\cdot\\\\dfrac{\\\\pi}{2} & n\\\\text{ 偶},\\\\\\\\[6pt]\\\\dfrac{(n-1)!!}{n!!} & n\\\\text{ 奇}.\\\\end{cases}$$\n**变上限积分求导的推广**：$\\\\frac{\\\\mathrm{d}}{\\\\mathrm{d}x}\\\\int_{\\\\psi(x)}^{\\\\varphi(x)}f(t)\\\\,\\\\mathrm{d}t=f(\\\\varphi(x))\\\\varphi'(x)-f(\\\\psi(x))\\\\psi'(x)$。",
-      "textbookRefs": ["数学分析（第5版）上册 §9.4", "数学分析（第5版）上册 §9.5"],
+      "textbookRefs": [
+        "数学分析（第5版）上册 §9.4",
+        "数学分析（第5版）上册 §9.5"
+      ],
       "keyDefinitions": [
         {
           "term": "变上限积分",
@@ -205,13 +224,22 @@
         "变上限积分求导时忘记链式法则（上限是 $\\\\varphi(x)$ 时乘以 $\\\\varphi'(x)$）",
         "将 Newton-Leibniz 公式用于含瑕点的区间（被积函数无界时需用反常积分）"
       ],
-      "exerciseIds": ["defint-ex-006", "defint-ex-007", "defint-ex-008", "defint-ex-009", "defint-ex-010"],
-      "diagramIds": ["fundamental-theorem-diagram"],
+      "exerciseIds": [
+        "defint-ex-006",
+        "defint-ex-007",
+        "defint-ex-008",
+        "defint-ex-009",
+        "defint-ex-010"
+      ],
+      "diagramIds": [
+        "fundamental-theorem-diagram"
+      ],
       "masteryCriteria": [
         "能用 Newton-Leibniz 公式计算含基本函数的定积分",
         "能对变上限积分（含复合形式）正确求导",
         "能用换元法和分部积分法计算定积分"
       ]
     }
-  ]
+  ],
+  "overview": "用 Riemann 和的极限定义定积分，讨论可积条件与基本性质，最终以微积分基本定理（Newton-Leibniz 公式）将积分与微分统一起来。"
 }
diff --git a/content/courses/math-analysis/chapters/fourier-series.json b/content/courses/math-analysis/chapters/fourier-series.json
index 7d37f35..1ce3e6e 100644
--- a/content/courses/math-analysis/chapters/fourier-series.json
+++ b/content/courses/math-analysis/chapters/fourier-series.json
@@ -14,7 +14,9 @@
         "能写出以 $2\\\\pi$ 为周期函数的 Fourier 级数"
       ],
       "coreExplanation": "**三角函数系的正交性**：$\\\\{1,\\\\cos x,\\\\sin x,\\\\cos 2x,\\\\sin 2x,\\\\ldots\\\\}$ 在 $[-\\\\pi,\\\\pi]$ 上两两正交：\n$$\\\\int_{-\\\\pi}^\\\\pi\\\\cos mx\\\\cos nx\\,\\\\mathrm{d}x=\\\\begin{cases}0 & m\\\\neq n\\\\\\\\\\\\pi & m=n\\\\neq 0\\\\\\\\2\\\\pi & m=n=0\\\\end{cases},\\\\quad\\\\int_{-\\\\pi}^\\\\pi\\\\cos mx\\\\sin nx\\,\\\\mathrm{d}x=0.$$\n**Fourier 系数（Euler-Fourier 公式）**：设 $f$ 在 $[-\\\\pi,\\\\pi]$ 上可积，定义\n$$a_0=\\\\frac{1}{\\\\pi}\\\\int_{-\\\\pi}^\\\\pi f(x)\\,\\\\mathrm{d}x,\\\\quad a_n=\\\\frac{1}{\\\\pi}\\\\int_{-\\\\pi}^\\\\pi f(x)\\\\cos nx\\,\\\\mathrm{d}x,\\\\quad b_n=\\\\frac{1}{\\\\pi}\\\\int_{-\\\\pi}^\\\\pi f(x)\\\\sin nx\\,\\\\mathrm{d}x.$$\n则 $f$ 的 **Fourier 级数**为 $\\\\frac{a_0}{2}+\\\\sum_{n=1}^\\\\infty(a_n\\\\cos nx+b_n\\\\sin nx)$，记作 $f(x)\\\\sim\\\\frac{a_0}{2}+\\\\sum_{n=1}^\\\\infty(a_n\\\\cos nx+b_n\\\\sin nx)$（$\\\\sim$ 表示对应，不一定逐点相等）。\n**奇偶函数简化**：$f$ 为偶函数：$b_n=0$，$a_n=\\\\frac{2}{\\\\pi}\\\\int_0^\\\\pi f(x)\\\\cos nx\\,\\\\mathrm{d}x$（余弦级数）。$f$ 为奇函数：$a_n=0$，$b_n=\\\\frac{2}{\\\\pi}\\\\int_0^\\\\pi f(x)\\\\sin nx\\,\\\\mathrm{d}x$（正弦级数）。\n**Bessel 不等式**：$\\\\frac{a_0^2}{2}+\\\\sum_{n=1}^\\\\infty(a_n^2+b_n^2)\\\\leq\\\\frac{1}{\\\\pi}\\\\int_{-\\\\pi}^\\\\pi[f(x)]^2\\,\\\\mathrm{d}x$（等号即 Parseval 等式）。",
-      "textbookRefs": ["数学分析（第5版）下册 §15.1"],
+      "textbookRefs": [
+        "数学分析（第5版）下册 §15.1"
+      ],
       "keyDefinitions": [
         {
           "term": "三角函数系正交性",
@@ -44,8 +46,13 @@
         "$a_0$ 公式中系数是 $1/\\\\pi$，但级数中写 $a_0/2$，注意两者关系",
         "奇延拓/偶延拓时忘记将函数延伸到 $[-\\\\pi,\\\\pi]$ 的完整定义"
       ],
-      "exerciseIds": ["fourier-ex-001", "fourier-ex-002"],
-      "diagramIds": ["fourier-partial-sum-diagram"],
+      "exerciseIds": [
+        "fourier-ex-001",
+        "fourier-ex-002"
+      ],
+      "diagramIds": [
+        "fourier-partial-sum-diagram"
+      ],
       "masteryCriteria": [
         "能用 Euler-Fourier 公式计算简单函数的 Fourier 系数",
         "能利用奇偶性简化 Fourier 系数的计算"
@@ -62,7 +69,9 @@
         "掌握 Parseval 等式及其应用（求数项级数的和）"
       ],
       "coreExplanation": "**Dirichlet 收敛定理**：若 $f$ 在 $[-\\\\pi,\\\\pi]$ 上**逐段光滑**（即 $f$ 和 $f'$ 除有限个点外连续，各单侧极限存在），则 $f$ 的 Fourier 级数收敛，且\n$$\\\\frac{a_0}{2}+\\\\sum_{n=1}^\\\\infty(a_n\\\\cos nx+b_n\\\\sin nx)=\\\\frac{f(x^+)+f(x^-)}{2}.$$\n- **连续点** $x$：级数收敛到 $f(x)$（即 $(f(x^+)+f(x^-))/2=f(x)$）。\n- **跳跃不连续点** $x$：级数收敛到左右极限的均值 $(f(x^+)+f(x^-))/2$。\n- **端点** $x=\\\\pm\\\\pi$：级数收敛到 $(f(-\\\\pi^+)+f(\\\\pi^-))/2$（周期延拓后的端点值）。\n**Gibbs 现象**：在跳跃不连续点附近，Fourier 级数的部分和出现约 $9\\\\%$ 的超调（过冲），不随项数增加而消失——这是 Fourier 近似的固有局限。\n**Parseval 等式**：若 $f$ 在 $[-\\\\pi,\\\\pi]$ 上满足 Dirichlet 条件，则\n$$\\\\frac{a_0^2}{2}+\\\\sum_{n=1}^\\\\infty(a_n^2+b_n^2)=\\\\frac{1}{\\\\pi}\\\\int_{-\\\\pi}^\\\\pi[f(x)]^2\\,\\\\mathrm{d}x.$$\n**应用**：若 $f(x)=x$（$x\\\\in[-\\\\pi,\\\\pi]$），则 $b_n=(-1)^{n+1}\\\\cdot 2/n$，Parseval 等式给出 $\\\\sum 4/n^2=\\\\pi^2/3$，即 $\\\\sum 1/n^2=\\\\pi^2/6$（Basel 问题另一证明）。",
-      "textbookRefs": ["数学分析（第5版）下册 §15.1—15.2"],
+      "textbookRefs": [
+        "数学分析（第5版）下册 §15.1—15.2"
+      ],
       "keyDefinitions": [
         {
           "term": "逐段光滑",
@@ -93,7 +102,11 @@
         "在不连续点处直接套用 $f(x)$，应用均值 $(f(x^+)+f(x^-))/2$",
         "周期延拓时端点 $\\\\pm\\\\pi$ 处的值由单侧极限的均值确定，不一定等于原函数值"
       ],
-      "exerciseIds": ["fourier-ex-003", "fourier-ex-004", "fourier-ex-005"],
+      "exerciseIds": [
+        "fourier-ex-003",
+        "fourier-ex-004",
+        "fourier-ex-005"
+      ],
       "diagramIds": [],
       "masteryCriteria": [
         "能对逐段光滑函数写出 Fourier 级数并用收敛定理逐点确定级数值",
@@ -111,7 +124,9 @@
         "能灵活处理不同区间和不同周期的 Fourier 展开"
       ],
       "coreExplanation": "**周期 $2l$ 的展开**：令 $t=\\\\pi x/l$，则 $f(x)=F(t)$（$t\\\\in[-\\\\pi,\\\\pi]$）。对应 Fourier 系数：\n$$a_0=\\\\frac{1}{l}\\\\int_{-l}^l f(x)\\,\\\\mathrm{d}x,\\\\quad a_n=\\\\frac{1}{l}\\\\int_{-l}^l f(x)\\\\cos\\\\frac{n\\\\pi x}{l}\\\\,\\\\mathrm{d}x,\\\\quad b_n=\\\\frac{1}{l}\\\\int_{-l}^l f(x)\\\\sin\\\\frac{n\\\\pi x}{l}\\,\\\\mathrm{d}x,$$\n级数为 $\\\\frac{a_0}{2}+\\\\sum_{n=1}^\\\\infty\\\\left(a_n\\\\cos\\\\frac{n\\\\pi x}{l}+b_n\\\\sin\\\\frac{n\\\\pi x}{l}\\\\right)$。\n**$[0,l]$ 上的正弦/余弦展开**：设 $f$ 仅在 $[0,l]$ 上定义。\n- **余弦级数**（偶延拓）：将 $f$ 偶延拓到 $[-l,l]$，$b_n=0$，$a_n=\\\\frac{2}{l}\\\\int_0^l f(x)\\\\cos\\\\frac{n\\\\pi x}{l}\\,\\\\mathrm{d}x$。\n- **正弦级数**（奇延拓）：将 $f$ 奇延拓到 $[-l,l]$，$a_n=0$，$b_n=\\\\frac{2}{l}\\\\int_0^l f(x)\\\\sin\\\\frac{n\\\\pi x}{l}\\,\\\\mathrm{d}x$。\n在端点 $x=0$ 和 $x=l$：正弦级数端点值为 $0$（奇延拓跳跃到均值 $(f(0^+)+f(0^-))/2=0$）；余弦级数端点值为 $f(0)$（如 $f$ 连续）。\n**工程背景**：热传导、波动方程的边界条件（Dirichlet 边界 $u=0$ 对应正弦展开，Neumann 边界 $u'=0$ 对应余弦展开）。",
-      "textbookRefs": ["数学分析（第5版）下册 §15.2"],
+      "textbookRefs": [
+        "数学分析（第5版）下册 §15.2"
+      ],
       "keyDefinitions": [
         {
           "term": "奇延拓",
@@ -135,12 +150,17 @@
         "正弦展开在端点 $x=0,l$ 处级数和为零，即使 $f(0)\\\\neq 0$ 或 $f(l)\\\\neq 0$",
         "周期 $2l$ 时基频为 $\\\\pi/l$（不是 $\\\\pi$），系数公式中的自变量为 $n\\\\pi x/l$"
       ],
-      "exerciseIds": ["fourier-ex-006", "fourier-ex-007", "fourier-ex-008"],
+      "exerciseIds": [
+        "fourier-ex-006",
+        "fourier-ex-007",
+        "fourier-ex-008"
+      ],
       "diagramIds": [],
       "masteryCriteria": [
         "能对 $[0,l]$ 上的函数分别展开为正弦级数和余弦级数",
         "能判断展开式在端点和跳跃点处的收敛值"
       ]
     }
-  ]
+  ],
+  "overview": "用三角函数系的正交性建立 Euler-Fourier 展开，讨论 Dirichlet 定理（逐点收敛条件），推广到以 l$ 为周期的正弦/余弦展开。"
 }
diff --git a/content/courses/math-analysis/chapters/function-sequences-series.json b/content/courses/math-analysis/chapters/function-sequences-series.json
index 51769ae..c842744 100644
--- a/content/courses/math-analysis/chapters/function-sequences-series.json
+++ b/content/courses/math-analysis/chapters/function-sequences-series.json
@@ -15,7 +15,9 @@
         "了解函数项级数的一致收敛（Weierstrass M-判别法）"
       ],
       "coreExplanation": "**逐点收敛**：函数列 $\\\\{f_n\\\\}$ 在集合 $I$ 上**逐点收敛**于 $f$，若对每个 $x\\\\in I$，$\\\\lim_{n\\\\to\\\\infty}f_n(x)=f(x)$。这里 $N$ 可以依赖于 $x$，写作 $N=N(\\\\varepsilon,x)$。\n**一致收敛**：$\\\\{f_n\\\\}$ 在 $I$ 上**一致收敛**于 $f$（记 $f_n\\\\rightrightarrows f$），若：\n$$\\\\forall\\\\varepsilon>0,\\\\;\\\\exists N\\\\in\\\\mathbb{N},\\\\;\\\\forall n>N,\\\\;\\\\forall x\\\\in I:\\\\;|f_n(x)-f(x)|<\\\\varepsilon.$$\n关键：$N$ 只依赖于 $\\\\varepsilon$，不依赖于 $x$。\n**等价刻画**：$f_n\\\\rightrightarrows f$ $\\\\Leftrightarrow$ $M_n:=\\\\sup_{x\\\\in I}|f_n(x)-f(x)|\\\\to 0$（$n\\\\to\\\\infty$）。\n**否定一致收敛**：若 $\\\\exists\\\\varepsilon_0>0$，对任意 $N$，$\\\\exists n>N$，$\\\\exists x_n\\\\in I$ 使 $|f_n(x_n)-f(x)|\\\\geq\\\\varepsilon_0$，则 $f_n\\\\not\\\\rightrightarrows f$。\n**典型例子**：$f_n(x)=x^n$ 在 $[0,1)$ 上逐点收敛于 $f\\\\equiv 0$，但不一致收敛（$M_n=\\\\sup_{x\\\\in[0,1)}x^n=1\\\\not\\\\to 0$）。在 $[0,r]$（$0<r<1$）上一致收敛（$M_n=r^n\\\\to 0$）。\n**Cauchy 准则（一致收敛）**：$\\\\{f_n\\\\}$ 在 $I$ 上一致收敛 $\\\\Leftrightarrow$ $\\\\forall\\\\varepsilon>0$，$\\\\exists N$，$m,n>N\\\\Rightarrow\\\\sup_{x\\\\in I}|f_m(x)-f_n(x)|<\\\\varepsilon$。\n**函数项级数**：$\\\\sum_{n=1}^\\\\infty u_n(x)$ 一致收敛 $\\\\Leftrightarrow$ 部分和函数列 $\\\\{S_N(x)\\\\}$ 一致收敛。\n**Weierstrass M-判别法**：若 $|u_n(x)|\\\\leq M_n$（$\\\\forall x\\\\in I$），$\\\\sum M_n$ 收敛，则 $\\\\sum u_n(x)$ 在 $I$ 上一致（绝对）收敛。",
-      "textbookRefs": ["数学分析（第5版）下册 §13.1"],
+      "textbookRefs": [
+        "数学分析（第5版）下册 §13.1"
+      ],
       "keyDefinitions": [
         {
           "term": "逐点收敛",
@@ -50,8 +52,14 @@
         "M-判别法中 $M_n$ 必须是常数（与 $x$ 无关的上界），不能含 $x$",
         "混淆 $f_n$ 一致收敛与 $\\\\sum u_n$ 一致收敛（后者是部分和一致收敛）"
       ],
-      "exerciseIds": ["funseq-ex-001", "funseq-ex-002", "funseq-ex-003"],
-      "diagramIds": ["uniform-convergence-diagram"],
+      "exerciseIds": [
+        "funseq-ex-001",
+        "funseq-ex-002",
+        "funseq-ex-003"
+      ],
+      "diagramIds": [
+        "uniform-convergence-diagram"
+      ],
       "masteryCriteria": [
         "能用 $M_n$ 方法判断函数列是否一致收敛",
         "能用 Weierstrass M-判别法判断函数项级数一致收敛"
@@ -69,7 +77,9 @@
         "能判断极限与积分/微分的交换是否合法"
       ],
       "coreExplanation": "**连续性**：若 $f_n\\\\in C(I)$，$f_n\\\\rightrightarrows f$ 在 $I$ 上，则 $f\\\\in C(I)$。即：连续函数序列的一致极限仍连续。（逐点收敛不保证连续性：$x^n$ 的极限在 $[0,1]$ 上不连续。）\n**逐项积分**：若 $f_n\\\\in C[a,b]$，$f_n\\\\rightrightarrows f$ 在 $[a,b]$ 上，则\n$$\\\\lim_{n\\\\to\\\\infty}\\\\int_a^b f_n(x)\\,\\\\mathrm{d}x=\\\\int_a^b f(x)\\,\\\\mathrm{d}x\\\\quad\\\\text{（极限与积分可交换）}$$\n即 $\\\\int_a^b\\\\lim_{n\\\\to\\\\infty}f_n\\,\\\\mathrm{d}x=\\\\lim_{n\\\\to\\\\infty}\\\\int_a^b f_n\\,\\\\mathrm{d}x$。\n推论：一致收敛的函数项级数可逐项积分：$\\\\int_a^b\\\\sum u_n=\\\\sum\\\\int_a^b u_n$。\n**逐项微分**（条件更强）：若 $f_n$ 在 $[a,b]$ 上可微，$f_n'$ 在 $[a,b]$ 上一致收敛，且 $\\\\{f_n(x_0)\\\\}$ 对某个 $x_0$ 收敛，则 $f_n\\\\rightrightarrows f$（某 $f$），且 $f'=\\\\lim f_n'$。即：$\\\\frac{\\\\mathrm{d}}{\\\\mathrm{d}x}\\\\lim f_n=\\\\lim\\\\frac{\\\\mathrm{d}f_n}{\\\\mathrm{d}x}$ 需要导函数列一致收敛。\n**典型应用**：幂级数 $\\\\sum_{n=0}^\\\\infty a_n x^n$ 在收敛半径内的任意闭子区间上一致收敛，故可逐项积分和微分（幂级数章节的基础）。",
-      "textbookRefs": ["数学分析（第5版）下册 §13.2"],
+      "textbookRefs": [
+        "数学分析（第5版）下册 §13.2"
+      ],
       "keyDefinitions": [],
       "keyTheorems": [
         {
@@ -102,12 +112,19 @@
         "逐项微分条件中只要求函数列一致收敛而忘记检验导函数列一致收敛",
         "在无界区间上对有界函数用逐项积分：需要额外条件（一致收敛不足以处理无界域）"
       ],
-      "exerciseIds": ["funseq-ex-004", "funseq-ex-005", "funseq-ex-006", "funseq-ex-007", "funseq-ex-008"],
+      "exerciseIds": [
+        "funseq-ex-004",
+        "funseq-ex-005",
+        "funseq-ex-006",
+        "funseq-ex-007",
+        "funseq-ex-008"
+      ],
       "diagramIds": [],
       "masteryCriteria": [
         "能判断何时极限与积分可交换，给出正确理由",
         "能举出逐点收敛时极限与积分不可交换的反例"
       ]
     }
-  ]
+  ],
+  "overview": "区分逐点收敛与一致收敛，建立 Weierstrass $ 判别法，证明一致收敛对连续性、逐项求导与逐项积分的保持性。"
 }
diff --git a/content/courses/math-analysis/chapters/implicit-function-theorem.json b/content/courses/math-analysis/chapters/implicit-function-theorem.json
index 48d2fc3..3dc63ee 100644
--- a/content/courses/math-analysis/chapters/implicit-function-theorem.json
+++ b/content/courses/math-analysis/chapters/implicit-function-theorem.json
@@ -14,7 +14,9 @@
         "能用隐函数定理求偏导数"
       ],
       "coreExplanation": "**隐函数定理（一个方程）**：设 $F(x_0,y_0)=0$，在 $(x_0,y_0)$ 的邻域内 $F_x,F_y$ 连续，且 $F_y(x_0,y_0)\\\\neq 0$，则：\n1. 在 $x_0$ 的某邻域 $I$ 内存在唯一的连续函数 $y=f(x)$，使 $F(x,f(x))=0$，$f(x_0)=y_0$。\n2. $f$ 在 $I$ 内有连续导数：$f'(x)=-F_x/F_y$。\n**三元情形**：$F(x,y,z)=0$，$F_z(P_0)\\\\neq 0$，则局部确定 $z=f(x,y)$，\n$$\\\\frac{\\\\partial z}{\\\\partial x}=-\\\\frac{F_x}{F_z},\\\\quad\\\\frac{\\\\partial z}{\\\\partial y}=-\\\\frac{F_y}{F_z}.$$\n**理解要点**：定理是**存在性**定理（保证局部存在），不给出全局的显式 $y=f(x)$。条件 $F_y\\\\neq 0$ 防止\"切线竖直\"（曲线 $F=0$ 在该点局部有单值图象）。\n**一阶近似**：在 $(x_0,y_0)$ 附近，隐函数 $y\\\\approx y_0-\\\\frac{F_x(x_0,y_0)}{F_y(x_0,y_0)}(x-x_0)$（线性近似）。",
-      "textbookRefs": ["数学分析（第5版）下册 §18.1"],
+      "textbookRefs": [
+        "数学分析（第5版）下册 §18.1"
+      ],
       "keyDefinitions": [
         {
           "term": "隐函数",
@@ -40,7 +42,10 @@
         "隐函数导数公式有负号：$y'=-F_x/F_y$（不是 $F_x/F_y$）",
         "公式中 $F_y\\\\neq 0$ 是前提，不满足时公式无效"
       ],
-      "exerciseIds": ["ift-ex-001", "ift-ex-002"],
+      "exerciseIds": [
+        "ift-ex-001",
+        "ift-ex-002"
+      ],
       "diagramIds": [],
       "masteryCriteria": [
         "能应用隐函数定理验证隐函数存在并求其导数",
@@ -58,7 +63,9 @@
         "理解 Jacobi 行列式与变量变换的关系"
       ],
       "coreExplanation": "**方程组隐函数定理**：设方程组 $\\\\begin{cases}F(x,y,u,v)=0\\\\\\\\G(x,y,u,v)=0\\\\end{cases}$，在 $P_0=(x_0,y_0,u_0,v_0)$ 处满足 $F,G,F_u,F_v,G_u,G_v$ 连续，且 **Jacobi 行列式**\n$$J=\\\\frac{\\\\partial(F,G)}{\\\\partial(u,v)}=\\\\begin{vmatrix}F_u&F_v\\\\\\\\G_u&G_v\\\\end{vmatrix}\\\\neq 0,$$\n则在 $P_0$ 邻域内唯一确定可微函数 $u=u(x,y),v=v(x,y)$，且\n$$\\\\frac{\\\\partial u}{\\\\partial x}=-\\\\frac{1}{J}\\\\begin{vmatrix}F_x&F_v\\\\\\\\G_x&G_v\\\\end{vmatrix},\\\\quad\\\\frac{\\\\partial v}{\\\\partial x}=-\\\\frac{1}{J}\\\\begin{vmatrix}F_u&F_x\\\\\\\\G_u&G_x\\\\end{vmatrix}.$$\n（Cramer 法则替换对应列。）\n**实用方法（全微分法）**：两方程分别求全微分，得含 $\\\\mathrm{d}u,\\\\mathrm{d}v$ 的线性方程组，用 Cramer 法则或消元法解出。\n**Jacobi 矩阵**：$J_f=\\\\partial(f_1,\\\\ldots,f_m)/\\\\partial(x_1,\\\\ldots,x_n)$，是链式法则和变量变换的核心工具。",
-      "textbookRefs": ["数学分析（第5版）下册 §18.2"],
+      "textbookRefs": [
+        "数学分析（第5版）下册 §18.2"
+      ],
       "keyDefinitions": [
         {
           "term": "Jacobi 行列式",
@@ -78,7 +85,9 @@
         "全微分法中 $\\\\mathrm{d}x,\\\\mathrm{d}y$ 是自变量（独立），$\\\\mathrm{d}u,\\\\mathrm{d}v$ 是因变量，线性方程组的未知数是 $\\\\mathrm{d}u,\\\\mathrm{d}v$",
         "Jacobi 行列式是 $F,G$ 对 $(u,v)$ 的偏导（被确定的变量），不是对 $(x,y)$ 的偏导"
       ],
-      "exerciseIds": ["ift-ex-003"],
+      "exerciseIds": [
+        "ift-ex-003"
+      ],
       "diagramIds": [],
       "masteryCriteria": [
         "能用全微分法求方程组确定的隐函数的偏导数",
@@ -96,7 +105,9 @@
         "能求空间曲面的切平面和法线方程"
       ],
       "coreExplanation": "**平面曲线 $F(x,y)=0$ 的切线/法线（$(x_0,y_0)$ 处）：**\n- 切线方向：$(1,-F_x/F_y)$（若 $F_y\\\\neq 0$），即斜率 $k=-F_x/F_y$。\n- 切线方程：$F_x(x_0,y_0)(x-x_0)+F_y(x_0,y_0)(y-y_0)=0$。\n- 法线：斜率为 $F_y/F_x$，方向为 $(F_x,F_y)=\\\\nabla F$（梯度方向）。\n**空间曲面 $F(x,y,z)=0$ 在 $(x_0,y_0,z_0)$ 处：**\n- **法向量**：$\\\\boldsymbol{n}=(F_x,F_y,F_z)$（梯度向量）。\n- **切平面**：$F_x(x-x_0)+F_y(y-y_0)+F_z(z-z_0)=0$。\n- **法线**：$\\\\dfrac{x-x_0}{F_x}=\\\\dfrac{y-y_0}{F_y}=\\\\dfrac{z-z_0}{F_z}$。\n**空间曲线**（参数式 $\\\\boldsymbol{r}(t)=(x(t),y(t),z(t))$ 在 $t_0$ 处）：\n- 切向量：$\\\\boldsymbol{r}'(t_0)=(x'(t_0),y'(t_0),z'(t_0))$。\n- 切线：$\\\\dfrac{x-x_0}{x'}=\\\\dfrac{y-y_0}{y'}=\\\\dfrac{z-z_0}{z'}$。\n- 法平面：$x'(x-x_0)+y'(y-y_0)+z'(z-z_0)=0$（过 $P_0$，垂直切向量）。\n**曲线由方程组确定** $F(x,y,z)=0,G(x,y,z)=0$：切向量 $=\\\\nabla F\\\\times\\\\nabla G$（两曲面法向量的叉积）。",
-      "textbookRefs": ["数学分析（第5版）下册 §18.3"],
+      "textbookRefs": [
+        "数学分析（第5版）下册 §18.3"
+      ],
       "keyDefinitions": [
         {
           "term": "曲面的切平面",
@@ -114,7 +125,10 @@
         "切平面法向量是 $\\\\nabla F$（不是 $-\\\\nabla F$），两者都垂直于切平面，方向不同",
         "空间曲线的切线方向是 $\\\\nabla F\\\\times\\\\nabla G$（两法向量叉积），不是 $\\\\nabla F$ 或 $\\\\nabla G$ 本身"
       ],
-      "exerciseIds": ["ift-ex-004", "ift-ex-005"],
+      "exerciseIds": [
+        "ift-ex-004",
+        "ift-ex-005"
+      ],
       "diagramIds": [],
       "masteryCriteria": [
         "能求给定曲面在指定点的切平面和法线方程",
@@ -132,7 +146,9 @@
         "能将实际优化问题建模并求解"
       ],
       "coreExplanation": "**条件极值**：求 $f(x,y)$ 在约束 $g(x,y)=0$ 下的极值。\n**几何直觉**：极值点处，$\\\\nabla f$ 与 $\\\\nabla g$（约束曲线法向量）平行（即 $f$ 的等值线与约束曲线相切）。\n**Lagrange 乘数法**：引入参数 $\\\\lambda$（Lagrange 乘子），极值点满足\n$$\\\\nabla f=\\\\lambda\\\\nabla g,\\\\quad g(x,y)=0,$$\n即三个方程：$f_x=\\\\lambda g_x$，$f_y=\\\\lambda g_y$，$g=0$。\n**多约束推广**：两约束 $g_1=0,g_2=0$，引入两乘子 $\\\\lambda_1,\\\\lambda_2$：$\\\\nabla f=\\\\lambda_1\\\\nabla g_1+\\\\lambda_2\\\\nabla g_2$。\n**实际判断极值**：Lagrange 方程的解是**候选极值点**，需比较所有候选点的函数值，最大/最小值即为极值（若问题有界则最值一定取到）。\n**典型应用**：等周问题（给定周长求最大面积），最短距离，椭圆上的极值，生产计划优化。",
-      "textbookRefs": ["数学分析（第5版）下册 §18.4"],
+      "textbookRefs": [
+        "数学分析（第5版）下册 §18.4"
+      ],
       "keyDefinitions": [
         {
           "term": "Lagrange 乘数法",
@@ -152,12 +168,17 @@
         "Lagrange 方程的解不一定都是极值点（可能是边界情形），需代入比较函数值",
         "问题中的 $\\\\lambda$ 是辅助变量，最终结果中不需要 $\\\\lambda$ 的值（除非题目要求）"
       ],
-      "exerciseIds": ["ift-ex-006", "ift-ex-007", "ift-ex-008"],
+      "exerciseIds": [
+        "ift-ex-006",
+        "ift-ex-007",
+        "ift-ex-008"
+      ],
       "diagramIds": [],
       "masteryCriteria": [
         "能用 Lagrange 乘数法建立方程组并求解条件极值",
         "能将等周问题、距离最短问题等建模为条件极值"
       ]
     }
-  ]
+  ],
+  "overview": "用 Jacobi 行列式保证隐函数的存在唯一性与可微性，推广到方程组情形，并应用于曲线/曲面的切线切平面和 Lagrange 条件极值法。"
 }
diff --git a/content/courses/math-analysis/chapters/improper-integral.json b/content/courses/math-analysis/chapters/improper-integral.json
index 643ed16..0f88ed1 100644
--- a/content/courses/math-analysis/chapters/improper-integral.json
+++ b/content/courses/math-analysis/chapters/improper-integral.json
@@ -15,7 +15,10 @@
         "能用 Newton-Leibniz 公式的推广计算反常积分"
       ],
       "coreExplanation": "**无穷限反常积分**：\n$$\\\\int_a^{+\\\\infty}f(x)\\,\\\\mathrm{d}x=\\\\lim_{b\\\\to+\\\\infty}\\\\int_a^b f(x)\\,\\\\mathrm{d}x,$$\n当极限存在（有限）时称收敛，否则称发散。类似定义 $\\\\int_{-\\\\infty}^b f$ 和 $\\\\int_{-\\\\infty}^{+\\\\infty}f$（后者须分拆为两段各自收敛）。\n**瑕积分（无界函数）**：若 $f$ 在 $[a,b)$ 上连续，$x\\\\to b^-$ 时 $|f(x)|\\\\to+\\\\infty$（$b$ 为**瑕点**），则\n$$\\\\int_a^b f(x)\\,\\\\mathrm{d}x=\\\\lim_{\\\\varepsilon\\\\to 0^+}\\\\int_a^{b-\\\\varepsilon}f(x)\\,\\\\mathrm{d}x.$$\n若瑕点在区间内部（如 $c\\\\in(a,b)$），须分拆：$\\\\int_a^b=\\\\int_a^c+\\\\int_c^b$，且两段均收敛时原积分才收敛。\n**计算方法**：若 $F$ 是 $f$ 的原函数且连续延拓到端点，则用广义 Newton-Leibniz：\n$$\\\\int_a^{+\\\\infty}f\\,\\\\mathrm{d}x=[F(x)]_a^{+\\\\infty}=\\\\lim_{x\\\\to+\\\\infty}F(x)-F(a).$$\n**典型例子**：\n- $\\\\int_1^{+\\\\infty}\\\\frac{1}{x^p}\\\\,\\\\mathrm{d}x$：$p>1$ 时收敛，值为 $\\\\frac{1}{p-1}$；$p\\\\leq 1$ 时发散（含调和级数对应 $p=1$）。\n- $\\\\int_0^1\\\\frac{1}{x^p}\\,\\\\mathrm{d}x$：$p<1$ 时收敛，值为 $\\\\frac{1}{1-p}$；$p\\\\geq 1$ 时发散。\n- $\\\\int_0^{+\\\\infty}e^{-x}\\,\\\\mathrm{d}x=1$（标准指数积分）。",
-      "textbookRefs": ["数学分析（第5版）上册 §11.1", "数学分析（第5版）上册 §11.2"],
+      "textbookRefs": [
+        "数学分析（第5版）上册 §11.1",
+        "数学分析（第5版）上册 §11.2"
+      ],
       "keyDefinitions": [
         {
           "term": "收敛（反常积分）",
@@ -54,8 +57,13 @@
         "瑕点在区间内部时忘记分拆，直接用 Newton-Leibniz 可能漏掉发散",
         "误认为 $\\\\int_a^{+\\\\infty}f\\,\\\\mathrm{d}x$ 收敛则 $f(x)\\\\to 0$（必要但不充分——见 $f(x)=\\\\sin(x^2)$ 的振幅不趋零但积分收敛）"
       ],
-      "exerciseIds": ["imp-ex-001", "imp-ex-002"],
-      "diagramIds": ["improper-integral-concept-diagram"],
+      "exerciseIds": [
+        "imp-ex-001",
+        "imp-ex-002"
+      ],
+      "diagramIds": [
+        "improper-integral-concept-diagram"
+      ],
       "masteryCriteria": [
         "能用极限定义判断 $\\\\int_1^\\\\infty x^{-p}$、$\\\\int_0^1 x^{-p}$ 的收敛性",
         "能识别并分拆含内部瑕点的积分"
@@ -73,7 +81,9 @@
         "能综合运用各判别法判断反常积分的收敛性"
       ],
       "coreExplanation": "**正值函数的比较判别法**：设 $0\\\\leq f(x)\\\\leq g(x)$，$x\\\\geq a$。\n- 若 $\\\\int_a^{+\\\\infty}g$ 收敛，则 $\\\\int_a^{+\\\\infty}f$ 收敛。\n- 若 $\\\\int_a^{+\\\\infty}f$ 发散，则 $\\\\int_a^{+\\\\infty}g$ 发散。\n**极限比较判别法**：设 $f,g\\\\geq 0$，$\\\\lim_{x\\\\to+\\\\infty}\\\\frac{f(x)}{g(x)}=L$。\n- $0<L<+\\\\infty$：$\\\\int f$ 与 $\\\\int g$ 同敛散。\n- $L=0$：$\\\\int g$ 收敛 $\\\\Rightarrow$ $\\\\int f$ 收敛。\n- $L=+\\\\infty$：$\\\\int g$ 发散 $\\\\Rightarrow$ $\\\\int f$ 发散。\n常用参考：$\\\\int_1^{+\\\\infty}x^{-p}$ 及 $\\\\int_0^1 x^{-p}$（$p$ 积分）。\n**Dirichlet 判别法**：$\\\\int_a^{+\\\\infty}f(x)g(x)\\,\\\\mathrm{d}x$ 收敛，若：$F(x)=\\\\int_a^x f(t)\\,\\\\mathrm{d}t$ 有界，且 $g(x)$ 单调趋于零。\n**Abel 判别法**：$\\\\int_a^{+\\\\infty}f(x)g(x)\\,\\\\mathrm{d}x$ 收敛，若：$\\\\int_a^{+\\\\infty}f$ 收敛，且 $g(x)$ 单调有界。\n典型：$\\\\int_1^{+\\\\infty}\\\\frac{\\\\sin x}{x}\\,\\\\mathrm{d}x$ 收敛（Dirichlet：$|\\\\int\\\\sin|\\\\leq 2$，$1/x\\\\downarrow 0$），但 $\\\\int_1^{+\\\\infty}\\\\left|\\\\frac{\\\\sin x}{x}\\\\right|\\,\\\\mathrm{d}x$ 发散（条件收敛）。",
-      "textbookRefs": ["数学分析（第5版）上册 §11.3"],
+      "textbookRefs": [
+        "数学分析（第5版）上册 §11.3"
+      ],
       "keyDefinitions": [
         {
           "term": "绝对收敛",
@@ -110,7 +120,11 @@
         "极限比较中 $L=0$ 时只能用\"$\\\\int g$ 收敛推 $\\\\int f$ 收敛\"，反向不成立",
         "误认为被积函数趋零就能推出反常积分收敛（$1/x$ 趋零但 $\\\\int 1/x$ 发散）"
       ],
-      "exerciseIds": ["imp-ex-003", "imp-ex-004", "imp-ex-005"],
+      "exerciseIds": [
+        "imp-ex-003",
+        "imp-ex-004",
+        "imp-ex-005"
+      ],
       "diagramIds": [],
       "masteryCriteria": [
         "能用比较判别法或极限比较法判断正值反常积分的收敛性",
@@ -128,7 +142,9 @@
         "了解 Gaussian 积分 $\\\\int_0^{+\\\\infty}e^{-x^2}\\,\\\\mathrm{d}x=\\\\frac{\\\\sqrt{\\\\pi}}{2}$（结论，证明不要求）"
       ],
       "coreExplanation": "**Gamma 函数**：$\\\\Gamma(s)=\\\\int_0^{+\\\\infty}x^{s-1}e^{-x}\\,\\\\mathrm{d}x$（$s>0$）。\n该积分在 $x=0$ 处可能为瑕积分（$s<1$ 时），在 $x\\\\to+\\\\infty$ 时为无穷限积分，需验证两端均收敛（$s>0$）。\n**递推公式**：$\\\\Gamma(s+1)=s\\\\Gamma(s)$（用分部积分：$\\\\int_0^\\\\infty x^s e^{-x}\\,\\\\mathrm{d}x$，令 $u=x^s$，$\\\\mathrm{d}v=e^{-x}\\,\\\\mathrm{d}x$）。\n**特殊值**：\n- $\\\\Gamma(1)=\\\\int_0^\\\\infty e^{-x}\\,\\\\mathrm{d}x=1$\n- 由递推：$\\\\Gamma(n+1)=n!$（$n\\\\in\\\\mathbb{N}$），故 Gamma 函数是阶乘的连续推广\n- $\\\\Gamma(1/2)=\\\\sqrt{\\\\pi}$（需用 Gaussian 积分），从而 $\\\\Gamma(3/2)=\\\\frac{1}{2}\\\\Gamma(1/2)=\\\\frac{\\\\sqrt{\\\\pi}}{2}$\n**Gaussian 积分**（结论）：$\\\\int_0^{+\\\\infty}e^{-x^2}\\\\,\\\\mathrm{d}x=\\\\frac{\\\\sqrt{\\\\pi}}{2}$（令 $x^2=t$ 化为 $\\\\frac{1}{2}\\\\Gamma(1/2)=\\\\frac{\\\\sqrt{\\\\pi}}{2}$）。完整证明需要重积分，在二重积分章节再给出。",
-      "textbookRefs": ["数学分析（第5版）上册 §11.4"],
+      "textbookRefs": [
+        "数学分析（第5版）上册 §11.4"
+      ],
       "keyDefinitions": [
         {
           "term": "Gamma 函数",
@@ -154,12 +170,17 @@
         "将 $\\\\Gamma(n)$ 与 $n!$ 混淆：$\\\\Gamma(n+1)=n!$（差一个）",
         "直接计算 $\\\\int_0^\\\\infty e^{-x^2}\\,\\\\mathrm{d}x$ 时，不能用初等方法求原函数——需要用 Gamma 函数或重积分"
       ],
-      "exerciseIds": ["imp-ex-006", "imp-ex-007", "imp-ex-008"],
+      "exerciseIds": [
+        "imp-ex-006",
+        "imp-ex-007",
+        "imp-ex-008"
+      ],
       "diagramIds": [],
       "masteryCriteria": [
         "能利用递推公式计算 $\\\\Gamma(n+1/2)$ 等特殊值",
         "能将 $\\\\int_0^\\\\infty x^n e^{-x}\\,\\\\mathrm{d}x$ 等积分化为 $\\\\Gamma$ 函数并计算"
       ]
     }
-  ]
+  ],
+  "overview": "将定积分推广到无穷区间与无界被积函数的情形，建立比较判别法、Cauchy 判别法等收敛理论，并深入研究 Gamma 函数与 Beta 函数。"
 }
diff --git a/content/courses/math-analysis/chapters/indefinite-integral.json b/content/courses/math-analysis/chapters/indefinite-integral.json
index dd61850..c018d5e 100644
--- a/content/courses/math-analysis/chapters/indefinite-integral.json
+++ b/content/courses/math-analysis/chapters/indefinite-integral.json
@@ -4,7 +4,7 @@
   "volumeId": "math-analysis-volume-1",
   "number": 8,
   "title": "不定积分",
-  "status": "draft",
+  "status": "sample-ready",
   "overview": "不定积分是导数的逆运算，也是下一章定积分计算的算法工具箱。本章先建立原函数（不定积分）的概念和基本性质，给出一张基本积分公式表；再系统讲授两种核心积分技法：换元积分法（用拼凑或正弦/有理式换元化简被积函数）和分部积分法（$\\\\int u\\\\,\\\\mathrm{d}v=uv-\\\\int v\\\\,\\\\mathrm{d}u$，适合乘积形式的被积函数）；最后讨论有理函数的部分分式分解，以及三角函数有理式和无理函数积分的有理化技巧。讲义、例子与题面均为自编或充分改写，公式用 LaTeX（四反斜线约定）。",
   "knowledgePoints": [
     {
@@ -46,7 +46,7 @@
       ],
       "exampleIds": [],
       "exerciseIds": ["indef-ex-001"],
-      "diagramIds": [],
+      "diagramIds": ["antiderivative-family", "basic-integral-table"],
       "masteryCriteria": [
         "能陈述原函数的定义和」差为常数」的定理。",
         "能默写 10 个以上基本积分公式。"
@@ -91,7 +91,7 @@
       ],
       "exampleIds": [],
       "exerciseIds": ["indef-ex-002", "indef-ex-003"],
-      "diagramIds": [],
+      "diagramIds": ["trig-sub-triangle"],
       "masteryCriteria": [
         "能用凑微分法处理常见形式的不定积分。",
         "能对含根号的积分选择合适的三角换元并正确换回。"
diff --git a/content/courses/math-analysis/chapters/line-integrals.json b/content/courses/math-analysis/chapters/line-integrals.json
index 549ab90..781be70 100644
--- a/content/courses/math-analysis/chapters/line-integrals.json
+++ b/content/courses/math-analysis/chapters/line-integrals.json
@@ -14,7 +14,9 @@
         "理解第一型曲线积分与路径方向无关"
       ],
       "coreExplanation": "**定义**：$\\\\int_L f(x,y)\\,\\\\mathrm{d}s=\\\\lim_{\\\\lambda\\\\to 0}\\\\sum_i f(\\\\xi_i,\\\\eta_i)\\\\Delta s_i$（$\\\\Delta s_i$ 为弧长元素，$\\\\lambda$ 为最大弧长）。物理意义：密度为 $f(x,y)$ 的曲线的总质量。\n**计算方法（参数化）**：设曲线 $L$ 的参数方程 $x=x(t),y=y(t)$（$t\\\\in[\\\\alpha,\\\\beta]$），弧长元素 $\\\\mathrm{d}s=\\\\sqrt{x'^2(t)+y'^2(t)}\\,\\\\mathrm{d}t$，故\n$$\\\\int_L f(x,y)\\,\\\\mathrm{d}s=\\\\int_\\\\alpha^\\\\beta f(x(t),y(t))\\\\sqrt{x'^2(t)+y'^2(t)}\\,\\\\mathrm{d}t.$$\n**各种曲线形式**：\n- 直角坐标 $y=g(x)$（$x\\\\in[a,b]$）：$\\\\mathrm{d}s=\\\\sqrt{1+g'^2(x)}\\,\\\\mathrm{d}x$。\n- 极坐标 $r=r(\\\\theta)$（$\\\\theta\\\\in[\\\\alpha,\\\\beta]$）：$\\\\mathrm{d}s=\\\\sqrt{r^2+r'^2}\\,\\\\mathrm{d}\\\\theta$。\n- 空间曲线 $\\\\boldsymbol{r}(t)=(x,y,z)$：$\\\\mathrm{d}s=\\\\sqrt{x'^2+y'^2+z'^2}\\,\\\\mathrm{d}t$。\n**性质**：与路径方向无关（$\\\\int_L=\\\\int_{-L}$，其中 $-L$ 为反向）；线性性；可加性。",
-      "textbookRefs": ["数学分析（第5版）下册 §20.1"],
+      "textbookRefs": [
+        "数学分析（第5版）下册 §20.1"
+      ],
       "keyDefinitions": [
         {
           "term": "第一型曲线积分",
@@ -32,7 +34,10 @@
         "参数化后 $\\\\mathrm{d}s$ 始终为正（弧长元素），不受方向影响",
         "曲线分段时各段的参数方向不必统一（只要覆盖整条曲线）"
       ],
-      "exerciseIds": ["li-ex-001", "li-ex-002"],
+      "exerciseIds": [
+        "li-ex-001",
+        "li-ex-002"
+      ],
       "diagramIds": [],
       "masteryCriteria": [
         "能将第一型曲线积分参数化后化为定积分",
@@ -50,7 +55,9 @@
         "理解曲线积分与路径无关的条件（保守场，恰当微分）"
       ],
       "coreExplanation": "**第二型曲线积分**：$\\\\int_L P\\,\\\\mathrm{d}x+Q\\,\\\\mathrm{d}y=\\\\int_\\\\alpha^\\\\beta[P(x(t),y(t))x'(t)+Q(x(t),y(t))y'(t)]\\,\\\\mathrm{d}t$。\n物理意义：力场 $(P,Q)$ 沿曲线 $L$ 所做的功。**与方向有关**：$\\\\int_{-L}=-\\\\int_L$。\n**Green 公式**：设 $D$ 为有界闭区域，其边界 $\\\\partial D$ 的方向为正向（逆时针，使 $D$ 在左侧）。若 $P,Q$ 在 $D$ 上有连续偏导数，则\n$$\\\\oint_{\\\\partial D}P\\,\\\\mathrm{d}x+Q\\,\\\\mathrm{d}y=\\\\iint_D\\\\left(\\\\frac{\\\\partial Q}{\\\\partial x}-\\\\frac{\\\\partial P}{\\\\partial y}\\\\right)\\,\\\\mathrm{d}A.$$\n**应用**：(1) 用二重积分计算曲线积分（化简）；(2) 面积公式 $A=\\\\frac{1}{2}\\\\oint(x\\,\\\\mathrm{d}y-y\\,\\\\mathrm{d}x)$；(3) 补线法（添加辅助线使曲线封闭）。\n**路径无关条件**：在单连通区域 $D$ 内，以下等价：\n1. 曲线积分 $\\\\int_L P\\,\\\\mathrm{d}x+Q\\,\\\\mathrm{d}y$ 与路径无关（只与端点有关）。\n2. 对 $D$ 内任意闭曲线 $C$：$\\\\oint_C P\\,\\\\mathrm{d}x+Q\\,\\\\mathrm{d}y=0$。\n3. $D$ 内 $P_y=Q_x$（混合偏导数相等）。\n4. 存在 $u$ 使 $\\\\mathrm{d}u=P\\,\\\\mathrm{d}x+Q\\,\\\\mathrm{d}y$（恰当微分，$u$ 为势函数）。\n**势函数求法**：$u(x,y)=\\\\int_{x_0}^x P(t,y_0)\\,\\\\mathrm{d}t+\\\\int_{y_0}^y Q(x,t)\\,\\\\mathrm{d}t$（折线路径积分）。",
-      "textbookRefs": ["数学分析（第5版）下册 §20.2"],
+      "textbookRefs": [
+        "数学分析（第5版）下册 §20.2"
+      ],
       "keyDefinitions": [
         {
           "term": "第二型曲线积分",
@@ -80,13 +87,21 @@
         "Green 公式的 $Q_x-P_y$（不是 $P_x-Q_y$）：$\\\\partial Q/\\\\partial x$ 减 $\\\\partial P/\\\\partial y$",
         "路径无关条件 $P_y=Q_x$ 需要在**单连通**区域成立；若区域有\"洞\"（如原点被挖掉），条件要修改"
       ],
-      "exerciseIds": ["li-ex-003", "li-ex-004", "li-ex-005", "li-ex-006"],
-      "diagramIds": ["green-formula-diagram"],
+      "exerciseIds": [
+        "li-ex-003",
+        "li-ex-004",
+        "li-ex-005",
+        "li-ex-006"
+      ],
+      "diagramIds": [
+        "green-formula-diagram"
+      ],
       "masteryCriteria": [
         "能计算第二型曲线积分（直接参数化法）",
         "能应用 Green 公式化曲线积分为二重积分",
         "能判断曲线积分是否与路径无关并求势函数"
       ]
     }
-  ]
+  ],
+  "overview": "建立第一型（对弧长）与第二型（对坐标）两种曲线积分，以 Green 公式揭示平面上曲线与区域积分的联系，讨论路径无关性与势函数。"
 }
diff --git a/content/courses/math-analysis/chapters/multiple-integrals.json b/content/courses/math-analysis/chapters/multiple-integrals.json
index b8dc799..87ede7c 100644
--- a/content/courses/math-analysis/chapters/multiple-integrals.json
+++ b/content/courses/math-analysis/chapters/multiple-integrals.json
@@ -14,7 +14,9 @@
         "能根据区域形状选择合适的积分顺序"
       ],
       "coreExplanation": "**二重积分定义**：$\\\\iint_D f(x,y)\\,\\\\mathrm{d}A=\\\\lim_{\\\\lambda\\\\to 0}\\\\sum_i f(\\\\xi_i,\\\\eta_i)\\\\Delta A_i$（$\\\\Delta A_i$ 为小块面积，$\\\\lambda$ 为最大直径）。几何意义：$f\\\\geq 0$ 时为曲顶柱体的体积。\n**$X$-型区域**：$D=\\\\{(x,y):\\,a\\\\leq x\\\\leq b,\\\\,\\\\varphi_1(x)\\\\leq y\\\\leq\\\\varphi_2(x)\\\\}$，\n$$\\\\iint_D f\\,\\\\mathrm{d}A=\\\\int_a^b\\,\\\\mathrm{d}x\\\\int_{\\\\varphi_1(x)}^{\\\\varphi_2(x)}f(x,y)\\,\\\\mathrm{d}y.$$\n**$Y$-型区域**：$D=\\\\{(x,y):\\,c\\\\leq y\\\\leq d,\\\\,\\\\psi_1(y)\\\\leq x\\\\leq\\\\psi_2(y)\\\\}$，先对 $x$ 积分后对 $y$。\n**对称性简化**：\n- $D$ 关于 $y$ 轴对称，$f(-x,y)=-f(x,y)$（$x$ 的奇函数）：$\\\\iint_D f\\,\\\\mathrm{d}A=0$。\n- $D$ 关于 $y$ 轴对称，$f(-x,y)=f(x,y)$（$x$ 的偶函数）：$\\\\iint_D f=2\\\\iint_{D_+}f$。\n- $D$ 关于直线 $y=x$ 对称：$\\\\iint_D f(x,y)\\,\\\\mathrm{d}A=\\\\iint_D f(y,x)\\,\\\\mathrm{d}A$（换序不变）。",
-      "textbookRefs": ["数学分析（第5版）下册 §21.1—21.2"],
+      "textbookRefs": [
+        "数学分析（第5版）下册 §21.1—21.2"
+      ],
       "keyDefinitions": [
         {
           "term": "二重积分",
@@ -32,8 +34,13 @@
         "交换积分顺序时，积分限必须重新从区域 $D$ 的几何描述出发确定",
         "累次积分的内层积分视外层变量为常数，外层变量的范围由区域的外边界确定"
       ],
-      "exerciseIds": ["mi-ex-001", "mi-ex-002"],
-      "diagramIds": ["double-integral-region-diagram"],
+      "exerciseIds": [
+        "mi-ex-001",
+        "mi-ex-002"
+      ],
+      "diagramIds": [
+        "double-integral-region-diagram"
+      ],
       "masteryCriteria": [
         "能将给定区域化为 $X$-型或 $Y$-型并写出累次积分",
         "能交换积分顺序"
@@ -50,7 +57,9 @@
         "能判断何时使用极坐标或其他特殊坐标"
       ],
       "coreExplanation": "**极坐标变换**：$x=r\\\\cos\\\\theta,y=r\\\\sin\\\\theta$，Jacobi 行列式 $J=r$，故\n$$\\\\iint_D f(x,y)\\,\\\\mathrm{d}A=\\\\iint_{D'} f(r\\\\cos\\\\theta,r\\\\sin\\\\theta)\\\\cdot r\\,\\\\mathrm{d}r\\,\\\\mathrm{d}\\\\theta.$$\n（不要忘记额外的 $r$！）\n**极坐标适用场景**：被积函数含 $x^2+y^2$，或积分区域为圆、扇形、圆环等。\n**一般变量变换**：$x=x(u,v),y=y(u,v)$，Jacobi 行列式 $J=\\\\partial(x,y)/\\\\partial(u,v)=\\\\det\\\\begin{pmatrix}x_u&x_v\\\\\\\\y_u&y_v\\\\end{pmatrix}$，\n$$\\\\iint_D f(x,y)\\,\\\\mathrm{d}x\\,\\\\mathrm{d}y=\\\\iint_{D'}f(x(u,v),y(u,v))|J|\\,\\\\mathrm{d}u\\,\\\\mathrm{d}v.$$\n**常用变换**：椭圆 $x=ar\\\\cos\\\\theta,y=br\\\\sin\\\\theta$（$J=abr$）；仿射变换（线性变换，$J=$ 常数）。",
-      "textbookRefs": ["数学分析（第5版）下册 §21.4"],
+      "textbookRefs": [
+        "数学分析（第5版）下册 §21.4"
+      ],
       "keyDefinitions": [
         {
           "term": "极坐标面积元素",
@@ -74,7 +83,10 @@
         "极坐标忘记 $r$：面积元素是 $r\\,\\\\mathrm{d}r\\,\\\\mathrm{d}\\\\theta$，不是 $\\\\mathrm{d}r\\,\\\\mathrm{d}\\\\theta$",
         "极坐标的 $\\\\theta$ 范围和 $r$ 范围要与原区域 $D$ 对应，不一定是 $[0,2\\\\pi]\\\\times[0,R]$"
       ],
-      "exerciseIds": ["mi-ex-003", "mi-ex-004"],
+      "exerciseIds": [
+        "mi-ex-003",
+        "mi-ex-004"
+      ],
       "diagramIds": [],
       "masteryCriteria": [
         "能将圆形、扇形、圆环区域上的积分转化为极坐标计算",
@@ -92,7 +104,9 @@
         "掌握球坐标变换"
       ],
       "coreExplanation": "**三重积分**：$\\\\iiint_V f(x,y,z)\\,\\\\mathrm{d}V$，$\\\\mathrm{d}V=\\\\mathrm{d}x\\,\\\\mathrm{d}y\\,\\\\mathrm{d}z$。\n**投影法（$Z$-型区域）**：$\\\\iiint_V f\\,\\\\mathrm{d}V=\\\\iint_{D_{xy}}\\,\\\\mathrm{d}x\\,\\\\mathrm{d}y\\\\int_{z_1(x,y)}^{z_2(x,y)}f\\,\\\\mathrm{d}z$（先对 $z$ 积分，再对 $xy$ 平面做二重积分）。\n**截面法**：$\\\\iiint_V f\\,\\\\mathrm{d}V=\\\\int_a^b\\,\\\\mathrm{d}z\\\\iint_{D_z}f(x,y,z)\\,\\\\mathrm{d}x\\,\\\\mathrm{d}y$（先对截面 $D_z$ 做二重积分，再对 $z$ 积分）。\n**柱坐标**：$x=r\\\\cos\\\\theta,y=r\\\\sin\\\\theta,z=z$，$\\\\mathrm{d}V=r\\,\\\\mathrm{d}r\\,\\\\mathrm{d}\\\\theta\\,\\\\mathrm{d}z$（适用于圆柱对称区域）。\n**球坐标**：$x=\\\\rho\\\\sin\\\\varphi\\\\cos\\\\theta,y=\\\\rho\\\\sin\\\\varphi\\\\sin\\\\theta,z=\\\\rho\\\\cos\\\\varphi$（$\\\\rho\\\\geq 0,\\\\varphi\\\\in[0,\\\\pi],\\\\theta\\\\in[0,2\\\\pi]$），$\\\\mathrm{d}V=\\\\rho^2\\\\sin\\\\varphi\\,\\\\mathrm{d}\\\\rho\\,\\\\mathrm{d}\\\\varphi\\,\\\\mathrm{d}\\\\theta$（适用于球、锥等球对称区域）。\n**应用**：\n- 体积：$V=\\\\iiint_D\\,\\\\mathrm{d}V$；质量：$m=\\\\iiint_D\\\\rho(x,y,z)\\,\\\\mathrm{d}V$。\n- 质心：$\\\\bar{x}=\\\\iiint x\\\\rho\\,\\\\mathrm{d}V/m$。\n- 转动惯量（对 $z$ 轴）：$I_z=\\\\iiint(x^2+y^2)\\\\rho\\,\\\\mathrm{d}V$。",
-      "textbookRefs": ["数学分析（第5版）下册 §21.5—21.6"],
+      "textbookRefs": [
+        "数学分析（第5版）下册 §21.5—21.6"
+      ],
       "keyDefinitions": [
         {
           "term": "球坐标体积元素",
@@ -112,12 +126,16 @@
         "球坐标 $\\\\varphi$（极角）从 $z$ 轴算起，范围 $[0,\\\\pi]$（不是 $[0,2\\\\pi]$）",
         "Jacobi $=\\\\rho^2\\\\sin\\\\varphi$（不是 $\\\\rho^2$），$\\\\sin\\\\varphi$ 在 $\\\\varphi\\\\in[0,\\\\pi]$ 上非负，无需绝对值"
       ],
-      "exerciseIds": ["mi-ex-005", "mi-ex-006"],
+      "exerciseIds": [
+        "mi-ex-005",
+        "mi-ex-006"
+      ],
       "diagramIds": [],
       "masteryCriteria": [
         "能用柱坐标或球坐标计算三重积分",
         "能用重积分求几何体的体积和质心"
       ]
     }
-  ]
+  ],
+  "overview": "从二重积分出发建立化累次积分、极坐标换元与一般变量替换（Jacobi 行列式）方法，推广至三重积分，计算体积、质量等几何量。"
 }
diff --git a/content/courses/math-analysis/chapters/multivariable-differential.json b/content/courses/math-analysis/chapters/multivariable-differential.json
index d1f590f..64b77c9 100644
--- a/content/courses/math-analysis/chapters/multivariable-differential.json
+++ b/content/courses/math-analysis/chapters/multivariable-differential.json
@@ -14,7 +14,9 @@
         "掌握高阶偏导数，特别是混合偏导数的相等条件"
       ],
       "coreExplanation": "**偏导数**：$f_x(x_0,y_0)=\\\\lim_{\\\\Delta x\\\\to 0}\\\\frac{f(x_0+\\\\Delta x,y_0)-f(x_0,y_0)}{\\\\Delta x}$（固定 $y$，对 $x$ 求导）。记法：$\\\\partial f/\\\\partial x$，$f_x$，$D_1f$。\n**可微性（全微分）**：$f$ 在 $(x_0,y_0)$ 可微 $\\\\iff$ $\\\\Delta f=f_x\\\\Delta x+f_y\\\\Delta y+o(\\\\sqrt{\\\\Delta x^2+\\\\Delta y^2})$（增量可以线性近似）。全微分 $\\\\mathrm{d}f=f_x\\,\\\\mathrm{d}x+f_y\\,\\\\mathrm{d}y$。\n**可微 vs 偏导数存在**：\n- 可微 $\\\\Rightarrow$ 偏导数存在（反之不真）。\n- 偏导数存在**且连续** $\\\\Rightarrow$ 可微（充分条件，较强但常用）。\n- 可微 $\\\\Rightarrow$ 连续；偏导数存在 $\\\\not\\\\Rightarrow$ 连续。\n**高阶偏导数**：$f_{xy}=\\\\frac{\\\\partial^2 f}{\\\\partial y\\\\partial x}$（先对 $x$，再对 $y$）。\n**混合偏导数相等定理**：若 $f_{xy}$ 和 $f_{yx}$ 在 $(x_0,y_0)$ 处都连续，则 $f_{xy}(x_0,y_0)=f_{yx}(x_0,y_0)$。\n**应用：切平面与法线**：可微函数 $z=f(x,y)$ 在 $(x_0,y_0,z_0)$ 处的切平面方程：$z-z_0=f_x(x_0,y_0)(x-x_0)+f_y(x_0,y_0)(y-y_0)$；法线方向向量 $(-f_x,-f_y,1)$。",
-      "textbookRefs": ["数学分析（第5版）下册 §17.1"],
+      "textbookRefs": [
+        "数学分析（第5版）下册 §17.1"
+      ],
       "keyDefinitions": [
         {
           "term": "全微分",
@@ -44,7 +46,10 @@
         "混淆偏导数存在（弱）和可微（强）：存在但不可微的函数有经典例子",
         "高阶混合偏导数：$f_{xy}$ 是先对 $x$ 后对 $y$（某些教材顺序相反），注意符号约定"
       ],
-      "exerciseIds": ["mvd-ex-001", "mvd-ex-002"],
+      "exerciseIds": [
+        "mvd-ex-001",
+        "mvd-ex-002"
+      ],
       "diagramIds": [],
       "masteryCriteria": [
         "能计算多元函数的偏导数和全微分",
@@ -62,7 +67,9 @@
         "能处理含隐函数的微分（直接法和公式法）"
       ],
       "coreExplanation": "**链式法则（基本形式）**：若 $z=f(u,v)$，$u=u(x,y)$，$v=v(x,y)$，则\n$$\\\\frac{\\\\partial z}{\\\\partial x}=\\\\frac{\\\\partial f}{\\\\partial u}\\\\frac{\\\\partial u}{\\\\partial x}+\\\\frac{\\\\partial f}{\\\\partial v}\\\\frac{\\\\partial v}{\\\\partial x},\\\\quad\\\\frac{\\\\partial z}{\\\\partial y}=\\\\frac{\\\\partial f}{\\\\partial u}\\\\frac{\\\\partial u}{\\\\partial y}+\\\\frac{\\\\partial f}{\\\\partial v}\\\\frac{\\\\partial v}{\\\\partial y}.$$\n**全导数**：若 $z=f(x,y(x))$，则 $\\\\frac{\\\\mathrm{d}z}{\\\\mathrm{d}x}=f_x+f_y\\\\frac{\\\\mathrm{d}y}{\\\\mathrm{d}x}$。\n**全微分形式不变性**：无论 $x,y$ 是自变量还是中间变量，$\\\\mathrm{d}f=f_x\\,\\\\mathrm{d}x+f_y\\,\\\\mathrm{d}y$ 形式不变（与一元相同）。\n**隐函数微分（直接法）**：$F(x,y)=0$ 两边对 $x$ 求导，$F_x+F_y\\\\frac{\\\\mathrm{d}y}{\\\\mathrm{d}x}=0$，得 $\\\\mathrm{d}y/\\\\mathrm{d}x=-F_x/F_y$（$F_y\\\\neq 0$）。二元 $F(x,y,z)=0$：$\\\\partial z/\\\\partial x=-F_x/F_z$，$\\\\partial z/\\\\partial y=-F_y/F_z$。\n**常用变量变换**：极坐标 $x=r\\\\cos\\\\theta,y=r\\\\sin\\\\theta$ 时，利用链式法则得 $\\\\partial/\\\\partial r$ 和 $\\\\partial/\\\\partial\\\\theta$ 的表达式。",
-      "textbookRefs": ["数学分析（第5版）下册 §17.2"],
+      "textbookRefs": [
+        "数学分析（第5版）下册 §17.2"
+      ],
       "keyDefinitions": [
         {
           "term": "全微分形式不变性",
@@ -82,7 +89,10 @@
         "链式法则中遗漏某个中间变量的贡献（尤其是 $z=f(u,v,x)$ 有直接依赖 $x$ 项）",
         "隐函数公式 $\\\\partial z/\\\\partial x=-F_x/F_z$：注意是 $-F_x/F_z$（有负号），$F_z\\\\neq 0$"
       ],
-      "exerciseIds": ["mvd-ex-003", "mvd-ex-004"],
+      "exerciseIds": [
+        "mvd-ex-003",
+        "mvd-ex-004"
+      ],
       "diagramIds": [],
       "masteryCriteria": [
         "能对各种复合结构用链式法则求偏导数",
@@ -100,7 +110,9 @@
         "理解梯度方向是函数增长最快的方向"
       ],
       "coreExplanation": "**方向导数**：$f$ 在 $(x_0,y_0)$ 沿方向 $\\\\boldsymbol{l}=(\\\\cos\\\\alpha,\\\\cos\\\\beta)$（单位向量）的方向导数：\n$$\\\\frac{\\\\partial f}{\\\\partial\\\\boldsymbol{l}}=\\\\lim_{t\\\\to 0^+}\\\\frac{f(x_0+t\\\\cos\\\\alpha,y_0+t\\\\cos\\\\beta)-f(x_0,y_0)}{t}.$$\n若 $f$ 在 $(x_0,y_0)$ 可微，则 $\\\\frac{\\\\partial f}{\\\\partial\\\\boldsymbol{l}}=f_x\\\\cos\\\\alpha+f_y\\\\cos\\\\beta$（与方向余弦的内积）。\n**梯度**：$\\\\nabla f=\\\\mathrm{grad}\\\\,f=(f_x,f_y)$（向量）。方向导数 $\\\\partial f/\\\\partial\\\\boldsymbol{l}=\\\\nabla f\\\\cdot\\\\boldsymbol{l}=|\\\\nabla f|\\\\cos\\\\varphi$（$\\\\varphi$ 是 $\\\\boldsymbol{l}$ 与梯度的夹角）。\n**梯度的几何意义**：\n- $\\\\varphi=0$（沿梯度方向）时方向导数最大，等于 $|\\\\nabla f|$。\n- $\\\\varphi=\\\\pi$（逆梯度）时方向导数最小（最负）。\n- $\\\\varphi=\\\\pi/2$（垂直梯度）时方向导数为零（沿等值线方向）。\n梯度方向垂直于等值线（曲面 $f=c$ 的切线），指向函数值增大方向。\n**$n$ 元推广**：$\\\\nabla f=(f_{x_1},\\\\ldots,f_{x_n})$，方向余弦 $(\\\\cos\\\\alpha_1,\\\\ldots,\\\\cos\\\\alpha_n)$（$\\\\sum\\\\cos^2\\\\alpha_i=1$）。",
-      "textbookRefs": ["数学分析（第5版）下册 §17.3"],
+      "textbookRefs": [
+        "数学分析（第5版）下册 §17.3"
+      ],
       "keyDefinitions": [
         {
           "term": "梯度",
@@ -126,8 +138,13 @@
         "方向导数公式要求 $\\\\boldsymbol{l}$ 为**单位**向量；若给的方向向量不是单位向量，需先规范化",
         "方向导数不一定等于偏导数——偏导数是沿坐标轴方向的特殊情形"
       ],
-      "exerciseIds": ["mvd-ex-005", "mvd-ex-006"],
-      "diagramIds": ["gradient-diagram"],
+      "exerciseIds": [
+        "mvd-ex-005",
+        "mvd-ex-006"
+      ],
+      "diagramIds": [
+        "gradient-diagram"
+      ],
       "masteryCriteria": [
         "能计算给定点处沿任意方向的方向导数",
         "能求函数的梯度并确定最大增长方向"
@@ -144,7 +161,9 @@
         "能求二元函数的极值"
       ],
       "coreExplanation": "**二元函数 Taylor 公式（二阶）**：$f(x_0+h,y_0+k)=f(x_0,y_0)+(f_xh+f_yk)+\\\\frac{1}{2}(f_{xx}h^2+2f_{xy}hk+f_{yy}k^2)+O(r^3)$（$r=\\\\sqrt{h^2+k^2}$）。\n**极值的必要条件**：若 $(x_0,y_0)$ 是极值点，则 $f_x(x_0,y_0)=0$，$f_y(x_0,y_0)=0$（驻点）。\n**极值的充分条件**：设 $(x_0,y_0)$ 是驻点，令 $A=f_{xx}$，$B=f_{xy}$，$C=f_{yy}$（均在 $(x_0,y_0)$ 处），$\\\\Delta=B^2-AC$：\n- $\\\\Delta<0$，$A<0$：极大值。\n- $\\\\Delta<0$，$A>0$：极小值。\n- $\\\\Delta>0$：鞍点（非极值）。\n- $\\\\Delta=0$：无法判断，需进一步分析。\n**Hessian 矩阵**：$H=\\\\begin{pmatrix}f_{xx}&f_{xy}\\\\\\\\f_{yx}&f_{yy}\\\\end{pmatrix}$，判别式 $\\\\Delta=f_{xy}^2-f_{xx}f_{yy}=-\\\\det H$。$\\\\det H>0$ 时二次型不定（鞍点）；$\\\\det H<0$ 时正定（极小）或负定（极大）。",
-      "textbookRefs": ["数学分析（第5版）下册 §17.4"],
+      "textbookRefs": [
+        "数学分析（第5版）下册 §17.4"
+      ],
       "keyDefinitions": [
         {
           "term": "驻点",
@@ -174,12 +193,16 @@
         "充分条件中 $\\\\Delta=B^2-AC$（不是 $AC-B^2$）；$\\\\Delta<0$ 时有极值",
         "驻点 $\\\\neq$ 极值点：鞍点也是驻点，需通过 $\\\\Delta$ 进一步判断"
       ],
-      "exerciseIds": ["mvd-ex-007", "mvd-ex-008"],
+      "exerciseIds": [
+        "mvd-ex-007",
+        "mvd-ex-008"
+      ],
       "diagramIds": [],
       "masteryCriteria": [
         "能求二元函数的驻点并用判别式确定极值类型",
         "能区分极值点和鞍点"
       ]
     }
-  ]
+  ],
+  "overview": "引入偏导数与全微分，以链式法则处理复合微分，引进方向导数与梯度，建立多元 Taylor 公式与无约束极值的充要条件。"
 }
diff --git a/content/courses/math-analysis/chapters/multivariable-limit-continuity.json b/content/courses/math-analysis/chapters/multivariable-limit-continuity.json
index dfd817b..eabc63e 100644
--- a/content/courses/math-analysis/chapters/multivariable-limit-continuity.json
+++ b/content/courses/math-analysis/chapters/multivariable-limit-continuity.json
@@ -14,7 +14,9 @@
         "掌握多元函数的定义域、值域和定义方式"
       ],
       "coreExplanation": "**平面点集基本概念**：\n- **$\\\\delta$ 邻域**：$U(P_0,\\\\delta)=\\\\{P:\\\\,|PP_0|<\\\\delta\\\\}$（以 $P_0$ 为中心、$\\\\delta$ 为半径的开圆盘）。\n- **内点**：存在 $\\\\delta>0$ 使 $U(P_0,\\\\delta)\\\\subset E$；**外点**：存在 $\\\\delta>0$ 使 $U(P_0,\\\\delta)\\\\cap E=\\\\emptyset$；**边界点**：任意 $\\\\delta>0$，$U(P_0,\\\\delta)$ 中既有 $E$ 的点也有 $E$ 的补集的点。\n- **开集**：每个点都是内点；**闭集**：包含所有边界点（等价：补集为开集）。\n- **有界集**：$\\\\exists M>0$ 使 $E\\\\subset U(O,M)$；**无界集**：非有界集。\n- **连通集**：$E$ 中任意两点可用 $E$ 内折线连接。\n- **区域（开区域）**：连通的开集；**闭区域**：开区域加上其边界。\n**多元函数**：$f:D\\\\to\\\\mathbb{R}$（$D\\\\subset\\\\mathbb{R}^2$），记 $z=f(x,y)$，$(x,y)\\\\in D$。$n$ 元函数 $u=f(x_1,\\\\ldots,x_n)$ 类似定义。**定义域**通常为使表达式有意义的最大集合（自然域）。",
-      "textbookRefs": ["数学分析（第5版）下册 §16.1"],
+      "textbookRefs": [
+        "数学分析（第5版）下册 §16.1"
+      ],
       "keyDefinitions": [
         {
           "term": "平面区域",
@@ -36,7 +38,9 @@
         "混淆\"边界点属于集合\"（闭集性质）与\"边界点的定义\"（无论属否，均称边界点）",
         "$\\\\mathbb{R}^2$ 中的开集不要求\"不含端点\"——这是一维的直觉，应用邻域定义"
       ],
-      "exerciseIds": ["mvlc-ex-001"],
+      "exerciseIds": [
+        "mvlc-ex-001"
+      ],
       "diagramIds": [],
       "masteryCriteria": [
         "能判断给定点集的内点、外点、边界点",
@@ -54,7 +58,9 @@
         "掌握极限不存在的证明方法（取不同路径）"
       ],
       "coreExplanation": "**二元函数极限定义**：\n$$\\\\lim_{(x,y)\\\\to(x_0,y_0)}f(x,y)=A \\\\iff \\\\forall\\\\varepsilon>0,\\\\,\\\\exists\\\\delta>0:\\\\,0<\\\\sqrt{(x-x_0)^2+(y-y_0)^2}<\\\\delta\\\\Rightarrow|f(x,y)-A|<\\\\varepsilon.$$\n**关键区别**：$(x,y)\\\\to(x_0,y_0)$ 意味着点 $(x,y)$ 以**任意方式**趋近 $(x_0,y_0)$，不仅是沿坐标轴方向。\n**极限不存在的证明**：若沿两条不同路径的极限值不同，则极限不存在。常用路径：直线 $y=kx$，抛物线 $y=kx^2$，曲线 $y=x^n$。\n**注意**：沿所有直线 $y=kx$ 的极限相同，**不能**断定极限存在（可能沿更复杂路径不同）。\n**极限的运算**：若 $\\\\lim f=A$，$\\\\lim g=B$，则 $f\\\\pm g,fg,f/g$（$B\\\\neq 0$）的极限成立，规则与一元相同。\n**夹逼原理**：若 $g\\\\leq f\\\\leq h$ 且 $\\\\lim g=\\\\lim h=A$，则 $\\\\lim f=A$。常用不等式：$|xy|\\\\leq(x^2+y^2)/2$，$|\\\\sin t|\\\\leq|t|$，$\\\\sqrt{x^2+y^2}\\\\geq|x|,|y|$。",
-      "textbookRefs": ["数学分析（第5版）下册 §16.2"],
+      "textbookRefs": [
+        "数学分析（第5版）下册 §16.2"
+      ],
       "keyDefinitions": [
         {
           "term": "二元函数极限",
@@ -75,7 +81,10 @@
         "\"沿 $x\\\\to 0$（固定 $y$）和 $y\\\\to 0$（固定 $x$）的累次极限相等\"不等于二元极限存在",
         "用极坐标 $x=r\\\\cos\\\\theta,y=r\\\\sin\\\\theta$ 后表达式含 $\\\\theta$，需证明对所有 $\\\\theta$ 一致趋零"
       ],
-      "exerciseIds": ["mvlc-ex-002", "mvlc-ex-003"],
+      "exerciseIds": [
+        "mvlc-ex-002",
+        "mvlc-ex-003"
+      ],
       "diagramIds": [],
       "masteryCriteria": [
         "能用路径法证明二元极限不存在",
@@ -93,7 +102,9 @@
         "理解有界闭区域上连续函数的三大性质（有界性、最值定理、介值定理）"
       ],
       "coreExplanation": "**连续性定义**：$f$ 在 $(x_0,y_0)$ 连续 $\\\\iff$ $\\\\lim_{(x,y)\\\\to(x_0,y_0)}f(x,y)=f(x_0,y_0)$（极限存在且等于函数值）。\n**间断点**：极限不存在，或极限存在但不等于函数值，或函数无定义的点均为间断点（二元函数的间断点一般为曲线，而非孤立点）。\n**二元初等函数**：由 $x,y$ 的基本初等运算和初等函数（$e^x,\\\\ln x,\\\\sin x,\\\\ldots$）经有限次四则和复合构成，在其**定义域**内处处连续。求极限可直接代入（若为初等函数且在该点有定义）。\n**有界闭区域上的连续函数**：设 $D$ 为有界闭区域，$f:D\\\\to\\\\mathbb{R}$ 连续，则：\n1. **有界性定理**：$f$ 在 $D$ 上有界（$\\\\exists M:\\,|f|\\\\leq M$）。\n2. **最值定理（最大最小值定理）**：$f$ 在 $D$ 上能取到最大值和最小值。\n3. **介值定理**：若 $m=\\\\min f$，$M=\\\\max f$，则对任意 $c\\\\in[m,M]$，存在 $P\\\\in D$ 使 $f(P)=c$。\n这三个定理是一元连续函数对应定理的推广，证明依赖于 $\\\\mathbb{R}^n$ 中有界闭集的紧致性（Heine-Borel）。",
-      "textbookRefs": ["数学分析（第5版）下册 §16.3"],
+      "textbookRefs": [
+        "数学分析（第5版）下册 §16.3"
+      ],
       "keyDefinitions": [
         {
           "term": "二元函数连续",
@@ -119,12 +130,16 @@
         "分段函数在分界曲线上的连续性需另外验证（不能仅靠两段各自是初等函数）",
         "\"$x=0$ 时 $f(0,y)=0$，$y=0$ 时 $f(x,0)=0$\"不能推出 $f$ 在原点连续"
       ],
-      "exerciseIds": ["mvlc-ex-004", "mvlc-ex-005"],
+      "exerciseIds": [
+        "mvlc-ex-004",
+        "mvlc-ex-005"
+      ],
       "diagramIds": [],
       "masteryCriteria": [
         "能判断二元函数在给定点的连续性",
         "能利用初等函数连续性直接代入求极限"
       ]
     }
-  ]
+  ],
+  "overview": "把 $\u000barepsilonhBc$delta$ 极限语言推广至二元函数：路径相关极限、连续的定义，以及有界闭域上的最值定理与一致连续性。"
 }
diff --git a/content/courses/math-analysis/chapters/numerical-series.json b/content/courses/math-analysis/chapters/numerical-series.json
index 07a9d3d..d9e82dd 100644
--- a/content/courses/math-analysis/chapters/numerical-series.json
+++ b/content/courses/math-analysis/chapters/numerical-series.json
@@ -15,7 +15,9 @@
         "了解级数的线性性质与去有限项不影响收敛性"
       ],
       "coreExplanation": "**定义**：给定数列 $\\\\{a_n\\\\}$，称 $\\\\sum_{n=1}^{\\\\infty}a_n=a_1+a_2+\\\\cdots$ 为**无穷级数**，前 $n$ 项和 $S_n=\\\\sum_{k=1}^n a_k$ 为**部分和**。若 $\\\\lim_{n\\\\to\\\\infty}S_n=S$（有限），则称级数**收敛**，$S$ 为其和；否则称**发散**。\n**收敛必要条件**：$\\\\sum a_n$ 收敛 $\\\\Rightarrow$ $\\\\lim_{n\\\\to\\\\infty}a_n=0$（逆命题不成立：调和级数 $\\\\sum 1/n$ 的通项趋零但发散）。\n**Cauchy 准则**：$\\\\sum a_n$ 收敛 $\\\\Leftrightarrow$ 对任意 $\\\\varepsilon>0$，$\\\\exists N$，$\\\\forall m>n>N$：$|a_{n+1}+\\\\cdots+a_m|<\\\\varepsilon$。\n**基本性质**：\n1. 线性性：若 $\\\\sum a_n=A$，$\\\\sum b_n=B$，则 $\\\\sum(\\\\alpha a_n+\\\\beta b_n)=\\\\alpha A+\\\\beta B$。\n2. 改变有限项：不影响级数的收敛性（但改变和值）。\n3. 加括号：收敛级数加括号后仍收敛，和不变。反之不成立（$(1-1)+(1-1)+\\\\cdots=0$ 但 $1-1+1-1+\\\\cdots$ 发散）。\n**典型级数**：\n- 等比级数 $\\\\sum_{n=0}^{\\\\infty}q^n=\\\\frac{1}{1-q}$（$|q|<1$ 收敛，$|q|\\\\geq 1$ 发散）\n- 调和级数 $\\\\sum_{n=1}^{\\\\infty}\\\\frac{1}{n}$ 发散（分组：$\\\\frac{1}{2}+\\\\frac{1}{3}+\\\\frac{1}{4}>\\\\frac{1}{2}$，$\\\\frac{1}{5}+\\\\cdots+\\\\frac{1}{8}>\\\\frac{1}{2}$，……）\n- $p$ 级数 $\\\\sum_{n=1}^{\\\\infty}\\\\frac{1}{n^p}$：$p>1$ 收敛，$p\\\\leq 1$ 发散",
-      "textbookRefs": ["数学分析（第5版）下册 §12.1"],
+      "textbookRefs": [
+        "数学分析（第5版）下册 §12.1"
+      ],
       "keyDefinitions": [
         {
           "term": "部分和",
@@ -51,8 +53,13 @@
         "对发散级数加括号得到收敛结果，误认为级数收敛",
         "级数相乘不等于积的级数（Cauchy 乘积需要至少一个绝对收敛）"
       ],
-      "exerciseIds": ["series-ex-001", "series-ex-002"],
-      "diagramIds": ["series-partial-sum-diagram"],
+      "exerciseIds": [
+        "series-ex-001",
+        "series-ex-002"
+      ],
+      "diagramIds": [
+        "series-partial-sum-diagram"
+      ],
       "masteryCriteria": [
         "能用部分和直接计算简单级数（等比、裂项）的和",
         "能用必要条件或 Cauchy 准则判断基本级数的收敛性"
@@ -70,7 +77,9 @@
         "了解积分判别法（Cauchy-Maclaurin）"
       ],
       "coreExplanation": "设 $a_n\\\\geq 0$（正项级数），$\\\\{S_n\\\\}$ 单调不减，收敛当且仅当有界。\n**比较判别法**：若 $0\\\\leq a_n\\\\leq b_n$，$\\\\sum b_n$ 收敛则 $\\\\sum a_n$ 收敛；$\\\\sum a_n$ 发散则 $\\\\sum b_n$ 发散。\n**极限比较**：若 $\\\\lim_{n\\\\to\\\\infty}\\\\frac{a_n}{b_n}=L$，$0<L<+\\\\infty$，则 $\\\\sum a_n$ 与 $\\\\sum b_n$ 同敛散。\n**比值判别法（D'Alembert）**：$\\\\lim_{n\\\\to\\\\infty}\\\\frac{a_{n+1}}{a_n}=r$。\n- $r<1$：$\\\\sum a_n$ 收敛\n- $r>1$：$\\\\sum a_n$ 发散\n- $r=1$：不确定\n**根值判别法（Cauchy）**：$\\\\lim_{n\\\\to\\\\infty}\\\\sqrt[n]{a_n}=r$，判断规则与比值判别相同。\n根值判别法比比值判别法更强（根值确定时比值也能确定，反之不然）。\n**积分判别法**：若 $f:[1,+\\\\infty)\\\\to[0,+\\\\infty)$ 单调递减，且 $a_n=f(n)$，则 $\\\\sum_{n=1}^\\\\infty a_n$ 与 $\\\\int_1^{+\\\\infty}f(x)\\,\\\\mathrm{d}x$ 同敛散。\n典型应用：$\\\\sum n^{-p}$ 由积分判别法（$\\\\int_1^\\\\infty x^{-p}$）得 $p>1$ 收敛，$p\\\\leq 1$ 发散。",
-      "textbookRefs": ["数学分析（第5版）下册 §12.2"],
+      "textbookRefs": [
+        "数学分析（第5版）下册 §12.2"
+      ],
       "keyDefinitions": [
         {
           "term": "正项级数",
@@ -107,7 +116,11 @@
         "比较判别法要求 $a_n,b_n\\\\geq 0$，对一般项级数须先取绝对值",
         "积分判别法只给出同敛散性，不能用来求级数的和"
       ],
-      "exerciseIds": ["series-ex-003", "series-ex-004", "series-ex-005"],
+      "exerciseIds": [
+        "series-ex-003",
+        "series-ex-004",
+        "series-ex-005"
+      ],
       "diagramIds": [],
       "masteryCriteria": [
         "能对含阶乘/指数的级数用比值判别法",
@@ -126,7 +139,9 @@
         "了解 Dirichlet 判别法和 Abel 判别法"
       ],
       "coreExplanation": "**交错级数**：形如 $\\\\sum_{n=1}^\\\\infty(-1)^{n-1}a_n$（$a_n>0$）的级数。\n**Leibniz 判别法**：若 $\\\\{a_n\\\\}$ 单调递减且 $a_n\\\\to 0$，则交错级数收敛，且余项估计 $|r_n|\\\\leq a_{n+1}$。\n典型：$\\\\sum_{n=1}^\\\\infty\\\\frac{(-1)^{n-1}}{n}=\\\\ln 2$（条件收敛）。\n**绝对收敛**：若 $\\\\sum|a_n|$ 收敛，则称 $\\\\sum a_n$ 绝对收敛，且 $\\\\sum a_n$ 也收敛。\n**条件收敛**：$\\\\sum a_n$ 收敛但 $\\\\sum|a_n|$ 发散。\n**绝对收敛 vs 条件收敛**：绝对收敛的级数可以任意重排项，和不变（Riemann 重排定理：条件收敛的级数可通过重排使和为任意值！）\n**Dirichlet 判别法（级数版）**：若 $A_n=\\\\sum_{k=1}^n a_k$ 有界，$\\\\{b_n\\\\}$ 单调趋零，则 $\\\\sum a_n b_n$ 收敛。\n**Abel 判别法（级数版）**：若 $\\\\sum a_n$ 收敛，$\\\\{b_n\\\\}$ 单调有界，则 $\\\\sum a_n b_n$ 收敛。",
-      "textbookRefs": ["数学分析（第5版）下册 §12.3"],
+      "textbookRefs": [
+        "数学分析（第5版）下册 §12.3"
+      ],
       "keyDefinitions": [
         {
           "term": "绝对收敛",
@@ -162,12 +177,18 @@
         "Leibniz 判别法要求 $\\\\{a_n\\\\}$ **单调**递减，仅 $a_n\\\\to 0$ 不够（$a_n$ 振荡趋零时不适用）",
         "混淆级数的 Dirichlet/Abel 判别法与反常积分版本（条件相同但对象不同）"
       ],
-      "exerciseIds": ["series-ex-006", "series-ex-007", "series-ex-008", "series-ex-009"],
+      "exerciseIds": [
+        "series-ex-006",
+        "series-ex-007",
+        "series-ex-008",
+        "series-ex-009"
+      ],
       "diagramIds": [],
       "masteryCriteria": [
         "能判断交错级数的收敛性，区分绝对/条件收敛",
         "能对含 $(-1)^n$ 的级数综合运用多种判别法"
       ]
     }
-  ]
+  ],
+  "overview": "以部分和数列的收敛性定义级数，建立正项级数（比较、比值、根值判别）与一般项级数（Leibniz、绝对收敛）的系统判别理论。"
 }
diff --git a/content/courses/math-analysis/chapters/parameter-integrals.json b/content/courses/math-analysis/chapters/parameter-integrals.json
index c898eb1..49280ea 100644
--- a/content/courses/math-analysis/chapters/parameter-integrals.json
+++ b/content/courses/math-analysis/chapters/parameter-integrals.json
@@ -14,7 +14,9 @@
         "掌握含参量积分的变限情形（上下限也依赖参数）"
       ],
       "coreExplanation": "**含参量正常积分**：$I(\\\\alpha)=\\\\int_a^b f(x,\\\\alpha)\\,\\\\mathrm{d}x$（$\\\\alpha$ 为参数，$a,b$ 固定）。\n**连续性**：若 $f(x,\\\\alpha)$ 在 $[a,b]\\\\times[\\\\alpha_1,\\\\alpha_2]$ 上连续，则 $I(\\\\alpha)$ 在 $[\\\\alpha_1,\\\\alpha_2]$ 上连续（可将 $\\\\lim$ 移入积分）。\n**可微性（Leibniz 积分法则）**：若 $f,f_\\\\alpha$ 在 $[a,b]\\\\times[\\\\alpha_1,\\\\alpha_2]$ 上连续，则 $I(\\\\alpha)$ 可微且\n$$I'(\\\\alpha)=\\\\int_a^b f_\\\\alpha(x,\\\\alpha)\\,\\\\mathrm{d}x.$$\n（积分号下求导：直接对参数 $\\\\alpha$ 求导移入积分。）\n**可积性**：$I(\\\\alpha)$ 在 $[\\\\alpha_1,\\\\alpha_2]$ 上可积，且可交换积分顺序：$\\\\int_{\\\\alpha_1}^{\\\\alpha_2}I(\\\\alpha)\\,\\\\mathrm{d}\\\\alpha=\\\\int_a^b\\,\\\\mathrm{d}x\\\\int_{\\\\alpha_1}^{\\\\alpha_2}f(x,\\\\alpha)\\,\\\\mathrm{d}\\\\alpha$（Fubini 定理，正常积分情形）。\n**变上限情形**：$I(\\\\alpha)=\\\\int_a^{\\\\varphi(\\\\alpha)}f(x,\\\\alpha)\\,\\\\mathrm{d}x$，则 $I'(\\\\alpha)=f(\\\\varphi(\\\\alpha),\\\\alpha)\\\\varphi'(\\\\alpha)+\\\\int_a^{\\\\varphi(\\\\alpha)}f_\\\\alpha(x,\\\\alpha)\\,\\\\mathrm{d}x$。",
-      "textbookRefs": ["数学分析（第5版）下册 §19.1"],
+      "textbookRefs": [
+        "数学分析（第5版）下册 §19.1"
+      ],
       "keyDefinitions": [
         {
           "term": "Leibniz 积分法则",
@@ -34,7 +36,10 @@
         "Leibniz 法则要求 $f_\\\\alpha$ 连续才能积分号下求导；若不连续需先验证",
         "变上限 $\\\\varphi(\\\\alpha)$ 时有额外项 $f(\\\\varphi(\\\\alpha),\\\\alpha)\\\\cdot\\\\varphi'(\\\\alpha)$（端点贡献）"
       ],
-      "exerciseIds": ["pi-ex-001", "pi-ex-002"],
+      "exerciseIds": [
+        "pi-ex-001",
+        "pi-ex-002"
+      ],
       "diagramIds": [],
       "masteryCriteria": [
         "能对含参量正常积分在积分号下求导",
@@ -52,7 +57,9 @@
         "掌握 Weierstrass M-检验、Dirichlet/Abel 判别法"
       ],
       "coreExplanation": "**含参量反常积分**：$I(\\\\alpha)=\\\\int_a^{+\\\\infty}f(x,\\\\alpha)\\,\\\\mathrm{d}x$（上限为无穷大，或被积函数有奇点）。\n**一致收敛定义**：$I(\\\\alpha)$ 在 $[\\\\alpha_1,\\\\alpha_2]$ 上**一致收敛** $\\\\iff$ $\\\\forall\\\\varepsilon>0,\\\\,\\\\exists A_0$，当 $A>A_0$ 时，对所有 $\\\\alpha\\\\in[\\\\alpha_1,\\\\alpha_2]$ 均有 $\\\\left|\\\\int_A^{+\\\\infty}f(x,\\\\alpha)\\,\\\\mathrm{d}x\\\\right|<\\\\varepsilon$（尾部对参数一致小）。\n**判别法**：\n- **Weierstrass M-检验**：若 $|f(x,\\\\alpha)|\\\\leq M(x)$ 且 $\\\\int_a^{+\\\\infty}M(x)\\,\\\\mathrm{d}x<\\\\infty$，则一致收敛（绝对且一致）。\n- **Dirichlet 判别法**：若 $F(x,\\\\alpha)=\\\\int_a^x f(t,\\\\alpha)\\,\\\\mathrm{d}t$ 一致有界，$g(x,\\\\alpha)$ 对 $x$ 单调趋零且一致，则 $\\\\int f\\\\cdot g$ 一致收敛。\n- **Abel 判别法**：若 $\\\\int f(x,\\\\alpha)$ 一致收敛，$g(x,\\\\alpha)$ 对 $x$ 单调且关于 $\\\\alpha$ 一致有界，则 $\\\\int f\\\\cdot g$ 一致收敛。\n**一致收敛的性质**：\n- **连续性**：若 $f(x,\\\\alpha)$ 连续且 $I(\\\\alpha)$ 一致收敛，则 $I(\\\\alpha)$ 连续。\n- **可微性**：若 $f_\\\\alpha$ 连续且 $\\\\int f_\\\\alpha$ 一致收敛，则 $I'(\\\\alpha)=\\\\int f_\\\\alpha\\,\\\\mathrm{d}x$（积分号下求导）。\n- **可积性**：一致收敛时可交换积分顺序。",
-      "textbookRefs": ["数学分析（第5版）下册 §19.2"],
+      "textbookRefs": [
+        "数学分析（第5版）下册 §19.2"
+      ],
       "keyDefinitions": [
         {
           "term": "含参量反常积分一致收敛",
@@ -76,7 +83,10 @@
         "非一致收敛时积分号下求导可能失效，要先验证一致收敛",
         "Dirichlet 判别法要求 $g\\\\to 0$ 且单调——两个条件缺一不可"
       ],
-      "exerciseIds": ["pi-ex-003", "pi-ex-004"],
+      "exerciseIds": [
+        "pi-ex-003",
+        "pi-ex-004"
+      ],
       "diagramIds": [],
       "masteryCriteria": [
         "能用 Weierstrass M-检验判断含参量反常积分的一致收敛性",
@@ -94,7 +104,9 @@
         "能用欧拉积分计算实际积分"
       ],
       "coreExplanation": "**Γ 函数**：$\\\\Gamma(s)=\\\\int_0^{+\\\\infty}x^{s-1}e^{-x}\\,\\\\mathrm{d}x$（$s>0$）。\n主要性质：$\\\\Gamma(s+1)=s\\\\Gamma(s)$，$\\\\Gamma(1)=1$，$\\\\Gamma(n+1)=n!$，$\\\\Gamma(1/2)=\\\\sqrt{\\\\pi}$。\n\n**B 函数**：$B(p,q)=\\\\int_0^1 t^{p-1}(1-t)^{q-1}\\,\\\\mathrm{d}t$（$p,q>0$）。\n对称性：$B(p,q)=B(q,p)$。等价表示：$B(p,q)=\\\\int_0^{+\\\\infty}\\\\frac{u^{p-1}}{(1+u)^{p+q}}\\,\\\\mathrm{d}u$（令 $t=u/(1+u)$）。\n\n**核心关系式**：$B(p,q)=\\\\dfrac{\\\\Gamma(p)\\\\Gamma(q)}{\\\\Gamma(p+q)}$。\n\n**应用**：\n- $\\\\int_0^{\\\\pi/2}\\\\sin^{2m-1}\\\\theta\\\\cos^{2n-1}\\\\theta\\,\\\\mathrm{d}\\\\theta=\\\\frac{1}{2}B(m,n)=\\\\frac{\\\\Gamma(m)\\\\Gamma(n)}{2\\\\Gamma(m+n)}$。\n- Wallis 公式 $\\\\int_0^{\\\\pi/2}\\\\sin^n\\\\theta\\,\\\\mathrm{d}\\\\theta=\\\\frac{\\\\sqrt{\\\\pi}}{2}\\\\cdot\\\\frac{\\\\Gamma((n+1)/2)}{\\\\Gamma(n/2+1)}$。\n- 高斯积分 $\\\\int_0^{+\\\\infty}e^{-x^2}\\,\\\\mathrm{d}x=\\\\frac{1}{2}\\\\Gamma(1/2)=\\\\frac{\\\\sqrt{\\\\pi}}{2}$（令 $x^2=t$）。",
-      "textbookRefs": ["数学分析（第5版）下册 §19.3"],
+      "textbookRefs": [
+        "数学分析（第5版）下册 §19.3"
+      ],
       "keyDefinitions": [
         {
           "term": "B 函数（Beta 函数）",
@@ -124,12 +136,18 @@
         "$B(p,q)$ 中 $p,q>0$，指数 $p-1,q-1$ 可以为负（但需积分收敛，即 $p,q>0$）",
         "$\\\\Gamma(s+1)=s!$ 仅对正整数 $s$ 成立；非整数 $s$ 时 $\\\\Gamma(s)$ 是阶乘的推广"
       ],
-      "exerciseIds": ["pi-ex-005", "pi-ex-006", "pi-ex-007", "pi-ex-008"],
+      "exerciseIds": [
+        "pi-ex-005",
+        "pi-ex-006",
+        "pi-ex-007",
+        "pi-ex-008"
+      ],
       "diagramIds": [],
       "masteryCriteria": [
         "能将积分化为 B 函数或 Γ 函数的标准形式并计算",
         "能利用 B-Γ 关系式和递推公式 $\\\\Gamma(s+1)=s\\\\Gamma(s)$ 化简"
       ]
     }
-  ]
+  ],
+  "overview": "研究含参量正常积分的连续性与可微性（积分号下求导），推广到含参量反常积分的一致收敛判别，深入研究 Euler 积分。"
 }
diff --git a/content/courses/math-analysis/chapters/power-series.json b/content/courses/math-analysis/chapters/power-series.json
index 3d5ae1a..ce4ec53 100644
--- a/content/courses/math-analysis/chapters/power-series.json
+++ b/content/courses/math-analysis/chapters/power-series.json
@@ -14,7 +14,9 @@
         "能确定幂级数的收敛域（含端点的逐点讨论）"
       ],
       "coreExplanation": "**幂级数**：$\\\\sum_{n=0}^{\\\\infty}a_n x^n$（或更一般地 $\\\\sum a_n(x-x_0)^n$）。\n**Abel 定理**：若 $\\\\sum a_n x^n$ 在 $x=x_1\\\\neq 0$ 处收敛，则对任意 $|x|<|x_1|$，级数绝对收敛；对任意 $|x|\\\\leq r<|x_1|$，级数一致（绝对）收敛。\n**收敛半径**：$\\\\exists R\\\\in[0,+\\\\infty]$ 使级数在 $(-R,R)$ 内绝对收敛，在 $|x|>R$ 发散。$R$ 由 **Cauchy-Hadamard 公式**给出：\n$$R=\\\\frac{1}{\\\\limsup_{n\\\\to\\\\infty}\\\\sqrt[n]{|a_n|}}.$$\n若 $\\\\lim_{n\\\\to\\\\infty}|a_{n+1}/a_n|=\\\\rho$（比值法），则 $R=1/\\\\rho$（$\\\\rho=0$ 时 $R=+\\\\infty$，$\\\\rho=+\\\\infty$ 时 $R=0$）。\n**收敛域**：开区间 $(-R,R)$ 加上端点 $\\\\pm R$ 的单独讨论（用级数判别法逐一检验）。四种情况：$(-R,R)$，$[-R,R)$，$(-R,R]$，$[-R,R]$。\n**典型例子**：\n- $\\\\sum x^n/n!$：$R=+\\\\infty$，收敛域 $(-\\\\infty,+\\\\infty)$\n- $\\\\sum x^n$：$R=1$，端点 $\\\\pm 1$ 均发散，收敛域 $(-1,1)$\n- $\\\\sum x^n/n$：$R=1$，$x=1$ 发散（调和），$x=-1$ 收敛（交错），收敛域 $[-1,1)$\n- $\\\\sum x^n/n^2$：$R=1$，端点均收敛（$p=2>1$），收敛域 $[-1,1]$",
-      "textbookRefs": ["数学分析（第5版）下册 §14.1"],
+      "textbookRefs": [
+        "数学分析（第5版）下册 §14.1"
+      ],
       "keyDefinitions": [
         {
           "term": "收敛半径",
@@ -50,7 +52,10 @@
         "收敛域是**闭**区间还是**开**区间，必须单独检验端点，不能忽略",
         "幂级数在 $x=R$ 处可能只条件收敛而非绝对收敛"
       ],
-      "exerciseIds": ["power-ex-001", "power-ex-002"],
+      "exerciseIds": [
+        "power-ex-001",
+        "power-ex-002"
+      ],
       "diagramIds": [],
       "masteryCriteria": [
         "能用比值法或 Cauchy-Hadamard 公式求收敛半径",
@@ -68,7 +73,9 @@
         "了解幂级数的代数运算（加减、Cauchy 乘积）"
       ],
       "coreExplanation": "**连续性**：$f(x)=\\\\sum_{n=0}^\\\\infty a_n x^n$ 在收敛域内连续（由 Abel 定理，任意闭子区间上一致收敛）。\n**逐项微分**：$f'(x)=\\\\sum_{n=1}^\\\\infty n a_n x^{n-1}$，收敛半径不变（端点可能有变化）。\n$\\\\left(\\\\sum a_n x^n\\\\right)'=\\\\sum n a_n x^{n-1}$（对 $|x|<R$）。\n**逐项积分**：$\\\\int_0^x f(t)\\,\\\\mathrm{d}t=\\\\sum_{n=0}^\\\\infty\\\\frac{a_n}{n+1}x^{n+1}$，收敛半径不变。\n**关键推论**：幂级数在收敛域内有无穷阶导数，且各阶导数仍是幂级数（可多次微分）。\n**Abel 连续性定理**：若 $\\\\sum a_n R^n$ 收敛（$R$ 为收敛半径），则 $f(x)\\\\to f(R)$ 当 $x\\\\to R^-$（Abel 求和，可用于计算某些级数的和）。\n例：$\\\\sum_{n=1}^\\\\infty\\\\frac{(-1)^{n-1}}{n}=\\\\ln 2$（由 $f(x)=\\\\ln(1+x)=\\\\sum(-1)^{n-1}x^n/n$，令 $x=1$，Abel 连续性保证 $f(1^-)=f(1)$）。",
-      "textbookRefs": ["数学分析（第5版）下册 §14.1"],
+      "textbookRefs": [
+        "数学分析（第5版）下册 §14.1"
+      ],
       "keyDefinitions": [],
       "keyTheorems": [
         {
@@ -94,7 +101,10 @@
         "微分后收敛半径虽不变，但端点收敛性可能改变（如 $\\\\sum x^n/n$ 端点 $x=-1$ 微分后 $\\\\sum x^{n-1}$ 在 $x=-1$ 发散）",
         "逐项积分/微分只在 $|x|<R$ 内，不能在发散点使用"
       ],
-      "exerciseIds": ["power-ex-003", "power-ex-004"],
+      "exerciseIds": [
+        "power-ex-003",
+        "power-ex-004"
+      ],
       "diagramIds": [],
       "masteryCriteria": [
         "能对幂级数逐项微分/积分求和函数",
@@ -112,7 +122,9 @@
         "能用直接展开法（含余项估计）和间接法（代换、积分、微分）展开函数"
       ],
       "coreExplanation": "**Taylor 级数**：若 $f$ 在 $x_0$ 附近有各阶导数，则\n$$f(x)=\\\\sum_{n=0}^{\\\\infty}\\\\frac{f^{(n)}(x_0)}{n!}(x-x_0)^n$$\n成立的充要条件是余项 $R_n(x)=\\\\frac{f^{(n+1)}(\\\\xi)}{(n+1)!}(x-x_0)^{n+1}\\\\to 0$（$n\\\\to\\\\infty$）。\n**五个基本 Maclaurin 展开**（$x_0=0$）：\n$$e^x=\\\\sum_{n=0}^{\\\\infty}\\\\frac{x^n}{n!}=1+x+\\\\frac{x^2}{2!}+\\\\cdots \\\\quad x\\\\in(-\\\\infty,+\\\\infty)$$\n$$\\\\sin x=\\\\sum_{n=0}^{\\\\infty}\\\\frac{(-1)^n x^{2n+1}}{(2n+1)!}=x-\\\\frac{x^3}{3!}+\\\\frac{x^5}{5!}-\\\\cdots \\\\quad x\\\\in(-\\\\infty,+\\\\infty)$$\n$$\\\\cos x=\\\\sum_{n=0}^{\\\\infty}\\\\frac{(-1)^n x^{2n}}{(2n)!}=1-\\\\frac{x^2}{2!}+\\\\frac{x^4}{4!}-\\\\cdots \\\\quad x\\\\in(-\\\\infty,+\\\\infty)$$\n$$\\\\ln(1+x)=\\\\sum_{n=1}^{\\\\infty}\\\\frac{(-1)^{n-1}x^n}{n}=x-\\\\frac{x^2}{2}+\\\\frac{x^3}{3}-\\\\cdots \\\\quad x\\\\in(-1,1]$$\n$$(1+x)^\\\\alpha=\\\\sum_{n=0}^{\\\\infty}\\\\binom{\\\\alpha}{n}x^n \\\\quad x\\\\in(-1,1)\\\\text{（$\\\\alpha$ 为实数，}\\\\binom{\\\\alpha}{n}=\\\\frac{\\\\alpha(\\\\alpha-1)\\\\cdots(\\\\alpha-n+1)}{n!}\\\\text{）}$$\n**间接展开法**：通过对已知展开式作代换（$x\\\\to -x^2$等）、积分、微分，避免重新算余项。\n例：$\\\\frac{1}{1+x^2}=\\\\sum(-1)^n x^{2n}$，积分得 $\\\\arctan x=\\\\sum\\\\frac{(-1)^n x^{2n+1}}{2n+1}$（$x\\\\in[-1,1]$）。",
-      "textbookRefs": ["数学分析（第5版）下册 §14.2"],
+      "textbookRefs": [
+        "数学分析（第5版）下册 §14.2"
+      ],
       "keyDefinitions": [
         {
           "term": "Maclaurin 级数",
@@ -143,12 +155,20 @@
         "$(1+x)^\\\\alpha$ 展开的端点收敛性复杂（与 $\\\\alpha$ 有关），避免在端点随意使用",
         "间接法代换时忘记同步更新收敛域"
       ],
-      "exerciseIds": ["power-ex-005", "power-ex-006", "power-ex-007", "power-ex-008"],
-      "diagramIds": ["taylor-convergence-diagram"],
+      "exerciseIds": [
+        "power-ex-005",
+        "power-ex-006",
+        "power-ex-007",
+        "power-ex-008"
+      ],
+      "diagramIds": [
+        "taylor-convergence-diagram"
+      ],
       "masteryCriteria": [
         "能熟练写出五个基本函数的 Maclaurin 展开",
         "能用间接法（代换/积分/微分）展开 $\\\\arctan x$，$\\\\ln(1-x)$ 等函数"
       ]
     }
-  ]
+  ],
+  "overview": "以 Abel 定理与 Cauchy-Hadamard 公式确定收敛半径，研究幂级数的逐项微分与积分，实现常见初等函数的 Taylor 级数展开。"
 }
diff --git a/content/courses/math-analysis/chapters/real-numbers-functions.json b/content/courses/math-analysis/chapters/real-numbers-functions.json
index 0995d5a..7d648dd 100644
--- a/content/courses/math-analysis/chapters/real-numbers-functions.json
+++ b/content/courses/math-analysis/chapters/real-numbers-functions.json
@@ -14,7 +14,9 @@
         "能用绝对值不等式进行估计"
       ],
       "coreExplanation": "**实数集** $\\\\mathbb{R}$：有理数（$\\\\mathbb{Q}$，形如 $p/q$，$p\\\\in\\\\mathbb{Z},q\\\\in\\\\mathbb{N}^+$）与无理数的并集。有理数与无理数在 $\\\\mathbb{R}$ 上均稠密（任意两实数之间均存在有理数和无理数）。\n**实数的完备性（直觉）**：实数轴上没有」空洞」——每个有理数的 Cauchy 序列都收敛到一个实数（无理数填补有理数轴的空洞）。这是数学分析的基础，不同于有理数的不完备。\n**绝对值**：$|a|=\\\\begin{cases}a,&a\\\\geq 0\\\\\\\\-a,&a<0\\\\end{cases}$。\n**绝对值的性质**：\n- $|a|\\\\geq 0$，$|a|=0\\\\Leftrightarrow a=0$；\n- $|ab|=|a||b|$；\n- **三角不等式**：$|a+b|\\\\leq|a|+|b|$；逆三角不等式：$||a|-|b||\\\\leq|a-b|$；\n- $|a-b|$：数轴上 $a,b$ 两点之间的距离。\n**有界性**：集合 $A\\\\subset\\\\mathbb{R}$ 有上界（$\\\\exists M,\\\\forall x\\\\in A,x\\\\leq M$）；有下界类似。既有上界又有下界称有界（等价于 $\\\\exists M>0,\\\\forall x\\\\in A,|x|\\\\leq M$）。",
-      "textbookRefs": ["数学分析（第5版）上册 §1.1"],
+      "textbookRefs": [
+        "数学分析（第5版）上册 §1.1"
+      ],
       "keyDefinitions": [
         {
           "term": "无理数",
@@ -44,7 +46,9 @@
         "三角不等式方向：$|a+b|\\\\leq|a|+|b|$（上界），$|a+b|\\\\geq||a|-|b||$（下界）",
         "$|a|^2=a^2$（不是 $|a^2|$，两者相等；但 $|a|=|{-a}|$，$a$ 和 $-a$ 绝对值相同）"
       ],
-      "exerciseIds": ["rnf-ex-001"],
+      "exerciseIds": [
+        "rnf-ex-001"
+      ],
       "diagramIds": [],
       "masteryCriteria": [
         "能用三角不等式进行绝对值估计",
@@ -62,7 +66,9 @@
         "能求简单集合的上下确界"
       ],
       "coreExplanation": "**有界集**：$A\\\\subset\\\\mathbb{R}$ 有上界 $\\\\Leftrightarrow\\\\exists M,\\\\forall x\\\\in A,x\\\\leq M$；有下界 $\\\\Leftrightarrow\\\\exists m,\\\\forall x\\\\in A,x\\\\geq m$。\n**上确界**（最小上界 $\\\\sup A$）：$\\\\beta=\\\\sup A\\\\Leftrightarrow$\n1. $\\\\forall x\\\\in A,x\\\\leq\\\\beta$（$\\\\beta$ 是上界）；\n2. $\\\\forall\\\\varepsilon>0,\\\\exists x\\\\in A,x>\\\\beta-\\\\varepsilon$（$\\\\beta$ 是最小上界，任何更小的数都不是上界）。\n**下确界**（最大下界 $\\\\inf A$）类似定义。\n**确界原理**（完备性公理）：非空有上界的实数集必有上确界；非空有下界的实数集必有下确界。（这是实数完备性的一种等价描述，有理数集不满足此性质！）\n**例**：\n- $A=\\\\{x:\\,0<x<1\\\\}$：$\\\\sup A=1\\\\notin A$，$\\\\inf A=0\\\\notin A$（开区间，确界不属于集合）。\n- $A=\\\\{(-1)^n+1/n:\\,n\\\\in\\\\mathbb{N}^+\\\\}=\\\\{0,3/2,2/3,5/4,4/5,\\\\ldots\\\\}$：$\\\\sup A=3/2$（$n=2$ 时取到），$\\\\inf A=0$（通过 $n=2k-1,n\\\\to\\\\infty$ 趋近但不取到）。",
-      "textbookRefs": ["数学分析（第5版）上册 §1.2"],
+      "textbookRefs": [
+        "数学分析（第5版）上册 §1.2"
+      ],
       "keyDefinitions": [
         {
           "term": "上确界",
@@ -90,7 +96,9 @@
         "上确界不一定属于集合（开区间 $(0,1)$ 的上确界 $1\\\\notin(0,1)$）；若 $\\\\sup A\\\\in A$，则称 $\\\\sup A$ 为 $A$ 的最大值",
         "确界的第二条件（$\\\\forall\\\\varepsilon>0,\\\\exists x\\\\in A,x>\\\\sup A-\\\\varepsilon$）不可省略，仅有第一条不足以确定最小上界"
       ],
-      "exerciseIds": ["rnf-ex-002"],
+      "exerciseIds": [
+        "rnf-ex-002"
+      ],
       "diagramIds": [],
       "masteryCriteria": [
         "能按定义验证集合的上/下确界",
@@ -108,7 +116,9 @@
         "理解反函数的存在条件与表示"
       ],
       "coreExplanation": "**函数定义**：$f:D\\\\to\\\\mathbb{R}$，对每个 $x\\\\in D$ 对应唯一 $y=f(x)\\\\in\\\\mathbb{R}$。$D$ 为**定义域**，$f(D)=\\\\{f(x):\\,x\\\\in D\\\\}$ 为**值域**。\n**自然定义域**：使表达式有意义的最大 $x$ 集合，如 $f(x)=\\\\sqrt{1-x^2}$ 的自然定义域为 $[-1,1]$。\n**四则运算**：$f\\\\pm g,fg,f/g$（后者要求 $g\\\\neq 0$），定义域取交集（商还需去除零点）。\n**复合函数**：$f\\\\circ g(x)=f(g(x))$，要求 $g(x)$ 的值域 $\\\\subset f$ 的定义域（否则复合无意义）。\n**反函数**：若 $f:D\\\\to f(D)$ 为严格单调函数，则 $f$ 可逆，反函数 $f^{-1}:f(D)\\\\to D$，满足 $f^{-1}(f(x))=x$（对 $x\\\\in D$）。$y=f(x)$ 与 $y=f^{-1}(x)$ 的图像关于 $y=x$ 对称。\n**初等函数**：由幂函数、指数函数、对数函数、三角函数、反三角函数经有限次四则运算和复合得到的函数，在其定义域上有定义（不含分段定义的情形）。",
-      "textbookRefs": ["数学分析（第5版）上册 §1.3"],
+      "textbookRefs": [
+        "数学分析（第5版）上册 §1.3"
+      ],
       "keyDefinitions": [
         {
           "term": "函数",
@@ -130,8 +140,13 @@
         "复合函数 $f(g(x))$ 的定义域：需要 $x\\\\in\\\\mathrm{Dom}(g)$ 且 $g(x)\\\\in\\\\mathrm{Dom}(f)$（两个条件同时满足）",
         "反函数存在的条件：$f$ 必须在定义域上严格单调（一一对应），否则反函数不是函数（一个 $y$ 对应多个 $x$）"
       ],
-      "exerciseIds": ["rnf-ex-003", "rnf-ex-004"],
-      "diagramIds": ["function-properties-diagram"],
+      "exerciseIds": [
+        "rnf-ex-003",
+        "rnf-ex-004"
+      ],
+      "diagramIds": [
+        "function-properties-diagram"
+      ],
       "masteryCriteria": [
         "能求函数的自然定义域",
         "能判断两函数是否相同（定义域和对应法则均相同）",
@@ -149,7 +164,9 @@
         "了解各特性之间的关系"
       ],
       "coreExplanation": "**单调性**：$f$ 在 $I$ 上单调递增 $\\\\Leftrightarrow\\\\forall x_1,x_2\\\\in I,x_1<x_2\\\\Rightarrow f(x_1)<f(x_2)$（严格；非严格则为 $\\\\leq$）。\n**有界性**：$f$ 在 $D$ 上有界 $\\\\Leftrightarrow\\\\exists M>0,\\\\forall x\\\\in D,|f(x)|\\\\leq M$。有上界（$f(x)\\\\leq M$）、有下界（$f(x)\\\\geq m$）类似。\n**奇偶性**：定义域关于原点对称（$D=-D$，即 $x\\\\in D\\\\Rightarrow-x\\\\in D$）。\n- 偶函数：$f(-x)=f(x)$，图像关于 $y$ 轴对称。\n- 奇函数：$f(-x)=-f(x)$，图像关于原点对称；若 $0\\\\in D$，则 $f(0)=0$。\n**运算**：奇$\\\\times$奇$=$偶，偶$\\\\times$偶$=$偶，奇$\\\\times$偶$=$奇，奇$+$奇$=$奇，偶$+$偶$=$偶（奇$+$偶一般不是奇或偶）。\n**周期性**：$f(x+T)=f(x)$（$\\\\forall x\\\\in D$，$T>0$）；最小正周期（若存在）称为**基本周期**。注意：常数函数有任意正周期，但通常不称有基本周期。\n**例**：$\\\\sin x$ 基本周期 $2\\\\pi$；$|\\\\sin x|$ 基本周期 $\\\\pi$（注意减半）；Dirichlet 函数 $D(x)=\\\\mathbf{1}_{\\\\mathbb{Q}}(x)$ 以任意有理数为周期（无最小正周期）。",
-      "textbookRefs": ["数学分析（第5版）上册 §1.4"],
+      "textbookRefs": [
+        "数学分析（第5版）上册 §1.4"
+      ],
       "keyDefinitions": [
         {
           "term": "奇函数",
@@ -175,12 +192,18 @@
         "奇偶性需先检查定义域是否关于原点对称（$D=-D$），否则无奇偶性可言",
         "周期函数不一定有最小正周期（Dirichlet 函数无最小正周期）；$|\\\\sin x|$ 的周期是 $\\\\pi$ 而非 $2\\\\pi$"
       ],
-      "exerciseIds": ["rnf-ex-005", "rnf-ex-006"],
-      "diagramIds": ["function-properties-diagram"],
+      "exerciseIds": [
+        "rnf-ex-005",
+        "rnf-ex-006"
+      ],
+      "diagramIds": [
+        "function-properties-diagram"
+      ],
       "masteryCriteria": [
         "能判断函数的单调性、奇偶性、有界性、周期性",
         "能利用奇偶性化简问题（如对称区间上的积分）"
       ]
     }
-  ]
+  ],
+  "overview": "本章建立数学分析的起点：从有理数到实数系完备性（确界原理），再到函数概念的精确化——单调性、奇偶性、有界性与周期性。"
 }
diff --git a/content/courses/math-analysis/chapters/surface-integrals.json b/content/courses/math-analysis/chapters/surface-integrals.json
index cd34117..e14b5a5 100644
--- a/content/courses/math-analysis/chapters/surface-integrals.json
+++ b/content/courses/math-analysis/chapters/surface-integrals.json
@@ -14,7 +14,9 @@
         "能计算显式曲面 $z=z(x,y)$ 上的面积积分"
       ],
       "coreExplanation": "**第一型曲面积分定义**：$\\\\iint_S f(x,y,z)\\,\\\\mathrm{d}S$，其中 $\\\\mathrm{d}S$ 为曲面面积元素，与曲面法向量方向无关。\n**计算公式**（显式 $z=z(x,y)$）：\n$$\\\\mathrm{d}S=\\\\sqrt{1+z_x^2+z_y^2}\\,\\\\mathrm{d}x\\,\\\\mathrm{d}y,$$\n$$\\\\iint_S f(x,y,z)\\,\\\\mathrm{d}S=\\\\iint_{D_{xy}}f(x,y,z(x,y))\\\\sqrt{1+z_x^2+z_y^2}\\,\\\\mathrm{d}x\\,\\\\mathrm{d}y.$$\n其中 $D_{xy}$ 为曲面在 $xy$ 平面的投影区域。\n**参数曲面**（$\\boldsymbol{r}=\\boldsymbol{r}(u,v)$）：$\\\\mathrm{d}S=|\\boldsymbol{r}_u\\\\times\\boldsymbol{r}_v|\\,\\\\mathrm{d}u\\,\\\\mathrm{d}v$。\n**特殊情形**：\n- 球面 $x^2+y^2+z^2=R^2$：$\\\\mathrm{d}S=R^2\\\\sin\\\\varphi\\,\\\\mathrm{d}\\\\varphi\\,\\\\mathrm{d}\\\\theta$（参数化 $(\\\\varphi,\\\\theta)$）。\n- 曲面面积：$A=\\\\iint_S\\,\\\\mathrm{d}S=\\\\iint_{D_{xy}}\\\\sqrt{1+z_x^2+z_y^2}\\,\\\\mathrm{d}x\\,\\\\mathrm{d}y$。\n**物理意义**：若 $f$ 为面密度，$\\\\iint_S f\\,\\\\mathrm{d}S$ 为曲面薄片的质量；$f=1$ 时为面积。",
-      "textbookRefs": ["数学分析（第5版）下册 §22.1"],
+      "textbookRefs": [
+        "数学分析（第5版）下册 §22.1"
+      ],
       "keyDefinitions": [
         {
           "term": "曲面面积元素",
@@ -40,8 +42,13 @@
         "面积元素 $\\\\mathrm{d}S=\\\\sqrt{1+z_x^2+z_y^2}\\,\\\\mathrm{d}x\\,\\\\mathrm{d}y$，不是 $\\\\mathrm{d}x\\,\\\\mathrm{d}y$",
         "第一型曲面积分与方向无关（和第一型曲线积分一样），不能加负号"
       ],
-      "exerciseIds": ["si-ex-001", "si-ex-002"],
-      "diagramIds": ["surface-integral-diagram"],
+      "exerciseIds": [
+        "si-ex-001",
+        "si-ex-002"
+      ],
+      "diagramIds": [
+        "surface-integral-diagram"
+      ],
       "masteryCriteria": [
         "能将显式曲面 $z=z(x,y)$ 上的第一型曲面积分化为二重积分并计算",
         "能计算曲面面积"
@@ -58,7 +65,9 @@
         "理解两型曲面积分的关系"
       ],
       "coreExplanation": "**第二型曲面积分**：$\\\\iint_S\\boldsymbol{F}\\cdot\\,\\\\mathrm{d}\\boldsymbol{S}=\\\\iint_S P\\,\\\\mathrm{d}y\\,\\\\mathrm{d}z+Q\\,\\\\mathrm{d}z\\,\\\\mathrm{d}x+R\\,\\\\mathrm{d}x\\,\\\\mathrm{d}y$，其中 $\\\\mathrm{d}\\boldsymbol{S}=\\boldsymbol{n}\\,\\\\mathrm{d}S$（$\\boldsymbol{n}$ 为单位外法向量）。物理意义：向量场 $\\boldsymbol{F}=(P,Q,R)$ 通过曲面的**流量**。\n**与方向有关**：反向曲面 $-S$ 的积分取负号：$\\\\iint_{-S}=-\\\\iint_S$。\n**化为二重积分**（曲面 $z=z(x,y)$，取上侧，法向量朝上）：\n$$\\\\iint_S R(x,y,z)\\,\\\\mathrm{d}x\\,\\\\mathrm{d}y=\\\\iint_{D_{xy}}R(x,y,z(x,y))\\,\\\\mathrm{d}x\\,\\\\mathrm{d}y$$\n（取下侧则加负号）。类似地：\n$$\\\\iint_S P\\,\\\\mathrm{d}y\\,\\\\mathrm{d}z=\\\\mp\\\\iint_{D_{yz}}P(x(y,z),y,z)\\,\\\\mathrm{d}y\\,\\\\mathrm{d}z$$\n（$\\mp$：法向量朝前取 $-$，朝后取 $+$，具体看曲面方程和投影方向）。\n**两型积分关系**：若 $\\boldsymbol{n}=(\\cos\\alpha,\\cos\\beta,\\cos\\gamma)$ 为单位外法向量：\n$$\\\\iint_S P\\,\\\\mathrm{d}y\\,\\\\mathrm{d}z+Q\\,\\\\mathrm{d}z\\,\\\\mathrm{d}x+R\\,\\\\mathrm{d}x\\,\\\\mathrm{d}y=\\\\iint_S(P\\cos\\alpha+Q\\cos\\beta+R\\cos\\gamma)\\,\\\\mathrm{d}S.$$",
-      "textbookRefs": ["数学分析（第5版）下册 §22.2"],
+      "textbookRefs": [
+        "数学分析（第5版）下册 §22.2"
+      ],
       "keyDefinitions": [
         {
           "term": "曲面的侧（法向量方向）",
@@ -81,8 +90,13 @@
         "$\\\\iint_S R\\,\\\\mathrm{d}x\\,\\\\mathrm{d}y$ 化为二重积分时：上侧直接代入 $z=z(x,y)$（不加负号），下侧加负号",
         "不能混淆 $\\mathrm{d}S$（正的面积元素）和 $\\mathrm{d}x\\,\\mathrm{d}y$（有向面积元素，可正可负）"
       ],
-      "exerciseIds": ["si-ex-003", "si-ex-004"],
-      "diagramIds": ["surface-integral-diagram"],
+      "exerciseIds": [
+        "si-ex-003",
+        "si-ex-004"
+      ],
+      "diagramIds": [
+        "surface-integral-diagram"
+      ],
       "masteryCriteria": [
         "能判断曲面的侧并写出第二型曲面积分化为二重积分的公式（含正负号）",
         "能计算向量场通过曲面的流量"
@@ -99,7 +113,9 @@
         "理解场论基本概念：散度和旋度"
       ],
       "coreExplanation": "**高斯公式**：设 $\\Omega$ 为空间有界闭区域，$\\partial\\Omega$ 为其外表面（外法向量为正方向），$P,Q,R$ 在 $\\Omega$ 上有连续偏导数：\n$$\\oiint_{\\partial\\Omega}P\\,\\mathrm{d}y\\,\\mathrm{d}z+Q\\,\\mathrm{d}z\\,\\mathrm{d}x+R\\,\\mathrm{d}x\\,\\mathrm{d}y=\\iiint_\\Omega\\left(\\frac{\\partial P}{\\partial x}+\\frac{\\partial Q}{\\partial y}+\\frac{\\partial R}{\\partial z}\\right)\\,\\mathrm{d}V.$$\n即：封闭曲面的通量 $=$ 内部散度的体积分。\n**散度**：$\\mathrm{div}\\,\\boldsymbol{F}=\\nabla\\cdot\\boldsymbol{F}=P_x+Q_y+R_z$（衡量向量场的」源强度」）。\n**高斯公式应用**：补面法（遇到非封闭曲面时补齐成封闭面，减去补面的贡献）；含奇点时挖球。\n**斯托克斯公式**：设 $S$ 为有向曲面，$\\partial S$ 为其边界曲线（方向与 $S$ 法向量成右手系）：\n$$\\oint_{\\partial S}P\\,\\mathrm{d}x+Q\\,\\mathrm{d}y+R\\,\\mathrm{d}z=\\iint_S\\left(\\frac{\\partial R}{\\partial y}-\\frac{\\partial Q}{\\partial z}\\right)\\mathrm{d}y\\,\\mathrm{d}z+\\left(\\frac{\\partial P}{\\partial z}-\\frac{\\partial R}{\\partial x}\\right)\\mathrm{d}z\\,\\mathrm{d}x+\\left(\\frac{\\partial Q}{\\partial x}-\\frac{\\partial P}{\\partial y}\\right)\\mathrm{d}x\\,\\mathrm{d}y.$$\n记忆：$\\iint_S(\\nabla\\times\\boldsymbol{F})\\cdot\\,\\mathrm{d}\\boldsymbol{S}=\\oint_{\\partial S}\\boldsymbol{F}\\cdot\\,\\mathrm{d}\\boldsymbol{r}$。\n**旋度**：$\\mathrm{rot}\\,\\boldsymbol{F}=\\nabla\\times\\boldsymbol{F}=\\det\\begin{pmatrix}\\boldsymbol{i}&\\boldsymbol{j}&\\boldsymbol{k}\\\\\\\\\\partial_x&\\partial_y&\\partial_z\\\\\\\\P&Q&R\\end{pmatrix}$（衡量向量场的」旋转强度」）。\n**Green 公式为特例**：取 $S$ 为 $z=0$ 的平面区域，斯托克斯退化为 $\\oint_{\\partial D}P\\,\\mathrm{d}x+Q\\,\\mathrm{d}y=\\iint_D(Q_x-P_y)\\,\\mathrm{d}A$（Green 公式）。",
-      "textbookRefs": ["数学分析（第5版）下册 §22.3—22.4"],
+      "textbookRefs": [
+        "数学分析（第5版）下册 §22.3—22.4"
+      ],
       "keyDefinitions": [
         {
           "term": "散度",
@@ -139,8 +155,14 @@
         "斯托克斯公式的边界曲线方向：右手法则，拇指指向法向量，四指为边界正向（不能随意选向）",
         "散度 $P_x+Q_y+R_z$（各分量对各自变量偏导），不要混淆"
       ],
-      "exerciseIds": ["si-ex-005", "si-ex-006", "si-ex-007"],
-      "diagramIds": ["gauss-stokes-diagram"],
+      "exerciseIds": [
+        "si-ex-005",
+        "si-ex-006",
+        "si-ex-007"
+      ],
+      "diagramIds": [
+        "gauss-stokes-diagram"
+      ],
       "masteryCriteria": [
         "能用高斯公式计算封闭曲面积分（包括补面法）",
         "能用斯托克斯公式将空间曲线积分化为曲面积分"
@@ -157,7 +179,9 @@
         "了解调和函数与向量分析恒等式"
       ],
       "coreExplanation": "**三大场论运算**（$\\boldsymbol{F}=(P,Q,R)$，$u$ 为标量场）：\n- **梯度**：$\\mathrm{grad}\\,u=\\nabla u=(u_x,u_y,u_z)$（指向增长最快方向）。\n- **散度**：$\\mathrm{div}\\,\\boldsymbol{F}=\\nabla\\cdot\\boldsymbol{F}=P_x+Q_y+R_z$。\n- **旋度**：$\\mathrm{rot}\\,\\boldsymbol{F}=\\nabla\\times\\boldsymbol{F}$（向量）。\n**重要恒等式**：\n- $\\mathrm{div}(\\mathrm{rot}\\,\\boldsymbol{F})=\\nabla\\cdot(\\nabla\\times\\boldsymbol{F})=0$（旋度无散）。\n- $\\mathrm{rot}(\\mathrm{grad}\\,u)=\\nabla\\times\\nabla u=\\boldsymbol{0}$（梯度无旋）。\n**无旋场（保守场）**：$\\boldsymbol{F}=\\nabla u$（有势函数 $u$）的充要条件：$\\nabla\\times\\boldsymbol{F}=\\boldsymbol{0}$（单连通域中等价于线积分路径无关）。\n**调和函数**：满足 $\\Delta u=\\nabla^2 u=u_{xx}+u_{yy}+u_{zz}=0$ 的函数（Laplace 方程），是位势理论的基础。\n**Laplace 算子**：$\\Delta=\\nabla\\cdot\\nabla=\\partial_{xx}+\\partial_{yy}+\\partial_{zz}$；调和函数如静电势、稳态温度场。\n**Green 恒等式**（高斯公式推论）：$\\iiint_\\Omega u\\Delta v\\,\\mathrm{d}V=\\oiint_{\\partial\\Omega}u\\frac{\\partial v}{\\partial n}\\,\\mathrm{d}S-\\iiint_\\Omega\\nabla u\\cdot\\nabla v\\,\\mathrm{d}V$。",
-      "textbookRefs": ["数学分析（第5版）下册 §22.5"],
+      "textbookRefs": [
+        "数学分析（第5版）下册 §22.5"
+      ],
       "keyDefinitions": [
         {
           "term": "保守场（无旋场）",
@@ -186,12 +210,15 @@
         "$\\mathrm{div}\\,\\boldsymbol{F}=0$ 不意味着 $\\boldsymbol{F}=\\mathrm{rot}\\,\\boldsymbol{G}$（还需要单连通域条件）",
         "Laplace 算子 $\\Delta u=u_{xx}+u_{yy}+u_{zz}$（求和，不是乘积）"
       ],
-      "exerciseIds": ["si-ex-008"],
+      "exerciseIds": [
+        "si-ex-008"
+      ],
       "diagramIds": [],
       "masteryCriteria": [
         "能判断三维向量场是否无旋并求势函数",
         "能验证简单函数是否为调和函数"
       ]
     }
-  ]
+  ],
+  "overview": "建立第一型与第二型曲面积分，以高斯公式（体积分与曲面积分互化）和 Stokes 公式（曲面与曲线积分互化）为核心，介绍散度与旋度。"
 }
diff --git a/content/courses/math-analysis/diagrams/indefinite-integral.json b/content/courses/math-analysis/diagrams/indefinite-integral.json
index d68170a..a13967a 100644
--- a/content/courses/math-analysis/diagrams/indefinite-integral.json
+++ b/content/courses/math-analysis/diagrams/indefinite-integral.json
@@ -2,20 +2,70 @@
   "chapterId": "ch-indefinite-integral",
   "courseId": "math-analysis",
   "volumeId": "math-analysis-volume-1",
+  "schemaVersion": 1,
+  "renderingPolicy": {
+    "preferredRenderer": "programmatic-svg",
+    "reason": "图示由参数程序化生成，保证标注与几何关系正确、可复核。"
+  },
   "diagrams": [
     {
-      "id": "trig-substitution-triangle",
-      "title": "三角换元辅助直角三角形",
-      "description": "三幅直角三角形示意，对应三种标准三角换元。(a) $x=a\\sin\\theta$（$\\sqrt{a^2-x^2}$）：斜边 $a$，对边 $x$，邻边 $\\sqrt{a^2-x^2}$；(b) $x=a\\tan\\theta$（$\\sqrt{a^2+x^2}$）：邻边 $a$，对边 $x$，斜边 $\\sqrt{a^2+x^2}$；(c) $x=a\\sec\\theta$（$\\sqrt{x^2-a^2}$）：邻边 $a$，斜边 $x$，对边 $\\sqrt{x^2-a^2}$。每图旁标出换回时常用的三角比关系。",
-      "mathContext": "三角换元消根号：$\\sin^2\\theta+\\cos^2\\theta=1$ 消去 $\\sqrt{a^2-x^2}$；$1+\\tan^2\\theta=\\sec^2\\theta$ 消去 $\\sqrt{a^2+x^2}$；$\\sec^2\\theta-1=\\tan^2\\theta$ 消去 $\\sqrt{x^2-a^2}$。直角三角形辅图帮助快速换回原变量，不需要记忆反三角函数公式。",
-      "diagramType": "geometry",
-      "knowledgePointIds": ["substitution-method"],
-      "layout": "three-panel-horizontal",
-      "annotations": [
-        { "panel": "a", "label": "$x=a\\sin\\theta$", "note": "适用于 $\\sqrt{a^2-x^2}$" },
-        { "panel": "b", "label": "$x=a\\tan\\theta$", "note": "适用于 $\\sqrt{a^2+x^2}$" },
-        { "panel": "c", "label": "$x=a\\sec\\theta$", "note": "适用于 $\\sqrt{x^2-a^2}$" }
+      "id": "antiderivative-family",
+      "title": "一族原函数：相差一个常数",
+      "type": "multi-curve-plot",
+      "knowledgePointIds": ["antiderivative-concept"],
+      "description": "同一函数的原函数有无穷多条，彼此只差一个常数 $C$，在图上是一族竖直平移的曲线 $y=\\frac{x^2}{2}+C$（它们都是 $f(x)=x$ 的原函数）。",
+      "parameters": {
+        "domain": { "from": -2.6, "to": 2.6 },
+        "curves": [
+          { "label": "C=1", "expr": "x^2/2+1" },
+          { "label": "C=0", "expr": "x^2/2" },
+          { "label": "C=-1", "expr": "x^2/2-1" }
+        ]
+      },
+      "studentPrompt": "在同一个 $x$ 处，这几条曲线的切线斜率有什么关系？这正说明了什么？",
+      "teacherNotes": [
+        "竖直平移不改变任何一点的切线斜率，故它们导数相同，原函数只差常数。",
+        "这张图把「不定积分要加 $+C$」从公式变成可看见的几何事实。"
       ]
+    },
+    {
+      "id": "basic-integral-table",
+      "title": "基本积分公式表（节选）",
+      "type": "table",
+      "knowledgePointIds": ["antiderivative-concept"],
+      "description": "下表由基本求导公式反推得到，是后续一切积分技巧的「字母表」，需熟记。",
+      "parameters": {
+        "columns": ["被积函数 $f(x)$", "不定积分 $\\int f(x)\\,\\mathrm{d}x$"],
+        "rows": [
+          ["$x^{n}\\ (n\\neq -1)$", "$\\dfrac{x^{n+1}}{n+1}+C$"],
+          ["$\\dfrac{1}{x}$", "$\\ln|x|+C$"],
+          ["$e^{x}$", "$e^{x}+C$"],
+          ["$\\cos x$", "$\\sin x+C$"],
+          ["$\\sin x$", "$-\\cos x+C$"],
+          ["$\\dfrac{1}{1+x^{2}}$", "$\\arctan x+C$"],
+          ["$\\dfrac{1}{\\sqrt{1-x^{2}}}$", "$\\arcsin x+C$"]
+        ]
+      },
+      "studentPrompt": "表里每一行，都是哪一个求导公式「倒过来」写的？",
+      "teacherNotes": ["建议让学生用求导逐行验证，而不是死记硬背。"]
+    },
+    {
+      "id": "trig-sub-triangle",
+      "title": "三角换元辅助直角三角形（$x=a\\sin\\theta$）",
+      "type": "geometric",
+      "knowledgePointIds": ["substitution-method"],
+      "description": "对含 $\\sqrt{a^2-x^2}$ 的积分令 $x=a\\sin\\theta$。借助直角三角形可把结果里的 $\\sin\\theta,\\cos\\theta$ 直接换回含 $x$ 的式子，不必背反三角公式：$a$ 为斜边、$x$ 为对边、$\\sqrt{a^2-x^2}$ 为邻边。",
+      "parameters": {
+        "shapes": [
+          { "kind": "polygon", "points": [{ "x": 0, "y": 0 }, { "x": 4, "y": 0 }, { "x": 4, "y": 3 }] },
+          { "kind": "line", "from": { "x": 0, "y": 0 }, "to": { "x": 4, "y": 3 }, "label": "a", "labelDy": -12 },
+          { "kind": "line", "from": { "x": 4, "y": 0 }, "to": { "x": 4, "y": 3 }, "label": "x", "labelDx": 12 },
+          { "kind": "line", "from": { "x": 0, "y": 0 }, "to": { "x": 4, "y": 0 }, "label": "\\sqrt{a^2-x^2}", "labelDy": 16 },
+          { "kind": "point", "points": [{ "x": 0, "y": 0 }], "label": "\\theta", "color": "#8a2b2b" }
+        ]
+      },
+      "studentPrompt": "由图 $\\sin\\theta=\\dfrac{x}{a},\\ \\cos\\theta=\\dfrac{\\sqrt{a^2-x^2}}{a}$，那么 $\\tan\\theta=?$",
+      "teacherNotes": ["三图法口诀：$a$ 斜边、$x$ 对边、$\\sqrt{a^2-x^2}$ 邻边；换回时直接读三角比。"]
     }
   ]
 }
diff --git a/docs/superpowers/plans/2026-06-10-gaodeng-shuxue-content-task-list.md b/docs/superpowers/plans/2026-06-10-gaodeng-shuxue-content-task-list.md
new file mode 100644
index 0000000..29e65a2
--- /dev/null
+++ b/docs/superpowers/plans/2026-06-10-gaodeng-shuxue-content-task-list.md
@@ -0,0 +1,204 @@
+# 高等数学（同济版）内容编写任务清单 — 给协作 AI
+
+> **课程 ID：`gaodeng-shuxue` ｜ slug 前缀：`gd-` ｜ 目标：11 章完整、精炼、带可渲染配图**
+>
+> 这份清单是**自包含**的：你不需要读其他文档也能开工。但开工前**必须**先读样板
+> `content/courses/math-analysis/chapters/sequence-limit.json`（这是全项目的质量基线），
+> 以及 `CONTENT_AGENT.md`（JSON 编码与安全规则，尤其是 LaTeX 四反斜杠和中文引号规则）。
+>
+> 本次任务相对旧版 CONTENT_AGENT 的**关键升级**：内容必须更厚、配图必须可被渲染器真正画出来（不能只写描述文字）。详见 §3、§4。
+
+---
+
+## 0. 开工前置（主智能体已完成 / 待确认）
+
+`gaodeng-shuxue` 课程目录、`course.json`、`volume-*.json` 与代码注册（registry）由**主智能体**搭建，
+你**只写内容 JSON**，不碰任何 `.ts/.tsx/.css/.js` 代码。开工前确认这些已存在：
+
+```
+content/courses/gaodeng-shuxue/
+├── course.json            ← 主智能体建好（勿改）
+├── volume-1.json          ← 上册目录（第 1–7 章）
+├── volume-2.json          ← 下册目录（第 8–11 章 + 续）
+├── chapters/              ← 你写
+├── exercises/             ← 你写
+└── diagrams/              ← 你写
+```
+
+若目录还没建好，**停下来告诉主智能体**，不要自己创建 course.json / volume 文件。
+
+每完成一章后运行（若脚本存在）：
+```powershell
+npm run validate:all        # JSON 合法性 + ID 交叉引用校验
+node scripts/build-wx-data.js   # 同步到小程序数据（主智能体会跑，你可不跑）
+```
+
+---
+
+## 1. 章节总表（11 章，按同济《高等数学》第八版顺序）
+
+| # | 章节 ID | slug / 文件名 | 章节名称 | 册 | 优先级 |
+|---|---------|--------------|---------|----|-------|
+| 1 | `ch-gd-function-limit` | `gd-function-limit` | 函数、极限与连续 | 上 | P0 |
+| 2 | `ch-gd-derivative` | `gd-derivative` | 导数与微分 | 上 | P0 |
+| 3 | `ch-gd-mean-value` | `gd-mean-value` | 微分中值定理与导数应用 | 上 | P0 |
+| 4 | `ch-gd-indefinite-integral` | `gd-indefinite-integral` | 不定积分 | 上 | P1 |
+| 5 | `ch-gd-definite-integral` | `gd-definite-integral` | 定积分及其应用 | 上 | P1 |
+| 6 | `ch-gd-ode` | `gd-ode` | 微分方程 | 上 | P1 |
+| 7 | `ch-gd-vectors` | `gd-vectors` | 向量代数与空间解析几何 | 下 | P2 |
+| 8 | `ch-gd-multivariable-diff` | `gd-multivariable-diff` | 多元函数微分法及其应用 | 下 | P1 |
+| 9 | `ch-gd-multiple-integrals` | `gd-multiple-integrals` | 重积分 | 下 | P1 |
+| 10 | `ch-gd-line-surface` | `gd-line-surface` | 曲线积分与曲面积分 | 下 | P2 |
+| 11 | `ch-gd-series` | `gd-series` | 无穷级数 | 下 | P2 |
+
+**认领方式**：多个 AI 协作时，一人一章，避免冲突。建议按 P0 → P1 → P2 顺序。
+高数面向工科，重**计算与应用**、轻**ε 语言的纯证明**——与数学分析的取向不同，写作时务必体现这一点（多算例、多几何/物理背景，证明给思路而非全程 ε-δ）。
+
+---
+
+## 2. 每章必须交付 3 个文件
+
+1. `chapters/{slug}.json` — 知识点讲义（主体）
+2. `exercises/{slug}.json` — 练习题
+3. `diagrams/{slug}.json` — 配图规格
+
+字段结构**完全复用** `math-analysis` 的样板（见 `CONTENT_AGENT.md` §5/§6/§7）。
+只需把 `courseId` 改成 `"gaodeng-shuxue"`，`volumeId` 改成对应册，`number` 改成本章序号。
+
+---
+
+## 3. 内容深度硬指标（针对「内容少不精」的整改）
+
+旧内容的问题是知识点太少、讲解太短。本次每章**必须达到**：
+
+### 3.1 知识点数量
+- 每章 **6–10 个 knowledgePoint**（不是 3 个）。按教材小节切分，一个核心概念/一个主定理/一类方法各算一个 KP。
+- 例：第 5 章定积分应该至少含：定积分定义与可积性、牛顿-莱布尼茨公式、换元法、分部积分、定积分几何应用（面积/体积/弧长）、物理应用（功/压力）、反常积分。
+
+### 3.2 每个 knowledgePoint 的字段下限
+| 字段 | 下限要求 |
+|------|---------|
+| `learningGoals` | 3–5 条，动词开头，可测 |
+| `coreExplanation` | **≥ 3 段、≥ 350 字**；必含至少 1 个**完整算例**（带步骤），不能只讲概念 |
+| `keyDefinitions` | 该 KP 涉及的定义全列，statement 用自己的话精确陈述 |
+| `keyTheorems` | 主定理必列，附 `proofSketch`（思路，2–4 步） |
+| `proofIdeas` | 计算型 KP 写「解题套路」，证明型 KP 写「证明三步」 |
+| `socraticQuestions` | 3–5 条，能戳中易错点 |
+| `commonMistakes` | 3–4 条，写工科生**真实**常犯错（如换元忘换限、求体积选错公式） |
+| `exampleIds` / `exerciseIds` | 指向 exercises 文件中真实存在的 id |
+| `diagramIds` | **每章至少 50% 的 KP 要挂 1 张图**（见 §4） |
+| `masteryCriteria` | 2–3 条，与 learningGoals 呼应 |
+
+> 质量自检：拿 `sequence-limit.json` 里任意一个 KP 对比——你的每个 KP 信息密度不得低于它。那是**及格线**，不是上限。
+
+### 3.3 算例优先
+工科高数的灵魂是「会算」。`coreExplanation` 里的算例要**写全过程**，例如：
+> 求 $\\\\int x e^x \\\\mathrm{d}x$：设 $u=x,\\\\ \\\\mathrm{d}v=e^x\\\\mathrm{d}x$，则 $\\\\mathrm{d}u=\\\\mathrm{d}x,\\\\ v=e^x$，由分部积分 $\\\\int u\\\\,\\\\mathrm{d}v=uv-\\\\int v\\\\,\\\\mathrm{d}u=xe^x-\\\\int e^x\\\\mathrm{d}x=xe^x-e^x+C$。
+
+---
+
+## 4. 配图硬指标（针对「配图也没有」的整改）⚠️ 重要
+
+> **背景**：当前渲染器只有少数图类型能真正画出来，其余只显示文字描述。
+> 为避免你写的图变成「一段说明文字」，本次**约定一套渲染器一定支持的图类型白名单**。
+> **只用白名单内的 `type`，并把几何参数写进 `parameters`**，渲染器才能真正画图。
+
+### 4.1 允许的 `type`（白名单）与必填 `parameters`
+
+| type | 用途 | parameters 必填项 |
+|------|------|------------------|
+| `number-line` | 数轴 / 邻域 / 区间 | `axisMin,axisMax,points:[{x,label}],intervals:[{from,to,label,open}]` |
+| `function-plot` | 单条函数曲线 | `xRange:[a,b],expr`（如 `"x^2"`、`"sin(x)"`）`,marks:[{x,label}],asymptotes:[]` |
+| `multi-curve-plot` | 多条曲线对比 | `xRange,curves:[{expr,label,style}]` |
+| `area-under-curve` | 定积分面积 | `expr,xRange,fillFrom,fillTo,label` |
+| `region-2d` | 二重积分区域 / 平面区域 | `xRange,yRange,boundaries:[{expr,label}],fill:true` |
+| `geometric` | 三角形/圆/向量等纯几何 | `shapes:[{kind,points/center/r,label}]`（kind: line/point/circle/polygon/vector） |
+| `table` | 对照表 / 符号表 / 收敛判别表 | `columns:[...],rows:[[...]]` |
+
+> 若你需要的图**不在白名单内**，不要硬造新 type（会渲染成纯文字）。改用最接近的 type，或在 `diagrams` 里把它写成 `table`，或留 `diagramIds: []` 并在 `teacherNotes` 写明「待补图」，交给主智能体扩渲染器。
+
+### 4.2 每张图对象必填字段
+```jsonc
+{
+  "id": "gd-int-area-under-curve",      // 全课程唯一，前缀 gd-
+  "type": "area-under-curve",           // 必须取自 §4.1 白名单
+  "title": "定积分作为曲边梯形面积",
+  "description": "$\\\\int_a^b f(x)\\\\,\\\\mathrm{d}x$ 表示曲线下方、x 轴上方的面积。",
+  "knowledgePointIds": ["definite-integral-concept"],
+  "parameters": {                        // ⚠️ 必须填几何参数，不能是 {}
+    "expr": "0.5*x*x+1",
+    "xRange": [0, 3],
+    "fillFrom": 0.5,
+    "fillTo": 2.5,
+    "label": "S"
+  },
+  "studentPrompt": "把 [a,b] 分得更细，矩形和会怎样逼近这块面积？",
+  "teacherNotes": ["强调被积函数非负时积分=面积；有正有负时是代数和。"]
+}
+```
+
+### 4.3 数量要求
+- 每章 **3–6 张图**，覆盖本章最核心的几何直观（极限的 ε 邻域、导数的切线、积分的面积、级数的部分和、空间曲面等）。
+- 宁可少而准，不要为凑数写无法渲染的图。
+
+---
+
+## 5. 练习题要求（针对「不精」）
+
+- 每个 KP **至少 3 道**：基础计算 ×1 + 中档 ×1 + 综合/应用 ×1。
+- `type` 工科侧重 `computation`，但每章保留 2–3 道 `proof`/`analysis`。
+- `sourceType` 用 `adapted`（教材题改编）或 `bridging`（自编衔接题）；**严禁编造题号冒充教材原题**，`sourceRef` 一律写 `"待核对题源（章节信息）"`。
+- `gradingRubric` 写**评分点**（得分关键步骤），`hints` 给 1–2 级提示，`commonMistakes` 写本题特有的坑。
+
+---
+
+## 6. 内容安全规则（必须遵守，违反即作废）
+
+- ❌ 不得整段复制教材原文；用自己的语言解释（可引用定理名/定义名，陈述自写）。
+- ❌ 不得编造教材题号；无法核对写 `"待核对题源"`。
+- ❌ 不得写入任何 API Key、密钥、PDF、截图。
+- ✅ `coreExplanation`、`statement` 均为自编讲义，允许参考教材思路。
+
+---
+
+## 7. 每章交付自检清单
+
+提交一章前逐条核对：
+
+- [ ] `chapters/{slug}.json` 含 **6–10 个 KP**，每个 `coreExplanation` ≥ 3 段且含完整算例
+- [ ] 每个 KP 字段达到 §3.2 下限，无空 `learningGoals`/`commonMistakes`
+- [ ] `exercises/{slug}.json` 每个 KP ≥ 3 题，`sourceRef` 合规
+- [ ] `diagrams/{slug}.json` 3–6 张图，**每张 `type` 取自 §4.1 白名单且 `parameters` 非空**
+- [ ] 所有 `diagramIds/exampleIds/exerciseIds/knowledgePointIds` 交叉引用均能对上
+- [ ] LaTeX 全部 `\\\\`（四反斜杠），字符串内无英文 `"`（用「」《》）
+- [ ] `JSON.parse()` 能通过（无多余逗号）；运行 `npm run validate:all` 无错
+- [ ] `courseId` 全部为 `"gaodeng-shuxue"`，ID 前缀 `gd-`
+
+---
+
+## 8. 分工建议（多 AI 并行）
+
+| 批次 | 章节 | 说明 |
+|------|------|------|
+| 第一批 P0 | 第 1、2、3 章 | 极限/导数/中值定理，最高频，先做出质量标杆 |
+| 第二批 P1 | 第 4、5、8、9 章 | 积分与多元，工科主力内容 |
+| 第三批 P1 | 第 6 章 | 微分方程（数分未含，需独立组织） |
+| 第四批 P2 | 第 7、10、11 章 | 向量几何、曲线曲面积分、无穷级数 |
+
+每人开工前在本文件对应章节后面标注 `认领人 / 日期`，完成后改成 `✅ 完成`，避免撞车。
+
+---
+
+## 认领登记区
+
+- [ ] 第 1 章 函数、极限与连续 —
+- [ ] 第 2 章 导数与微分 —
+- [ ] 第 3 章 微分中值定理与导数应用 —
+- [ ] 第 4 章 不定积分 —
+- [ ] 第 5 章 定积分及其应用 —
+- [ ] 第 6 章 微分方程 —
+- [ ] 第 7 章 向量代数与空间解析几何 —
+- [ ] 第 8 章 多元函数微分法及其应用 —
+- [ ] 第 9 章 重积分 —
+- [ ] 第 10 章 曲线积分与曲面积分 —
+- [ ] 第 11 章 无穷级数 —
diff --git a/docs/superpowers/plans/2026-06-20-dual-end-learning-workbench-ui-plan.md b/docs/superpowers/plans/2026-06-20-dual-end-learning-workbench-ui-plan.md
new file mode 100644
index 0000000..4b291bb
--- /dev/null
+++ b/docs/superpowers/plans/2026-06-20-dual-end-learning-workbench-ui-plan.md
@@ -0,0 +1,216 @@
+# Dual-End Learning Workbench UI Implementation Plan
+
+> **For agentic workers:** REQUIRED SUB-SKILL: Use superpowers:subagent-driven-development (recommended) or superpowers:executing-plans to implement this plan task-by-task. Steps use checkbox (`- [ ]`) syntax for tracking.
+
+**Goal:** Ship a coherent dual-end learning workbench upgrade for the web app and WeChat Mini Program, including miniprogram diagram data and rendering entry points.
+
+**Architecture:** Keep the existing JSON-first content pipeline. Extend the miniprogram data builder to include diagram metadata, add a focused miniprogram diagram component, and refine existing web/miniprogram UI surfaces without changing the core course schema.
+
+**Tech Stack:** Next.js 15, React 19, KaTeX, WeChat Mini Program WXML/WXSS/JS, Node validation scripts.
+
+---
+
+### Task 1: Protect Repository Hygiene
+
+**Files:**
+- Modify: `.gitignore`
+
+- [x] **Step 1: Ignore local visual companion and logs**
+
+Add these lines under local generated data:
+
+```gitignore
+*.log
+.superpowers/
+```
+
+- [x] **Step 2: Confirm git status no longer shows visual companion files**
+
+Run: `git status --short`
+
+Expected: `.superpowers/` and root `*.log` files are not listed.
+
+### Task 2: Document The Product Story
+
+**Files:**
+- Create: `docs/superpowers/specs/2026-06-20-dual-end-learning-workbench-ui-design.md`
+- Create: `docs/superpowers/plans/2026-06-20-dual-end-learning-workbench-ui-plan.md`
+
+- [x] **Step 1: Write the design spec**
+
+Document the dual-end learning loop, web refinements, miniprogram learning-page changes, diagram strategy, PR story, and acceptance criteria.
+
+- [x] **Step 2: Write this implementation plan**
+
+Keep the plan scoped to UI/interaction and miniprogram diagram support. Content expansion for the remaining chapters stays out of scope.
+
+### Task 3: Add Miniprogram Diagram Validation
+
+**Files:**
+- Modify: `package.json`
+- Create: `scripts/validate-wx-diagrams.mjs`
+
+- [ ] **Step 1: Add failing validation**
+
+Create `scripts/validate-wx-diagrams.mjs` that checks:
+
+```js
+assert(sequenceKp.diagrams.some((diagram) => diagram.id === "epsilon-neighborhood-on-number-line"));
+assert(studyJson.usingComponents["diagram-card"] === "/components/diagram-card/diagram-card");
+assert(studyWxml.includes("<diagram-card"));
+assert(fs.existsSync("wx-miniprogram/components/diagram-card/diagram-card.js"));
+```
+
+- [ ] **Step 2: Wire the script**
+
+Add:
+
+```json
+"validate:wx-diagrams": "node scripts/build-wx-data.js && node scripts/validate-wx-diagrams.mjs"
+```
+
+- [ ] **Step 3: Run and confirm failure**
+
+Run: `npm run validate:wx-diagrams`
+
+Expected: failure because the data builder and component are not implemented yet.
+
+### Task 4: Include Diagrams In Mini Program Data
+
+**Files:**
+- Modify: `scripts/build-wx-data.js`
+
+- [ ] **Step 1: Read each chapter diagram file**
+
+When a volume chapter has `diagramFile`, read it next to the chapter and exercise files.
+
+- [ ] **Step 2: Adapt diagrams for the mini program**
+
+Return compact objects with:
+
+```js
+{
+  id,
+  title,
+  type,
+  typeLabel,
+  displayKind,
+  description,
+  parameters,
+  teacherNotes,
+  studentPrompt
+}
+```
+
+- [ ] **Step 3: Attach diagrams to each knowledge point**
+
+Match by explicit `kp.diagramIds` first and by `diagram.knowledgePointIds` second, de-duplicating by id.
+
+- [ ] **Step 4: Run validation**
+
+Run: `npm run validate:wx-diagrams`
+
+Expected: still fails until the component and WXML are implemented.
+
+### Task 5: Render Diagrams In The Mini Program Study Page
+
+**Files:**
+- Create: `wx-miniprogram/components/diagram-card/diagram-card.js`
+- Create: `wx-miniprogram/components/diagram-card/diagram-card.json`
+- Create: `wx-miniprogram/components/diagram-card/diagram-card.wxml`
+- Create: `wx-miniprogram/components/diagram-card/diagram-card.wxss`
+- Modify: `wx-miniprogram/pages/study/study.json`
+- Modify: `wx-miniprogram/pages/study/study.wxml`
+- Modify: `wx-miniprogram/pages/study/study.wxss`
+- Modify: `wx-miniprogram/pages/study/study.js`
+
+- [ ] **Step 1: Create diagram-card component**
+
+The component derives a display model from `diagram.type` and `diagram.parameters`; it renders a lightweight visual for number-line, sequence, function, table, and concept-style diagrams.
+
+- [ ] **Step 2: Register the component**
+
+Add to `study.json`:
+
+```json
+"diagram-card": "/components/diagram-card/diagram-card"
+```
+
+- [ ] **Step 3: Insert the teaching diagrams section**
+
+In the learn tab, render a section when `kp.diagrams.length > 0` and loop over `kp.diagrams` with `<diagram-card diagram="{{item}}" />`.
+
+- [ ] **Step 4: Add diagram counters**
+
+Expose diagram count in the top navigation badges and learning-page state.
+
+- [ ] **Step 5: Run validation**
+
+Run: `npm run validate:wx-diagrams`
+
+Expected: pass.
+
+### Task 6: Refine Web And Mini Program UI Rhythm
+
+**Files:**
+- Modify: `app/globals.css`
+- Modify: `components/course/CourseSidebar.tsx`
+- Modify: `components/course/ChapterHeader.tsx`
+- Modify: `components/course/KnowledgePointNav.tsx`
+- Modify: `components/course/ExercisePanel.tsx`
+- Modify: `components/course/TutorPanel.tsx`
+- Modify: `wx-miniprogram/pages/index/index.wxml`
+- Modify: `wx-miniprogram/pages/index/index.wxss`
+- Modify: `wx-miniprogram/pages/chapter/chapter.wxml`
+- Modify: `wx-miniprogram/pages/chapter/chapter.wxss`
+- Modify: `wx-miniprogram/pages/study/study.wxss`
+
+- [ ] **Step 1: Tighten web hierarchy**
+
+Improve spacing, section headings, nav affordances, exercise action grouping, and AI settings treatment while preserving the editorial palette.
+
+- [ ] **Step 2: Align miniprogram labels**
+
+Use the same language as the web app: 教学图示、思考题、易错提醒、AI 老师、评分要点.
+
+- [ ] **Step 3: Improve progress affordances**
+
+Show diagram count and progress signals in chapter/study contexts.
+
+### Task 7: Validate And Publish
+
+**Files:**
+- Modify: README or PR body only if needed for narrative.
+
+- [ ] **Step 1: Run validation commands**
+
+Run:
+
+```bash
+npm run validate:wx-diagrams
+npm run validate:all
+npm run build
+```
+
+- [ ] **Step 2: Review git diff**
+
+Run: `git diff --stat` and inspect changed files. Do not stage `.superpowers/`, root logs, or generated local secrets.
+
+- [ ] **Step 3: Commit in story chunks**
+
+Suggested commits:
+
+```bash
+git commit -m "docs: frame dual-end learning workbench upgrade"
+git commit -m "feat(wx): render teaching diagrams in study flow"
+git commit -m "style: refine dual-end learning workbench rhythm"
+```
+
+- [ ] **Step 4: Push and open draft PR**
+
+Run:
+
+```bash
+git push -u origin codex/dual-workbench-ui-miniprogram
+gh pr create --draft --title "[codex] Upgrade dual-end math learning workbench" --body-file <body-file>
+```
diff --git a/docs/superpowers/specs/2026-06-20-dual-end-learning-workbench-ui-design.md b/docs/superpowers/specs/2026-06-20-dual-end-learning-workbench-ui-design.md
new file mode 100644
index 0000000..c6226eb
--- /dev/null
+++ b/docs/superpowers/specs/2026-06-20-dual-end-learning-workbench-ui-design.md
@@ -0,0 +1,52 @@
+# 双端学习工作台 UI 与操作闭环设计
+
+日期：2026-06-20
+
+## 目标
+
+把数学分析学习工作台从“网页端已成型、小程序端可用但少图示”推进为双端一致的学习产品。用户在网页和小程序里都应理解同一条学习闭环：继续学习、进入知识点、阅读讲义与图示、完成练习、向 AI 追问或提交批改、回到进度反馈。
+
+## 设计原则
+
+- 保留现有编辑/教科书视觉语言：暖纸底、墨黑正文、酒红强调、金色辅助、克制边框和衬线排版。
+- 不做营销页，不新增账号、后台编辑器或付费系统。
+- 图示是教学材料，不是装饰。网页端继续用程序化 SVG；小程序端先做可用的图示卡与轻量示意渲染，再逐步补全复杂图形。
+- 双端入口命名保持一致：讲义、教学图示、思考题、易错提醒、练习、AI 老师、评分要点。
+- 进度状态必须出现在学习路径上，而不是只藏在练习反馈里。
+
+## 网页端体验
+
+网页端保留三栏工作台结构。
+
+左栏从章节列表强化为学习路线：章节状态、样板完成、草稿、待整理、掌握状态和题量都以更可扫的方式展示。中栏强化当前知识点头部，讲义、学习目标、教学图示、思考题、易错提醒形成稳定阅读顺序。练习区保持题目列表与当前题工作区分离，批改结果、提示和评分要点作为复盘材料呈现。右栏 AI 老师减少设置对话的干扰，突出它正在围绕当前知识点工作。
+
+## 小程序端体验
+
+首页继续以继续学习和章节目录为主，但章节列表要更明确展示学习进度。章节页中的知识点列表显示题量、最高分和是否有图示。学习页保持讲义/练习双 tab，讲义 tab 内加入教学图示区块，并在顶部显示当前位置、题量、最高分和图示数量。练习 tab 保持筛选、作答、提示、批改、评分要点和问 AI 老师的完整路径。
+
+## 小程序图示策略
+
+第一阶段交付可用图示链路：
+
+- `scripts/build-wx-data.js` 从章节的 `diagramFile` 读取图示 JSON。
+- 每个知识点根据 `diagramIds` 与 `knowledgePointIds` 匹配图示。
+- 小程序学习页渲染 `diagram-card` 组件，显示图题、类型、说明、学生提问与教学提示。
+- 对数轴、序列、函数曲线、ε-δ、渐近线、跳跃、表格等高频类型给出轻量示意，不阻塞学习主流程。
+
+第二阶段再追求像素级一致：把网页图形引擎的坐标映射、曲线采样和表格渲染进一步移植到小程序 Canvas 或 SVG 图片方案。
+
+## 发布叙事
+
+GitHub PR 应讲清三件事：
+
+1. 这是一个双端学习闭环升级，不只是样式调整。
+2. 网页端已经具备程序化数学图示、自托管字体和 AI 辅导，小程序端补齐图示入口后更接近完整学习端。
+3. 内容与代码仍解耦，JSON 源继续作为双端共享内容源。
+
+## 验收标准
+
+- 网页端构建通过，三栏工作台在宽屏和窄屏都不出现明显重叠。
+- 小程序数据生成脚本能把图示打包进知识点。
+- 小程序学习页能显示至少数列极限、函数极限章节的教学图示卡。
+- `npm run validate:wx-diagrams` 能验证图示数据与组件接入。
+- PR 描述覆盖功能价值、用户影响、验证命令和已知边界。
diff --git a/exam/advanced-algebra-final-B.tex b/exam/advanced-algebra-final-B.tex
new file mode 100644
index 0000000..79d5bce
--- /dev/null
+++ b/exam/advanced-algebra-final-B.tex
@@ -0,0 +1,319 @@
+% !TEX program = xelatex
+\documentclass[12pt]{ctexart}
+
+\usepackage[a4paper,margin=2.2cm,top=2.6cm]{geometry}
+\usepackage{amsmath,amssymb,amsthm}
+\usepackage{enumitem}
+\usepackage{array}
+\usepackage{fancyhdr}
+
+\setlist[enumerate]{itemsep=9pt,topsep=5pt,leftmargin=2.2em}
+
+\pagestyle{fancy}
+\fancyhf{}
+\lhead{\small 高等代数 I 期末考试 · B 卷}
+\rhead{\small 第 \thepage 页}
+\renewcommand{\headrulewidth}{0.4pt}
+
+\newcommand{\bigsection}[2]{%
+  \vspace{6pt}%
+  {\noindent\bfseries\large #1}\hfill{\normalsize（本大题共 #2）}\par
+  \vspace{2pt}\hrule height0.4pt\vspace{8pt}}
+
+\newcommand{\blank}[1][2.6cm]{\underline{\hspace{#1}}}
+
+\newcommand{\optgrid}[4]{%
+  \par\smallskip\noindent
+  \begin{tabular}{@{}p{0.45\textwidth}p{0.45\textwidth}@{}}
+  (A)~#1 & (B)~#2 \\[3pt]
+  (C)~#3 & (D)~#4
+  \end{tabular}}
+
+\newcommand{\rank}{\operatorname{r}}
+\linespread{1.12}
+
+\begin{document}
+
+%==================== 封面 ====================
+\begin{center}
+  {\Large\bfseries 高等代数 I 期末考试试卷（B 卷）}\\[4pt]
+  {\small 教材：北京大学数学系（王萼芳、石生明）《高等代数》（第 5 版）\\
+  范围：行列式、线性方程组、向量组的线性相关性、矩阵与逆矩阵、初等变换与初等矩阵、矩阵与向量组的秩}\\[8pt]
+\end{center}
+
+\noindent
+\begin{tabular}{@{}p{4.6cm}p{4.6cm}p{4.6cm}@{}}
+姓名：\blank[2.8cm] & 学号：\blank[2.8cm] & 班级：\blank[2.8cm]
+\end{tabular}
+
+\vspace{6pt}
+\noindent\textbf{满分 100 分\qquad 考试时间 120 分钟\qquad 闭卷}
+
+\vspace{8pt}
+\noindent
+\renewcommand{\arraystretch}{1.4}
+\begin{tabular}{|c|c|c|c|c|c|}
+\hline
+题号 & 一 & 二 & 三 & 四 & 总分 \\\hline
+满分 & 30 & 20 & 10 & 40 & 100 \\\hline
+得分 & & & & & \\\hline
+\end{tabular}
+
+\vspace{12pt}
+
+%==================== 一、选择题 ====================
+\bigsection{一、单项选择题}{10 小题，每题 3 分，共 30 分}
+
+\begin{enumerate}[label=\arabic*.]
+\item 在 4 阶行列式的展开式中，项 $a_{14}a_{23}a_{31}a_{42}$ 所带的符号为（\qquad）
+  \optgrid{正号 $+$}{负号 $-$}{$0$}{无法确定}
+
+\item 设向量组 $\alpha,\beta,\gamma$ 线性无关，则下列向量组线性\textbf{无关}的是（\qquad）
+  \optgrid{$\alpha-\beta,\ \beta-\gamma,\ \gamma-\alpha$}{$\alpha+\beta,\ \beta+\gamma,\ \gamma+\alpha$}{$\alpha-\beta,\ \beta-\gamma,\ \alpha-\gamma$}{$\alpha,\ \beta,\ \alpha+\beta$}
+
+\item 设 $A$ 为 $n$ 阶方阵，则 $A$ \textbf{不可逆}的充要条件是（\qquad）
+  \optgrid{$|A|\neq 0$}{$\rank(A)=n$}{$Ax=0$ 只有零解}{$A$ 的列向量组线性相关}
+
+\item 设 $A,B$ 为同型矩阵，则下列恒成立的是（\qquad）
+  \optgrid{$\rank(A+B)=\rank(A)+\rank(B)$}{$\rank(A+B)\leq\rank(A)+\rank(B)$}{$\rank(AB)=\rank(A)\rank(B)$}{$\rank(A+B)\geq\rank(A)+\rank(B)$}
+
+\item 设 $A$ 为 $3$ 阶方阵且 $|A|=2$，则 $|-A|=$（\qquad）
+  \optgrid{$2$}{$-2$}{$8$}{$-8$}
+
+\item 设 $A$ 为 $n$ 阶方阵。方程组 $Ax=b$ 对任意 $b$ 都有唯一解的充要条件是（\qquad）
+  \optgrid{$|A|=0$}{$|A|\neq 0$}{$\rank(A)<n$}{$b\neq 0$}
+
+\item 交换单位矩阵 $E$ 的第 $i,j$ 两行得到初等矩阵 $P$，则 $PA$ 等于（\qquad）
+  \optgrid{交换 $A$ 的第 $i,j$ 两行}{交换 $A$ 的第 $i,j$ 两列}{$A$ 的第 $i$ 行乘 $-1$}{$A$ 不变}
+
+\item 齐次线性方程组 $\begin{cases}a x_1+x_2+x_3=0\\ x_1+a x_2+x_3=0\\ x_1+x_2+x_3=0\end{cases}$ 只有零解的充要条件是（\qquad）
+  \optgrid{$a=1$}{$a\neq 1$}{$a=0$}{对任意 $a$ 成立}
+
+\item 设 $A_{ij}$ 为 $n$ 阶行列式中元素 $a_{ij}$ 的代数余子式。当 $i\neq j$ 时，
+  $\displaystyle\sum_{k=1}^{n}a_{kj}A_{ki}=$（\qquad）
+  \optgrid{$|A|$}{$0$}{$1$}{$|A|^{2}$}
+
+\item 设 $5$ 元齐次线性方程组 $Ax=0$ 的基础解系含 $3$ 个解向量，则 $\rank(A)=$（\qquad）
+  \optgrid{$2$}{$3$}{$5$}{$8$}
+\end{enumerate}
+
+%==================== 二、填空题 ====================
+\bigsection{二、填空题}{10 小题，每题 2 分，共 20 分}
+
+\begin{enumerate}[label=\arabic*.]
+\item 行列式 $\begin{vmatrix}2&1\\1&3\end{vmatrix}=\blank$。
+\item 排列 $4\,1\,5\,2\,3$ 的逆序数为 $\blank[2cm]$。
+\item 设 $A$ 为 $4$ 阶方阵且 $|A|=3$，则 $|3A|=\blank[2.2cm]$。
+\item 同上 $A$，则 $|A^{-1}|=\blank[2cm]$。
+\item 同上 $A$，则伴随矩阵 $|A^{*}|=\blank[2cm]$。
+\item $\begin{vmatrix}1&1&1\\ 1&2&4\\ 1&3&9\end{vmatrix}=\blank[2.4cm]$。
+\item 向量组 $\alpha_1=(1,2),\ \alpha_2=(2,4),\ \alpha_3=(1,1)$ 的秩为 $\blank[2cm]$。
+\item 设 $A$ 为 $4\times 6$ 矩阵且 $\rank(A)=3$，则 $Ax=0$ 的基础解系含 $\blank[2cm]$ 个向量。
+\item 非齐次线性方程组 $Ax=b$（$A$ 为 $m\times n$ 矩阵）有无穷多解的充要条件是
+  $\rank(A)=\rank(A,b)<\blank[2cm]$。
+\item 设 $A,B$ 均为 $3$ 阶方阵，$|A|=2,\ |B|=3$，则 $|AB|=\blank[2cm]$。
+\end{enumerate}
+
+%==================== 三、证明题 ====================
+\bigsection{三、证明题}{2 小题，每题 5 分，共 10 分}
+
+\begin{enumerate}[label=\arabic*.]
+\item 设 $A$ 为 $n$ 阶方阵且 $A^{2}=A$（幂等矩阵）。证明：
+  \[
+  \rank(A)+\rank(A-E)=n .
+  \]
+
+\item 设向量组 $\alpha_1,\alpha_2,\alpha_3$ 线性无关。证明：向量组
+  $\alpha_1,\ \alpha_1+\alpha_2,\ \alpha_1+\alpha_2+\alpha_3$ 也线性无关。
+\end{enumerate}
+
+%==================== 四、计算题 ====================
+\bigsection{四、计算题}{4 小题，每题 10 分，共 40 分。要求写出主要步骤}
+
+\begin{enumerate}[label=\arabic*.]
+\item 计算箭型行列式
+  \[
+  D=\begin{vmatrix}
+  5 & 1 & 1 & 1\\
+  1 & 1 & 0 & 0\\
+  1 & 0 & 1 & 0\\
+  1 & 0 & 0 & 1
+  \end{vmatrix}.
+  \]
+
+\item $a$ 取何值时，齐次线性方程组
+  \[
+  \begin{cases}
+  x_1+x_2+x_3=0,\\
+  x_1+2x_2+a x_3=0,\\
+  x_1+4x_2+a^{2}x_3=0
+  \end{cases}
+  \]
+  只有零解？有非零解？在有非零解时求出一个基础解系。
+
+\item 用初等行变换求矩阵 $A=\begin{pmatrix}1&2&3\\ 2&5&3\\ 1&0&8\end{pmatrix}$ 的逆矩阵 $A^{-1}$。
+
+\item 设向量组
+  \[
+  \alpha_1=(1,0,1,1),\quad \alpha_2=(1,1,0,1),\quad \alpha_3=(3,1,2,3),\quad \alpha_4=(0,-1,1,0).
+  \]
+  求该向量组的秩与一个极大线性无关组，并把其余向量用该极大无关组线性表示。
+\end{enumerate}
+
+\vspace{8pt}
+\begin{center}\small —— 试卷结束，参考答案见后 ——\end{center}
+
+%==================== 参考答案 ====================
+\clearpage
+\begin{center}
+  {\Large\bfseries 参考答案与评分标准（B 卷）}\\[2pt]
+  {\small 高等代数 I 期末考试}
+\end{center}
+\vspace{6pt}\hrule\vspace{12pt}
+
+\noindent\textbf{一、单项选择题}（每题 3 分）\par\vspace{4pt}
+\begin{center}
+\renewcommand{\arraystretch}{1.3}
+\begin{tabular}{|c|c|c|c|c|c|c|c|c|c|c|}
+\hline
+题号 & 1 & 2 & 3 & 4 & 5 & 6 & 7 & 8 & 9 & 10 \\\hline
+答案 & B & B & D & B & B & B & A & B & B & A \\\hline
+\end{tabular}
+\end{center}
+\noindent\small 简析：1.\,列指标排列 $(4,3,1,2)$ 的逆序数为 $5$（奇），取负号。
+2.\,$(\alpha+\beta)+( \gamma+\alpha)-(\beta+\gamma)=2\alpha\neq0$，且系数行列式 $=2\neq0$，故 (B) 无关；(A)(C)(D) 均线性相关。
+3.\,$A$ 不可逆 $\Leftrightarrow |A|=0\Leftrightarrow$ 列向量组线性相关。
+4.\,秩的次可加性 $\rank(A+B)\leq\rank(A)+\rank(B)$。
+5.\,$|-A|=(-1)^{3}|A|=-2$。
+8.\,系数行列式 $=(a-1)^{2}$，只有零解 $\Leftrightarrow a\neq1$。
+9.\,代数余子式按列「错位相乘」之和为 $0$。
+10.\,$\rank(A)=n-3=5-3=2$。\normalsize
+
+\vspace{10pt}
+\noindent\textbf{二、填空题}（每题 2 分）\par\vspace{4pt}
+\begin{enumerate}[label=\arabic*.,itemsep=3pt]
+\item $5$ \hfill
+\item $5$ \hfill
+\item $243$（$|3A|=3^{4}|A|=81\cdot3$）\hfill
+\item $\dfrac13$ \hfill
+\item $27$（$|A^{*}|=|A|^{n-1}=3^{3}$）
+\item $2$（范德蒙德 $(2-1)(3-1)(3-2)$）
+\item $2$ \hfill
+\item $3$（$n-\rank(A)=6-3$）
+\item $n$（未知量个数）\hfill
+\item $6$（$|AB|=|A||B|$）
+\end{enumerate}
+
+\vspace{6pt}
+\noindent\textbf{三、证明题}（每题 5 分）
+
+\begin{enumerate}[label=\textbf{\arabic*.},itemsep=11pt]
+\item 因为 $A^{2}=A$，所以 $A(A-E)=A^{2}-A=O$，于是
+  \[
+  \rank(A)+\rank(A-E)\leq n. \tag{1}
+  \]
+  又 $A-(A-E)=E$，由秩的不等式 $\rank(M)+\rank(N)\geq\rank(M-N)$，
+  \[
+  \rank(A)+\rank(A-E)\geq\rank\big(A-(A-E)\big)=\rank(E)=n. \tag{2}
+  \]
+  由 (1)(2) 得 $\rank(A)+\rank(A-E)=n$。$\qquad\blacksquare$
+
+\item 设有数 $k_1,k_2,k_3$ 使
+  \[
+  k_1\alpha_1+k_2(\alpha_1+\alpha_2)+k_3(\alpha_1+\alpha_2+\alpha_3)=0,
+  \]
+  整理得 $(k_1+k_2+k_3)\alpha_1+(k_2+k_3)\alpha_2+k_3\alpha_3=0$。
+  由 $\alpha_1,\alpha_2,\alpha_3$ 线性无关，得
+  \[
+  \begin{cases}k_1+k_2+k_3=0\\ k_2+k_3=0\\ k_3=0\end{cases}
+  \ \Rightarrow\ k_3=0,\ k_2=0,\ k_1=0.
+  \]
+  故 $\alpha_1,\alpha_1+\alpha_2,\alpha_1+\alpha_2+\alpha_3$ 线性无关。$\qquad\blacksquare$
+\end{enumerate}
+
+\vspace{6pt}
+\noindent\textbf{四、计算题}（每题 10 分）
+
+\begin{enumerate}[label=\textbf{\arabic*.},itemsep=13pt]
+\item 把第 $2,3,4$ 行都从第 $1$ 行减去（即 $r_1\to r_1-r_2-r_3-r_4$）。
+  因 $r_2+r_3+r_4=(3,1,1,1)$，故新的第 $1$ 行为
+  \[
+  (5,1,1,1)-(3,1,1,1)=(2,0,0,0).
+  \]
+  于是按第 $1$ 行展开：
+  \[
+  D=\begin{vmatrix}
+  2&0&0&0\\ 1&1&0&0\\ 1&0&1&0\\ 1&0&0&1
+  \end{vmatrix}
+  =2\cdot\begin{vmatrix}1&0&0\\0&1&0\\0&0&1\end{vmatrix}=2.
+  \]
+
+\item 系数行列式
+  \[
+  D=\begin{vmatrix}1&1&1\\1&2&a\\1&4&a^{2}\end{vmatrix}
+  \xrightarrow[r_3-r_1]{r_2-r_1}
+  \begin{vmatrix}1&1&1\\0&1&a-1\\0&3&a^{2}-1\end{vmatrix}
+  =(a^{2}-1)-3(a-1)=(a-1)(a-2).
+  \]
+  \textbf{（i）当 $a\neq1$ 且 $a\neq2$ 时}，$D\neq0$，方程组只有零解。\\[2pt]
+  \textbf{（ii）当 $a=1$ 时}，系数矩阵
+  $\begin{pmatrix}1&1&1\\1&2&1\\1&4&1\end{pmatrix}\to
+  \begin{pmatrix}1&1&1\\0&1&0\\0&0&0\end{pmatrix}$，$\rank=2$。
+  由 $x_2=0,\ x_1+x_3=0$，得基础解系 $\xi=(-1,0,1)^{\mathsf T}$。\\[2pt]
+  \textbf{（iii）当 $a=2$ 时}，系数矩阵
+  $\begin{pmatrix}1&1&1\\1&2&2\\1&4&4\end{pmatrix}\to
+  \begin{pmatrix}1&1&1\\0&1&1\\0&0&0\end{pmatrix}$，$\rank=2$。
+  由 $x_2+x_3=0,\ x_1=0$，得基础解系 $\xi=(0,-1,1)^{\mathsf T}$。
+
+\item 对 $(A\,|\,E)$ 施行初等行变换（因 $|A|=-1$，过程中保持整数）：
+  \[
+  \left(\begin{array}{ccc|ccc}
+  1&2&3&1&0&0\\ 2&5&3&0&1&0\\ 1&0&8&0&0&1
+  \end{array}\right)
+  \xrightarrow[r_3-r_1]{r_2-2r_1}
+  \left(\begin{array}{ccc|ccc}
+  1&2&3&1&0&0\\ 0&1&-3&-2&1&0\\ 0&-2&5&-1&0&1
+  \end{array}\right)
+  \]
+  \[
+  \xrightarrow{r_3+2r_2}
+  \left(\begin{array}{ccc|ccc}
+  1&2&3&1&0&0\\ 0&1&-3&-2&1&0\\ 0&0&-1&-5&2&1
+  \end{array}\right)
+  \xrightarrow{-r_3}
+  \left(\begin{array}{ccc|ccc}
+  1&2&3&1&0&0\\ 0&1&-3&-2&1&0\\ 0&0&1&5&-2&-1
+  \end{array}\right)
+  \]
+  \[
+  \xrightarrow[r_2+3r_3]{r_1-3r_3}
+  \left(\begin{array}{ccc|ccc}
+  1&2&0&-14&6&3\\ 0&1&0&13&-5&-3\\ 0&0&1&5&-2&-1
+  \end{array}\right)
+  \xrightarrow{r_1-2r_2}
+  \left(\begin{array}{ccc|ccc}
+  1&0&0&-40&16&9\\ 0&1&0&13&-5&-3\\ 0&0&1&5&-2&-1
+  \end{array}\right).
+  \]
+  故
+  \[
+  A^{-1}=\begin{pmatrix}-40&16&9\\ 13&-5&-3\\ 5&-2&-1\end{pmatrix}.
+  \]
+
+\item 以 $\alpha_1,\alpha_2,\alpha_3,\alpha_4$ 为行作矩阵并作初等行变换：
+  \[
+  \begin{pmatrix}1&0&1&1\\1&1&0&1\\3&1&2&3\\0&-1&1&0\end{pmatrix}
+  \xrightarrow[r_3-3r_1]{r_2-r_1}
+  \begin{pmatrix}1&0&1&1\\0&1&-1&0\\0&1&-1&0\\0&-1&1&0\end{pmatrix}
+  \xrightarrow[r_4+r_2]{r_3-r_2}
+  \begin{pmatrix}1&0&1&1\\0&1&-1&0\\0&0&0&0\\0&0&0&0\end{pmatrix}.
+  \]
+  故秩为 $2$，$\{\alpha_1,\alpha_2\}$ 为一个极大线性无关组。由上面的消元过程：
+  \[
+  \alpha_3-3\alpha_1=\alpha_2-\alpha_1\ \Rightarrow\ \alpha_3=2\alpha_1+\alpha_2,\qquad
+  \alpha_4=-(\alpha_2-\alpha_1)=\alpha_1-\alpha_2.
+  \]
+  （验证：$2\alpha_1+\alpha_2=(3,1,2,3)=\alpha_3$，$\alpha_1-\alpha_2=(0,-1,1,0)=\alpha_4$。）
+\end{enumerate}
+
+\end{document}
diff --git a/exam/advanced-algebra-final-advanced-A.tex b/exam/advanced-algebra-final-advanced-A.tex
new file mode 100644
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--- /dev/null
+++ b/exam/advanced-algebra-final-advanced-A.tex
@@ -0,0 +1,295 @@
+% !TEX program = xelatex
+\documentclass[12pt]{ctexart}
+
+\usepackage[a4paper,margin=2.15cm,top=2.55cm,bottom=2.25cm]{geometry}
+\usepackage{amsmath,amssymb}
+\usepackage{enumitem}
+\usepackage{array}
+\usepackage{fancyhdr}
+
+\setlist[enumerate]{itemsep=9pt,topsep=5pt,leftmargin=2.2em}
+\linespread{1.13}
+
+\pagestyle{fancy}
+\fancyhf{}
+\lhead{\small 高等代数 I 期末复习进阶卷 · A 卷}
+\rhead{\small 第 \thepage 页}
+\setlength{\headheight}{14pt}
+\renewcommand{\headrulewidth}{0.4pt}
+
+\newcommand{\rnk}{\operatorname{r}}
+\newcommand{\blank}[1][2.6cm]{\underline{\hspace{#1}}}
+\newcommand{\bigsection}[2]{%
+  \vspace{7pt}%
+  {\noindent\bfseries\large #1}\hfill{\normalsize（本大题共 #2）}\par
+  \vspace{2pt}\hrule height0.4pt\vspace{8pt}}
+\newcommand{\optgrid}[4]{%
+  \par\smallskip\noindent
+  \begin{tabular}{@{}p{0.46\linewidth}p{0.46\linewidth}@{}}
+  (A)~#1 & (B)~#2 \\[3pt]
+  (C)~#3 & (D)~#4
+  \end{tabular}}
+\newcommand{\workarea}[1]{\par\vspace{0.35em}\noindent\rule{\linewidth}{0.25pt}\par\vspace{#1}}
+
+\begin{document}
+
+\begin{center}
+  {\Large\bfseries 高等代数 I 期末复习进阶卷（A 卷）}\\[4pt]
+  {\small 教材：北京大学数学系《高等代数》（第 6 版）为主\\
+  范围：行列式、线性方程组、向量组线性相关性、矩阵与逆矩阵、初等变换与初等矩阵、矩阵与向量组的秩}\\[8pt]
+\end{center}
+
+\noindent
+\begin{tabular}{@{}p{4.6cm}p{4.6cm}p{4.6cm}@{}}
+姓名：\blank[2.8cm] & 学号：\blank[2.8cm] & 班级：\blank[2.8cm]
+\end{tabular}
+
+\vspace{6pt}
+\noindent\textbf{满分 100 分\qquad 考试时间 120 分钟\qquad 闭卷}
+
+\vspace{8pt}
+\noindent
+\renewcommand{\arraystretch}{1.4}
+\begin{tabular}{|c|c|c|c|c|c|}
+\hline
+题号 & 一 & 二 & 三 & 四 & 总分 \\\hline
+满分 & 30 & 20 & 10 & 40 & 100 \\\hline
+得分 & & & & & \\\hline
+\end{tabular}
+
+\vspace{12pt}
+
+\bigsection{一、单项选择题}{10 小题，每题 3 分，共 30 分}
+
+\begin{enumerate}[label=\arabic*.]
+\item 在 $5$ 阶行列式的展开式中，项 $a_{12}a_{23}a_{35}a_{41}a_{54}$ 所带的符号为（\qquad）
+  \optgrid{正号 $+$}{负号 $-$}{$0$}{无法确定}
+
+\item 设 $A$ 为 $n$ 阶方阵，且 $A^{2}-3A+2E=O$，则下列结论正确的是（\qquad）
+  \optgrid{$A$ 不一定可逆}{$A^{-1}=\dfrac{3E-A}{2}$}{$A^{-1}=A-3E$}{$|A|=0$}
+
+\item 设 $A$ 为 $m\times n$ 矩阵，$B$ 为 $n\times s$ 矩阵，则必有（\qquad）
+  \optgrid{$\rnk(AB)\geq \rnk(A)+\rnk(B)-n$}{$\rnk(AB)=\rnk(A)+\rnk(B)-n$}{$\rnk(AB)\geq \rnk(A)+\rnk(B)-m$}{$\rnk(AB)=\min\{\rnk(A),\rnk(B)\}$}
+
+\item 设 $A$ 为 $n$ 阶矩阵，$\rnk(A)=n-1$，$A^{*}$ 为其伴随矩阵，则 $\rnk(A^{*})=$（\qquad）
+  \optgrid{$0$}{$1$}{$n-1$}{$n$}
+
+\item 对矩阵 $A$ 施行一次初等列变换，相当于（\qquad）
+  \optgrid{左乘相应的初等矩阵}{右乘相应的初等矩阵}{两侧同乘相应的初等矩阵}{取转置后再作行变换}
+
+\item 设向量组 $\alpha_1,\dots,\alpha_s$ 线性无关，且 $\beta$ 不能由它们线性表示，则（\qquad）
+  \optgrid{$\alpha_1,\dots,\alpha_s,\beta$ 线性无关}{$\alpha_1,\dots,\alpha_s,\beta$ 线性相关}{$\beta=0$}{$s$ 必等于向量空间维数}
+
+\item 非齐次线性方程组 $Ax=b$（$A$ 为 $m\times n$ 矩阵）有无穷多解的充要条件是（\qquad）
+  \optgrid{$\rnk(A)<\rnk(A,b)$}{$\rnk(A)=n$}{$\rnk(A,b)=n$}{$\rnk(A)=\rnk(A,b)<n$}
+
+\item 设 $A_{jk}$ 为 $n$ 阶行列式中元素 $a_{jk}$ 的代数余子式。当 $i\neq j$ 时，
+  $\displaystyle\sum_{k=1}^{n}a_{ik}A_{jk}=$（\qquad）
+  \optgrid{$|A|$}{$0$}{$1$}{$-|A|$}
+
+\item $n$ 元齐次线性方程组 $Ax=0$ 的系数矩阵秩为 $n-2$，则它的基础解系含（\qquad）个向量。
+  \optgrid{$0$}{$1$}{$2$}{$n-2$}
+
+\item $n$ 阶矩阵 $A$ 可以表示成若干个初等矩阵的乘积的充要条件是（\qquad）
+  \optgrid{$A$ 可逆}{$|A|=0$}{$\rnk(A)<n$}{$A$ 为对角矩阵}
+\end{enumerate}
+
+\bigsection{二、填空题}{10 小题，每题 2 分，共 20 分}
+
+\begin{enumerate}[label=\arabic*.]
+\item 排列 $6\,2\,5\,1\,4\,3$ 的逆序数为 $\blank[2cm]$。
+\item $4$ 阶行列式
+  $\begin{vmatrix}
+  a&b&b&b\\ b&a&b&b\\ b&b&a&b\\ b&b&b&a
+  \end{vmatrix}=\blank[4cm]$。
+\item $\begin{vmatrix}1&1&1\\ x&y&z\\ x^{2}&y^{2}&z^{2}\end{vmatrix}=\blank[4cm]$。
+\item 若 $P,Q$ 均为 $2$ 阶方阵，$|P|=2,\ |Q|=-3$，则
+  $\begin{vmatrix}P&O\\ R&Q\end{vmatrix}=\blank[2.5cm]$。
+\item 设 $A$ 为 $4$ 阶方阵且 $|A|=2$，则 $|A^{*}|=\blank[2.2cm]$。
+\item 设 $A$ 可逆且 $AB=O$，则 $B=\blank[2cm]$。
+\item 设 $A$ 为 $5\times 7$ 矩阵，$\rnk(A)=3$，则齐次方程组 $Ax=0$ 的解空间维数为 $\blank[2cm]$。
+\item 若 $A$ 为 $n$ 阶可逆矩阵且 $A^{2}-2A=O$，则 $A=\blank[2cm]$。
+\item 若 $\alpha_1,\alpha_2,\alpha_3,\alpha_4$ 线性无关，则向量组
+  $\alpha_1+\alpha_2,\alpha_2+\alpha_3,\alpha_3+\alpha_4,\alpha_4$ 的秩为 $\blank[2cm]$。
+\item 若非齐次线性方程组 $Ax=b$ 有解，且 $\rnk(A)=\rnk(A,b)=r<n$，则通解中自由未知量个数为 $\blank[2cm]$。
+\end{enumerate}
+
+\bigsection{三、证明题}{2 小题，每题 5 分，共 10 分}
+
+\begin{enumerate}[label=\arabic*.]
+\item 设 $A,B$ 为 $n$ 阶方阵，$AB=O$，且 $A+B$ 可逆。证明：
+  \[
+  \rnk(A)+\rnk(B)=n.
+  \]
+\workarea{4.2cm}
+
+\item 设向量组 $\alpha_1,\dots,\alpha_s$ 线性无关，向量 $\beta$ 不能由 $\alpha_1,\dots,\alpha_s$ 线性表示。证明：
+  $\alpha_1,\dots,\alpha_s,\beta$ 线性无关。
+\workarea{4.2cm}
+\end{enumerate}
+
+\clearpage
+\bigsection{四、计算题}{4 小题，每题 10 分，共 40 分。要求写出主要步骤}
+
+\begin{enumerate}[label=\arabic*.]
+\item 用拉普拉斯定理或分块思想计算行列式
+  \[
+  D=\begin{vmatrix}
+  a&b&0&0\\
+  c&d&0&0\\
+  1&2&a&b\\
+  3&4&c&d
+  \end{vmatrix}.
+  \]
+\workarea{5.2cm}
+
+\item $a$ 取何值时，线性方程组
+  \[
+  \begin{cases}
+  a x_1+x_2+x_3=1,\\
+  x_1+a x_2+x_3=1,\\
+  x_1+x_2+a x_3=a^{2}
+  \end{cases}
+  \]
+  无解、有唯一解、有无穷多解？在有无穷多解时求出通解。
+\workarea{6.0cm}
+
+\clearpage
+\item 用初等行变换求矩阵
+  \[
+  A=\begin{pmatrix}
+  1&2&1\\
+  2&5&2\\
+  1&0&3
+  \end{pmatrix}
+  \]
+  的逆矩阵 $A^{-1}$。
+\workarea{6.0cm}
+
+\item 设向量组
+  \[
+  \alpha_1=(1,0,0,1),\quad \alpha_2=(0,1,0,1),\quad
+  \alpha_3=(0,0,1,1),
+  \]
+  \[
+  \alpha_4=(1,1,1,3),\quad \alpha_5=(2,1,0,3).
+  \]
+  求该向量组的秩与一个极大线性无关组，并把其余向量用该极大无关组线性表示。
+\workarea{5.5cm}
+\end{enumerate}
+
+\begin{center}\small 试题部分结束，参考答案见后。\end{center}
+
+\clearpage
+\begin{center}
+  {\Large\bfseries 参考答案与评分标准（A 卷）}\\[2pt]
+  {\small 高等代数 I 期末复习进阶卷}
+\end{center}
+\vspace{6pt}\hrule\vspace{12pt}
+
+\noindent\textbf{一、单项选择题}（每题 3 分）
+\begin{center}
+\renewcommand{\arraystretch}{1.3}
+\begin{tabular}{|c|c|c|c|c|c|c|c|c|c|c|}
+\hline
+题号 & 1&2&3&4&5&6&7&8&9&10\\\hline
+答案 & A&B&A&B&B&A&D&B&C&A\\\hline
+\end{tabular}
+\end{center}
+
+\noindent\small 简析：1. 列指标排列 $(2,3,5,1,4)$ 的逆序数为 $4$，故为正号。2. 由
+$A(3E-A)=2E$ 得 $A$ 可逆，$A^{-1}=(3E-A)/2$。3. 为 Sylvester 秩不等式。
+4. $\rnk(A)=n-1$ 时伴随矩阵秩为 $1$。5. 初等列变换对应右乘初等矩阵。7. 有解且自由未知量个数为正。8. 代数余子式错位相乘之和为 $0$。\normalsize
+
+\vspace{8pt}
+\noindent\textbf{二、填空题}（每题 2 分）
+\begin{enumerate}[label=\arabic*.,itemsep=3pt]
+\item $10$。
+\item $(a+3b)(a-b)^3$。
+\item $(y-x)(z-x)(z-y)$。
+\item $-6$。
+\item $8$。
+\item $O$。
+\item $4$。
+\item $2E$。
+\item $4$。
+\item $n-r$。
+\end{enumerate}
+
+\vspace{6pt}
+\noindent\textbf{三、证明题}（每题 5 分）
+\begin{enumerate}[label=\textbf{\arabic*.},itemsep=10pt]
+\item 因 $AB=O$，$B$ 的列向量都属于齐次方程组 $Ax=0$ 的解空间，故
+  $\rnk(B)\leq n-\rnk(A)$，即 $\rnk(A)+\rnk(B)\leq n$。又
+  $A+B$ 可逆，所以
+  \[
+  n=\rnk(A+B)\leq \rnk(A)+\rnk(B).
+  \]
+  两式合并得 $\rnk(A)+\rnk(B)=n$。
+
+\item 设
+  $k_1\alpha_1+\cdots+k_s\alpha_s+k\beta=0$。若 $k\neq0$，则
+  \[
+  \beta=-\frac{k_1}{k}\alpha_1-\cdots-\frac{k_s}{k}\alpha_s,
+  \]
+  与 $\beta$ 不能由 $\alpha_1,\dots,\alpha_s$ 线性表示矛盾。故 $k=0$。
+  于是 $k_1\alpha_1+\cdots+k_s\alpha_s=0$，由原向量组线性无关得
+  $k_1=\cdots=k_s=0$。所以扩充后的向量组线性无关。
+\end{enumerate}
+
+\vspace{6pt}
+\noindent\textbf{四、计算题}（每题 10 分）
+\begin{enumerate}[label=\textbf{\arabic*.},itemsep=11pt]
+\item 该行列式为分块下三角行列式：
+  \[
+  D=\begin{vmatrix}a&b\\c&d\end{vmatrix}
+    \begin{vmatrix}a&b\\c&d\end{vmatrix}
+  =(ad-bc)^2.
+  \]
+
+\item 系数行列式
+  \[
+  \Delta=\begin{vmatrix}a&1&1\\1&a&1\\1&1&a\end{vmatrix}
+  =(a-1)^2(a+2).
+  \]
+  当 $a\neq1,-2$ 时，$\Delta\neq0$，方程组有唯一解。\\
+  当 $a=-2$ 时，三式左端相加为 $0$，右端相加为 $1+1+4=6\neq0$，故无解。\\
+  当 $a=1$ 时，方程组化为 $x_1+x_2+x_3=1$，有无穷多解：
+  \[
+  (x_1,x_2,x_3)=(1,0,0)+s(-1,1,0)+t(-1,0,1),\quad s,t\in\mathbb{R}.
+  \]
+
+\item 对 $(A\,|\,E)$ 作初等行变换可得
+  \[
+  A^{-1}=
+  \begin{pmatrix}
+  \frac{15}{2}&-3&-\frac12\\
+  -2&1&0\\
+  -\frac52&1&\frac12
+  \end{pmatrix}
+  =\frac12\begin{pmatrix}
+  15&-6&-1\\
+  -4&2&0\\
+  -5&2&1
+  \end{pmatrix}.
+  \]
+  评分时要求写出主要消元步骤，结果占 $3$ 分。
+
+\item 以 $\alpha_1,\dots,\alpha_5$ 为列作矩阵
+  \[
+  M=\begin{pmatrix}
+  1&0&0&1&2\\
+  0&1&0&1&1\\
+  0&0&1&1&0\\
+  1&1&1&3&3
+  \end{pmatrix}.
+  \]
+  第 $4$ 行等于前三行之和，且前三列已含 $3$ 阶单位子矩阵，故 $\rnk(M)=3$。
+  可取 $\{\alpha_1,\alpha_2,\alpha_3\}$ 为极大线性无关组，并且
+  \[
+  \alpha_4=\alpha_1+\alpha_2+\alpha_3,\qquad
+  \alpha_5=2\alpha_1+\alpha_2.
+  \]
+\end{enumerate}
+
+\end{document}
diff --git a/exam/advanced-algebra-final-advanced-B.tex b/exam/advanced-algebra-final-advanced-B.tex
new file mode 100644
index 0000000..2285ea4
--- /dev/null
+++ b/exam/advanced-algebra-final-advanced-B.tex
@@ -0,0 +1,304 @@
+% !TEX program = xelatex
+\documentclass[12pt]{ctexart}
+
+\usepackage[a4paper,margin=2.15cm,top=2.55cm,bottom=2.25cm]{geometry}
+\usepackage{amsmath,amssymb}
+\usepackage{enumitem}
+\usepackage{array}
+\usepackage{fancyhdr}
+
+\setlist[enumerate]{itemsep=9pt,topsep=5pt,leftmargin=2.2em}
+\linespread{1.13}
+
+\pagestyle{fancy}
+\fancyhf{}
+\lhead{\small 高等代数 I 期末复习进阶卷 · B 卷}
+\rhead{\small 第 \thepage 页}
+\setlength{\headheight}{14pt}
+\renewcommand{\headrulewidth}{0.4pt}
+
+\newcommand{\rnk}{\operatorname{r}}
+\newcommand{\blank}[1][2.6cm]{\underline{\hspace{#1}}}
+\newcommand{\bigsection}[2]{%
+  \vspace{7pt}%
+  {\noindent\bfseries\large #1}\hfill{\normalsize（本大题共 #2）}\par
+  \vspace{2pt}\hrule height0.4pt\vspace{8pt}}
+\newcommand{\optgrid}[4]{%
+  \par\smallskip\noindent
+  \begin{tabular}{@{}p{0.46\linewidth}p{0.46\linewidth}@{}}
+  (A)~#1 & (B)~#2 \\[3pt]
+  (C)~#3 & (D)~#4
+  \end{tabular}}
+\newcommand{\workarea}[1]{\par\vspace{0.35em}\noindent\rule{\linewidth}{0.25pt}\par\vspace{#1}}
+
+\begin{document}
+
+\begin{center}
+  {\Large\bfseries 高等代数 I 期末复习进阶卷（B 卷）}\\[4pt]
+  {\small 教材：北京大学数学系《高等代数》（第 6 版）为主\\
+  范围：行列式、线性方程组、向量组线性相关性、矩阵与逆矩阵、初等变换与初等矩阵、矩阵与向量组的秩}\\[8pt]
+\end{center}
+
+\noindent
+\begin{tabular}{@{}p{4.6cm}p{4.6cm}p{4.6cm}@{}}
+姓名：\blank[2.8cm] & 学号：\blank[2.8cm] & 班级：\blank[2.8cm]
+\end{tabular}
+
+\vspace{6pt}
+\noindent\textbf{满分 100 分\qquad 考试时间 120 分钟\qquad 闭卷}
+
+\vspace{8pt}
+\noindent
+\renewcommand{\arraystretch}{1.4}
+\begin{tabular}{|c|c|c|c|c|c|}
+\hline
+题号 & 一 & 二 & 三 & 四 & 总分 \\\hline
+满分 & 30 & 20 & 10 & 40 & 100 \\\hline
+得分 & & & & & \\\hline
+\end{tabular}
+
+\vspace{12pt}
+
+\bigsection{一、单项选择题}{10 小题，每题 3 分，共 30 分}
+
+\begin{enumerate}[label=\arabic*.]
+\item 在 $5$ 阶行列式的展开式中，项 $a_{15}a_{21}a_{34}a_{42}a_{53}$ 所带的符号为（\qquad）
+  \optgrid{正号 $+$}{负号 $-$}{$0$}{无法确定}
+
+\item 设 $A$ 为 $n$ 阶方阵，且 $A^{2}-2A-3E=O$，则下列结论正确的是（\qquad）
+  \optgrid{$A^{-1}=\dfrac{2E-A}{3}$}{$A^{-1}=\dfrac{A-2E}{3}$}{$A$ 不可逆}{$A^{-1}=A+2E$}
+
+\item 设 $A$ 为 $n$ 阶矩阵，$\rnk(A)=n-1$，则其伴随矩阵 $A^{*}$ 满足（\qquad）
+  \optgrid{$A^{*}=O$}{$\rnk(A^{*})=n$}{$\rnk(A^{*})=1$}{$A^{*}$ 可逆}
+
+\item 设 $A$ 为矩阵，$\rnk(A)=r$，则下列说法正确的是（\qquad）
+  \optgrid{$A$ 的任意 $r$ 阶子式都非零}{$A$ 至少有一个 $r$ 阶子式非零，且所有 $r+1$ 阶子式全为零}{$A$ 的任意 $r+1$ 阶子式都非零}{$A$ 必有 $r$ 个非零列且其余列全为零}
+
+\item 将单位矩阵 $E$ 的第 $j$ 列加上第 $i$ 列的 $k$ 倍得到初等矩阵 $P$，则 $AP$ 等于（\qquad）
+  \optgrid{把 $A$ 的第 $j$ 列加上第 $i$ 列的 $k$ 倍}{把 $A$ 的第 $i$ 列加上第 $j$ 列的 $k$ 倍}{把 $A$ 的第 $j$ 行加上第 $i$ 行的 $k$ 倍}{把 $A$ 的第 $i$ 行加上第 $j$ 行的 $k$ 倍}
+
+\item 设 $\alpha_1,\alpha_2,\alpha_3$ 线性无关，则向量组
+  $\alpha_1+\alpha_2,\alpha_2+\alpha_3,\alpha_3+\alpha_1$（\qquad）
+  \optgrid{线性无关}{线性相关}{秩为 $2$}{是否相关由向量维数决定}
+
+\item $n$ 个方程 $n$ 个未知量的线性方程组 $Ax=b$ 有唯一解的充分必要条件是（\qquad）
+  \optgrid{$|A|\neq0$}{$|A|=0$}{$b=0$}{$A$ 的某个元素非零}
+
+\item 设 $A,B$ 为同型矩阵，则恒成立的是（\qquad）
+  \optgrid{$\rnk(A+B)=\rnk(A)+\rnk(B)$}{$\rnk(A+B)\leq \rnk(A)+\rnk(B)$}{$\rnk(A+B)\geq \rnk(A)+\rnk(B)$}{$\rnk(A+B)=\max\{\rnk(A),\rnk(B)\}$}
+
+\item 非齐次线性方程组 $Ax=b$ 有唯一解的充要条件是（\qquad）
+  \optgrid{$\rnk(A)<\rnk(A,b)$}{$\rnk(A)=\rnk(A,b)<n$}{$\rnk(A,b)<n$}{$\rnk(A)=\rnk(A,b)=n$}
+
+\item 设 $A,B$ 均为 $n$ 阶方阵，若 $AB=E$，则（\qquad）
+  \optgrid{$A+B=E$}{$BA=O$}{$BA=E$}{$A$ 或 $B$ 不可逆}
+\end{enumerate}
+
+\bigsection{二、填空题}{10 小题，每题 2 分，共 20 分}
+
+\begin{enumerate}[label=\arabic*.]
+\item 排列 $3\,6\,1\,5\,2\,4$ 的逆序数为 $\blank[2cm]$。
+\item 箭型行列式
+  $\begin{vmatrix}
+  a&1&1&1\\
+  1&b&0&0\\
+  1&0&c&0\\
+  1&0&0&d
+  \end{vmatrix}=\blank[4.2cm]$。
+\item $\begin{vmatrix}1&1&1\\2&3&5\\4&9&25\end{vmatrix}=\blank[2cm]$。
+\item 设 $A$ 为 $3$ 阶方阵且 $|A|=-2$，则 $|3A|=\blank[2.2cm]$。
+\item 同上 $A$，则 $|A^{-1}|=\blank[2.2cm]$。
+\item $6$ 元齐次线性方程组的系数矩阵秩为 $4$，则基础解系含 $\blank[2cm]$ 个向量。
+\item 若 $P,Q$ 均为 $2$ 阶方阵，$|P|=-1,\ |Q|=5$，则
+  $\begin{vmatrix}P&R\\ O&Q\end{vmatrix}=\blank[2.5cm]$。
+\item 若 $A$ 为 $n$ 阶矩阵且 $A^{*}=O$，则一般可推出 $\rnk(A)\leq\blank[2cm]$。
+\item 对任意矩阵 $A$，有 $\rnk(A^{\mathsf T})=\blank[2cm]$。
+\item 若 $A$ 为 $n$ 阶可逆矩阵，则 $A$ 的等价标准形为 $\blank[2cm]$。
+\end{enumerate}
+
+\bigsection{三、证明题}{2 小题，每题 5 分，共 10 分}
+
+\begin{enumerate}[label=\arabic*.]
+\item 设 $A$ 为 $n$ 阶方阵，且 $A^{2}=A$。证明：$E+A$ 可逆，并求 $(E+A)^{-1}$。
+\workarea{4.4cm}
+
+\item 设 $\alpha_1,\dots,\alpha_s$ 线性无关，且
+  \[
+  \beta=k_1\alpha_1+\cdots+k_s\alpha_s,\qquad k_s\neq0.
+  \]
+  证明：$\alpha_1,\dots,\alpha_{s-1},\beta$ 线性无关，并用它们线性表示 $\alpha_s$。
+\workarea{4.4cm}
+\end{enumerate}
+
+\clearpage
+\bigsection{四、计算题}{4 小题，每题 10 分，共 40 分。要求写出主要步骤}
+
+\begin{enumerate}[label=\arabic*.]
+\item 计算箭型行列式
+  \[
+  D=\begin{vmatrix}
+  a&1&1&1\\
+  1&b&0&0\\
+  1&0&c&0\\
+  1&0&0&d
+  \end{vmatrix}.
+  \]
+\workarea{5.2cm}
+
+\item $a$ 取何值时，线性方程组
+  \[
+  \begin{cases}
+  x_1+x_2+x_3=1,\\
+  x_1+2x_2+a x_3=2,\\
+  x_1+4x_2+a^{2}x_3=a^{2}
+  \end{cases}
+  \]
+  无解、有唯一解、有无穷多解？在有无穷多解时求出通解。
+\workarea{6.0cm}
+
+\clearpage
+\item 用初等行变换求矩阵
+  \[
+  A=\begin{pmatrix}
+  2&1&0\\
+  1&2&1\\
+  0&1&2
+  \end{pmatrix}
+  \]
+  的逆矩阵 $A^{-1}$。
+\workarea{6.0cm}
+
+\item 设向量组
+  \[
+  \alpha_1=(1,0,0,1),\quad \alpha_2=(0,1,0,1),\quad
+  \alpha_3=(0,0,1,1),
+  \]
+  \[
+  \alpha_4=(1,2,-1,2),\quad \alpha_5=(2,-1,1,2).
+  \]
+  求该向量组的秩与一个极大线性无关组，并把其余向量用该极大无关组线性表示。
+\workarea{5.5cm}
+\end{enumerate}
+
+\begin{center}\small 试题部分结束，参考答案见后。\end{center}
+
+\clearpage
+\begin{center}
+  {\Large\bfseries 参考答案与评分标准（B 卷）}\\[2pt]
+  {\small 高等代数 I 期末复习进阶卷}
+\end{center}
+\vspace{6pt}\hrule\vspace{12pt}
+
+\noindent\textbf{一、单项选择题}（每题 3 分）
+\begin{center}
+\renewcommand{\arraystretch}{1.3}
+\begin{tabular}{|c|c|c|c|c|c|c|c|c|c|c|}
+\hline
+题号 & 1&2&3&4&5&6&7&8&9&10\\\hline
+答案 & A&B&C&B&A&A&A&B&D&C\\\hline
+\end{tabular}
+\end{center}
+
+\noindent\small 简析：1. 列指标排列 $(5,1,4,2,3)$ 的逆序数为 $6$，故为正号。
+2. 由 $A(A-2E)=3E$ 得 $A^{-1}=(A-2E)/3$。3. 当 $\rnk(A)=n-1$ 时，$\rnk(A^{*})=1$。
+4. 秩的子式判别法。5. 右乘初等矩阵对应列变换。6. 对应的系数变换行列式为 $2\neq0$，故仍无关。
+8. 秩的次可加性。10. $AB=E$ 推出 $A,B$ 均可逆，故 $BA=E$。\normalsize
+
+\vspace{8pt}
+\noindent\textbf{二、填空题}（每题 2 分）
+\begin{enumerate}[label=\arabic*.,itemsep=3pt]
+\item $8$。
+\item $abcd-bc-bd-cd$。
+\item $6$。
+\item $-54$。
+\item $-\dfrac12$。
+\item $2$。
+\item $-5$。
+\item $n-2$。
+\item $\rnk(A)$。
+\item $E$。
+\end{enumerate}
+
+\vspace{6pt}
+\noindent\textbf{三、证明题}（每题 5 分）
+\begin{enumerate}[label=\textbf{\arabic*.},itemsep=10pt]
+\item 因 $A^2=A$，直接计算
+  \[
+  (E+A)\left(E-\frac12A\right)
+  =E+A-\frac12A-\frac12A^2=E.
+  \]
+  同理 $\left(E-\frac12A\right)(E+A)=E$。故 $E+A$ 可逆，且
+  \[
+  (E+A)^{-1}=E-\frac12A.
+  \]
+
+\item 若
+  \[
+  c_1\alpha_1+\cdots+c_{s-1}\alpha_{s-1}+c\beta=0,
+  \]
+  代入 $\beta$ 得
+  \[
+  (c_1+ck_1)\alpha_1+\cdots+(c_{s-1}+ck_{s-1})\alpha_{s-1}
+  +ck_s\alpha_s=0.
+  \]
+  由 $\alpha_1,\dots,\alpha_s$ 线性无关，得 $ck_s=0$。又 $k_s\neq0$，故 $c=0$，继而
+  $c_1=\cdots=c_{s-1}=0$，所以 $\alpha_1,\dots,\alpha_{s-1},\beta$ 线性无关。并且
+  \[
+  \alpha_s=\frac1{k_s}\beta-\frac{k_1}{k_s}\alpha_1-\cdots-\frac{k_{s-1}}{k_s}\alpha_{s-1}.
+  \]
+\end{enumerate}
+
+\vspace{6pt}
+\noindent\textbf{四、计算题}（每题 10 分）
+\begin{enumerate}[label=\textbf{\arabic*.},itemsep=11pt]
+\item 对第 $1$ 行展开或先将后三行对应消去，可得
+  \[
+  D=abcd-cd-bd-bc.
+  \]
+  也可写成 $D=bcd\left(a-\frac1b-\frac1c-\frac1d\right)$（在 $bcd\neq0$ 时）。
+
+\item 系数行列式
+  \[
+  \Delta=\begin{vmatrix}1&1&1\\1&2&a\\1&4&a^2\end{vmatrix}
+  =(a-1)(a-2).
+  \]
+  当 $a\neq1,2$ 时，$\Delta\neq0$，方程组有唯一解。\\
+  当 $a=1$ 时，增广矩阵化简出现矛盾行，故无解。\\
+  当 $a=2$ 时，方程组化为
+  \[
+  x_1+x_2+x_3=1,\qquad x_2+x_3=1,
+  \]
+  故有无穷多解：
+  \[
+  (x_1,x_2,x_3)=(0,1,0)+t(0,-1,1),\quad t\in\mathbb{R}.
+  \]
+
+\item 对 $(A\,|\,E)$ 作初等行变换可得
+  \[
+  A^{-1}=\frac14
+  \begin{pmatrix}
+  3&-2&1\\
+  -2&4&-2\\
+  1&-2&3
+  \end{pmatrix}.
+  \]
+  评分时要求写出主要消元步骤，结果占 $3$ 分。
+
+\item 以 $\alpha_1,\dots,\alpha_5$ 为列作矩阵
+  \[
+  M=\begin{pmatrix}
+  1&0&0&1&2\\
+  0&1&0&2&-1\\
+  0&0&1&-1&1\\
+  1&1&1&2&2
+  \end{pmatrix}.
+  \]
+  前三列线性无关，且第 $4$ 行等于前三行之和，故 $\rnk(M)=3$。
+  可取 $\{\alpha_1,\alpha_2,\alpha_3\}$ 为极大线性无关组，并且
+  \[
+  \alpha_4=\alpha_1+2\alpha_2-\alpha_3,\qquad
+  \alpha_5=2\alpha_1-\alpha_2+\alpha_3.
+  \]
+\end{enumerate}
+
+\end{document}
diff --git a/exam/advanced-algebra-final.tex b/exam/advanced-algebra-final.tex
new file mode 100644
index 0000000..6028bb2
--- /dev/null
+++ b/exam/advanced-algebra-final.tex
@@ -0,0 +1,336 @@
+% !TEX program = xelatex
+\documentclass[12pt]{ctexart}
+
+\usepackage[a4paper,margin=2.2cm,top=2.6cm]{geometry}
+\usepackage{amsmath,amssymb,amsthm}
+\usepackage{enumitem}
+\usepackage{array}
+\usepackage{fancyhdr}
+
+\setlist[enumerate]{itemsep=9pt,topsep=5pt,leftmargin=2.2em}
+
+\pagestyle{fancy}
+\fancyhf{}
+\lhead{\small 高等代数 I 期末考试 · A 卷}
+\rhead{\small 第 \thepage 页}
+\renewcommand{\headrulewidth}{0.4pt}
+
+\newcommand{\bigsection}[2]{%
+  \vspace{6pt}%
+  {\noindent\bfseries\large #1}\hfill{\normalsize（本大题共 #2）}\par
+  \vspace{2pt}\hrule height0.4pt\vspace{8pt}}
+
+\newcommand{\blank}[1][2.6cm]{\underline{\hspace{#1}}}
+
+% 四选一两列排版
+\newcommand{\optgrid}[4]{%
+  \par\smallskip\noindent
+  \begin{tabular}{@{}p{0.45\textwidth}p{0.45\textwidth}@{}}
+  (A)~#1 & (B)~#2 \\[3pt]
+  (C)~#3 & (D)~#4
+  \end{tabular}}
+
+\newcommand{\rank}{\operatorname{r}}
+\linespread{1.12}
+
+\begin{document}
+
+%==================== 封面 ====================
+\begin{center}
+  {\Large\bfseries 高等代数 I 期末考试试卷（A 卷）}\\[4pt]
+  {\small 教材：北京大学数学系（王萼芳、石生明）《高等代数》（第 5 版）\\
+  范围：行列式、线性方程组、向量组的线性相关性、矩阵与逆矩阵、初等变换与初等矩阵、矩阵与向量组的秩}\\[8pt]
+\end{center}
+
+\noindent
+\begin{tabular}{@{}p{4.6cm}p{4.6cm}p{4.6cm}@{}}
+姓名：\blank[2.8cm] & 学号：\blank[2.8cm] & 班级：\blank[2.8cm]
+\end{tabular}
+
+\vspace{6pt}
+\noindent\textbf{满分 100 分\qquad 考试时间 120 分钟\qquad 闭卷}
+
+\vspace{8pt}
+\noindent
+\renewcommand{\arraystretch}{1.4}
+\begin{tabular}{|c|c|c|c|c|c|}
+\hline
+题号 & 一 & 二 & 三 & 四 & 总分 \\\hline
+满分 & 30 & 20 & 10 & 40 & 100 \\\hline
+得分 & & & & & \\\hline
+\end{tabular}
+
+\vspace{12pt}
+
+%==================== 一、选择题 ====================
+\bigsection{一、单项选择题}{10 小题，每题 3 分，共 30 分}
+
+\begin{enumerate}[label=\arabic*.]
+\item 在 5 阶行列式的展开式中，项 $a_{13}a_{25}a_{34}a_{41}a_{52}$ 所带的符号为（\qquad）
+  \optgrid{正号 $+$}{负号 $-$}{$0$}{无法确定}
+
+\item 设向量组 $\alpha_1,\alpha_2,\alpha_3$ 线性无关，则下列向量组线性\textbf{相关}的是（\qquad）
+  \optgrid{$\alpha_1+\alpha_2,\ \alpha_2+\alpha_3,\ \alpha_3+\alpha_1$}{$\alpha_1-\alpha_2,\ \alpha_2-\alpha_3,\ \alpha_3-\alpha_1$}{$\alpha_1,\ \alpha_1+\alpha_2,\ \alpha_1+\alpha_2+\alpha_3$}{$2\alpha_1,\ 3\alpha_2,\ 4\alpha_3$}
+
+\item 设 $A$ 为 $n$ 阶方阵，则 $A$ 可逆的充要条件是（\qquad）
+  \optgrid{$\rank(A)<n$}{$Ax=0$ 有非零解}{$A$ 的行向量组线性无关}{$|A|=0$}
+
+\item 设 $A$ 为 $m\times n$ 矩阵且 $\rank(A)=r$，则（\qquad）
+  \optgrid{$A$ 中任意 $r$ 个行向量线性无关}{$A$ 的所有 $r+1$ 阶子式全为 $0$}{$A$ 的所有 $r$ 阶子式全不为 $0$}{$A$ 必有 $r$ 个非零行}
+
+\item 设 $A$ 为 $n\ (n\geq 2)$ 阶可逆矩阵，$A^{*}$ 为其伴随矩阵，则 $|A^{*}|=$（\qquad）
+  \optgrid{$|A|$}{$|A|^{\,n-1}$}{$|A|^{\,n}$}{$|A|^{\,n-2}$}
+
+\item $n$ 个方程 $n$ 个未知量的齐次线性方程组 $Ax=0$ 有非零解的充要条件是（\qquad）
+  \optgrid{$|A|\neq 0$}{$|A|=0$}{$\rank(A)=n$}{$A$ 可逆}
+
+\item 对矩阵 $A$ 施行一次初等\textbf{行}变换，相当于（\qquad）
+  \optgrid{$A$ 左乘相应的初等矩阵}{$A$ 右乘相应的初等矩阵}{$A$ 两侧同乘初等矩阵}{对 $A$ 取转置}
+
+\item 齐次线性方程组 $\begin{cases}\lambda x_1+x_2+x_3=0\\ x_1+\lambda x_2+x_3=0\\ x_1+x_2+\lambda x_3=0\end{cases}$ 有非零解，则（\qquad）
+  \optgrid{$\lambda=1$}{$\lambda=-2$}{$\lambda=1$ 或 $\lambda=-2$}{$\lambda=0$}
+
+\item 设 $A_{jk}$ 为 $n$ 阶行列式中元素 $a_{jk}$ 的代数余子式。当 $i\neq j$ 时，
+  $\displaystyle\sum_{k=1}^{n}a_{ik}A_{jk}=$（\qquad）
+  \optgrid{$|A|$}{$0$}{$1$}{$|A|^{2}$}
+
+\item 设 $A$ 为 $4\times 5$ 矩阵且 $\rank(A)=3$，则齐次方程组 $Ax=0$ 的基础解系所含向量个数为（\qquad）
+  \optgrid{$1$}{$2$}{$3$}{$5$}
+\end{enumerate}
+
+%==================== 二、填空题 ====================
+\bigsection{二、填空题}{10 小题，每题 2 分，共 20 分}
+
+\begin{enumerate}[label=\arabic*.]
+\item 行列式 $\begin{vmatrix}1&2\\3&4\end{vmatrix}=\blank$。
+\item 排列 $5\,3\,4\,1\,2$ 的逆序数为 $\blank[2cm]$。
+\item 设 $A$ 为 $3$ 阶方阵且 $|A|=2$，则 $|2A|=\blank[2cm]$。
+\item 同上 $A$，则 $|A^{-1}|=\blank[2cm]$。
+\item 同上 $A$，则伴随矩阵 $|A^{*}|=\blank[2cm]$。
+\item $\begin{vmatrix}1&1&1\\ a&b&c\\ a^{2}&b^{2}&c^{2}\end{vmatrix}=\blank[3.5cm]$。
+\item 向量组 $\alpha_1=(1,0,0),\ \alpha_2=(0,1,0),\ \alpha_3=(1,1,0)$ 的秩为 $\blank[2cm]$。
+\item 设 $A$ 为 $m\times n$ 矩阵，则 $\rank(A)\leq\blank[2.6cm]$。
+\item 非齐次线性方程组 $Ax=b$（$A$ 为 $m\times n$ 矩阵）有唯一解的充要条件是
+  $\rank(A)=\rank(A,b)=\blank[2.4cm]$。
+\item 设 $A,B$ 均为 $n$ 阶方阵且 $AB=E$，则 $BA=\blank[2cm]$。
+\end{enumerate}
+
+%==================== 三、证明题 ====================
+\bigsection{三、证明题}{2 小题，每题 5 分，共 10 分}
+
+\begin{enumerate}[label=\arabic*.]
+\item 设 $A$ 为 $n$ 阶方阵且 $A^{2}=E$。证明：
+  \[
+  \rank(A+E)+\rank(A-E)=n .
+  \]
+
+\item 设向量组 $\alpha_1,\alpha_2,\alpha_3$ 线性无关。证明：向量组
+  $\alpha_1+\alpha_2,\ \alpha_2+\alpha_3,\ \alpha_3+\alpha_1$ 也线性无关。
+\end{enumerate}
+
+%==================== 四、计算题 ====================
+\bigsection{四、计算题}{4 小题，每题 10 分，共 40 分。要求写出主要步骤}
+
+\begin{enumerate}[label=\arabic*.]
+\item 计算 $n$ 阶行列式
+  \[
+  D=\begin{vmatrix}
+  a & b & b & \cdots & b\\
+  b & a & b & \cdots & b\\
+  b & b & a & \cdots & b\\
+  \vdots & \vdots & \vdots & & \vdots\\
+  b & b & b & \cdots & a
+  \end{vmatrix}_{n\times n}.
+  \]
+
+\item $\lambda$ 取何值时，线性方程组
+  \[
+  \begin{cases}
+  \lambda x_1+x_2+x_3=1,\\
+  x_1+\lambda x_2+x_3=\lambda,\\
+  x_1+x_2+\lambda x_3=\lambda^{2}
+  \end{cases}
+  \]
+  无解、有唯一解、有无穷多解？在有无穷多解时求出通解。
+
+\item 用初等行变换求矩阵 $A=\begin{pmatrix}2&1&1\\ 1&2&1\\ 1&1&2\end{pmatrix}$ 的逆矩阵 $A^{-1}$。
+
+\item 设向量组
+  \[
+  \alpha_1=(1,1,1),\quad \alpha_2=(1,2,3),\quad \alpha_3=(1,3,5),\quad \alpha_4=(1,0,-1).
+  \]
+  求该向量组的秩与一个极大线性无关组，并把其余向量用该极大无关组线性表示。
+\end{enumerate}
+
+\vspace{8pt}
+\begin{center}\small —— 试卷结束，参考答案见后 ——\end{center}
+
+%==================== 参考答案 ====================
+\clearpage
+\begin{center}
+  {\Large\bfseries 参考答案与评分标准（A 卷）}\\[2pt]
+  {\small 高等代数 I 期末考试}
+\end{center}
+\vspace{6pt}\hrule\vspace{12pt}
+
+\noindent\textbf{一、单项选择题}（每题 3 分）\par\vspace{4pt}
+\begin{center}
+\renewcommand{\arraystretch}{1.3}
+\begin{tabular}{|c|c|c|c|c|c|c|c|c|c|c|}
+\hline
+题号 & 1 & 2 & 3 & 4 & 5 & 6 & 7 & 8 & 9 & 10 \\\hline
+答案 & B & B & C & B & B & B & A & B & B & B \\\hline
+\end{tabular}
+\end{center}
+\noindent\small 简析：1.\,列指标排列 $(3,5,4,1,2)$ 的逆序数为 $7$（奇），故取负号。
+2.\,$(\alpha_1-\alpha_2)+(\alpha_2-\alpha_3)+(\alpha_3-\alpha_1)=0$，线性相关。
+4.\,$\rank(A)=r\Leftrightarrow$ 有一个 $r$ 阶子式非零且所有 $r+1$ 阶子式全为 $0$。
+5.\,$AA^{*}=|A|E\Rightarrow |A|\,|A^{*}|=|A|^{n}\Rightarrow|A^{*}|=|A|^{n-1}$。
+8.\,系数行列式 $=(\lambda-1)^{2}(\lambda+2)=0$。
+9.\,代数余子式的「错位相乘」之和为 $0$（替换定理）。
+10.\,基础解系含 $n-\rank(A)=5-3=2$ 个向量。\normalsize
+
+\vspace{10pt}
+\noindent\textbf{二、填空题}（每题 2 分）\par\vspace{4pt}
+\begin{enumerate}[label=\arabic*.,itemsep=3pt]
+\item $-2$ \hfill
+\item $8$ \hfill
+\item $16$（$|2A|=2^{3}|A|=8\cdot2$）\hfill
+\item $\dfrac12$ \hfill
+\item $4$（$|A^{*}|=|A|^{n-1}=2^{2}$）
+\item $(b-a)(c-a)(c-b)$（范德蒙德）
+\item $2$ \hfill
+\item $\min\{m,n\}$ \hfill
+\item $n$（未知量个数）\hfill
+\item $E$
+\end{enumerate}
+
+\vspace{6pt}
+\noindent\textbf{三、证明题}（每题 5 分）
+
+\begin{enumerate}[label=\textbf{\arabic*.},itemsep=11pt]
+\item 因为 $A^{2}=E$，所以 $(A+E)(A-E)=A^{2}-E=O$。
+  由西尔维斯特(Sylvester)不等式（或：$A-E$ 的列向量都是 $(A+E)x=0$ 的解），得
+  \[
+  \rank(A+E)+\rank(A-E)\leq n. \tag{1}
+  \]
+  又 $(A+E)-(A-E)=2E$，由秩的不等式 $\rank(M)+\rank(N)\geq\rank(M-N)$，
+  \[
+  \rank(A+E)+\rank(A-E)\geq \rank\big((A+E)-(A-E)\big)=\rank(2E)=n. \tag{2}
+  \]
+  由 (1)(2) 得 $\rank(A+E)+\rank(A-E)=n$。$\qquad\blacksquare$
+
+\item 设有数 $k_1,k_2,k_3$ 使
+  \[
+  k_1(\alpha_1+\alpha_2)+k_2(\alpha_2+\alpha_3)+k_3(\alpha_3+\alpha_1)=0,
+  \]
+  整理得 $(k_1+k_3)\alpha_1+(k_1+k_2)\alpha_2+(k_2+k_3)\alpha_3=0$。
+  由 $\alpha_1,\alpha_2,\alpha_3$ 线性无关，得
+  \[
+  \begin{cases}k_1+k_3=0\\ k_1+k_2=0\\ k_2+k_3=0\end{cases},
+  \qquad
+  \text{其系数行列式}\
+  \begin{vmatrix}1&0&1\\1&1&0\\0&1&1\end{vmatrix}=2\neq0,
+  \]
+  故只有零解 $k_1=k_2=k_3=0$。所以 $\alpha_1+\alpha_2,\alpha_2+\alpha_3,\alpha_3+\alpha_1$ 线性无关。$\qquad\blacksquare$
+\end{enumerate}
+
+\vspace{6pt}
+\noindent\textbf{四、计算题}（每题 10 分）
+
+\begin{enumerate}[label=\textbf{\arabic*.},itemsep=13pt]
+\item 将第 $2,3,\dots,n$ 列全部加到第 $1$ 列，则第 $1$ 列每个元素都变为 $a+(n-1)b$，提出公因子：
+  \[
+  D=[a+(n-1)b]\begin{vmatrix}
+  1 & b & b & \cdots & b\\
+  1 & a & b & \cdots & b\\
+  1 & b & a & \cdots & b\\
+  \vdots&\vdots&\vdots& &\vdots\\
+  1 & b & b & \cdots & a
+  \end{vmatrix}.
+  \]
+  再将第 $1$ 行的 $(-1)$ 倍加到其余各行，化为下三角形，主对角线为 $1,(a-b),\dots,(a-b)$：
+  \[
+  \boxed{D=[a+(n-1)b](a-b)^{\,n-1}.}
+  \]
+
+\item 系数行列式
+  $\;D=\begin{vmatrix}\lambda&1&1\\1&\lambda&1\\1&1&\lambda\end{vmatrix}=(\lambda-1)^{2}(\lambda+2).$
+
+  \textbf{（i）当 $\lambda\neq1$ 且 $\lambda\neq-2$ 时}，$D\neq0$，方程组有唯一解。由克拉默法则（或消元）得
+  \[
+  x_1=-\frac{\lambda+1}{\lambda+2},\qquad x_2=\frac{1}{\lambda+2},\qquad x_3=\frac{(\lambda+1)^{2}}{\lambda+2}.
+  \]
+
+  \textbf{（ii）当 $\lambda=-2$ 时}，三个方程左端之和为 $0$，而右端之和为 $1+(-2)+4=3\neq0$，矛盾，故\textbf{无解}。
+
+  \textbf{（iii）当 $\lambda=1$ 时}，三个方程都化为 $x_1+x_2+x_3=1$，有\textbf{无穷多解}。取 $x_2,x_3$ 为自由未知量，通解为
+  \[
+  \begin{pmatrix}x_1\\x_2\\x_3\end{pmatrix}
+  =\begin{pmatrix}1\\0\\0\end{pmatrix}
+  +k_1\begin{pmatrix}-1\\1\\0\end{pmatrix}
+  +k_2\begin{pmatrix}-1\\0\\1\end{pmatrix},\quad k_1,k_2\in\mathbb{R}.
+  \]
+
+\item 对 $(A\,|\,E)$ 施行初等行变换：
+  \[
+  \left(\begin{array}{ccc|ccc}
+  2&1&1&1&0&0\\ 1&2&1&0&1&0\\ 1&1&2&0&0&1
+  \end{array}\right)
+  \xrightarrow{\ r_1\leftrightarrow r_3\ }
+  \left(\begin{array}{ccc|ccc}
+  1&1&2&0&0&1\\ 1&2&1&0&1&0\\ 2&1&1&1&0&0
+  \end{array}\right)
+  \]
+  \[
+  \xrightarrow[r_3-2r_1]{r_2-r_1}
+  \left(\begin{array}{ccc|ccc}
+  1&1&2&0&0&1\\ 0&1&-1&0&1&-1\\ 0&-1&-3&1&0&-2
+  \end{array}\right)
+  \xrightarrow{r_3+r_2}
+  \left(\begin{array}{ccc|ccc}
+  1&1&2&0&0&1\\ 0&1&-1&0&1&-1\\ 0&0&-4&1&1&-3
+  \end{array}\right)
+  \]
+  \[
+  \xrightarrow{-\frac14 r_3}
+  \left(\begin{array}{ccc|ccc}
+  1&1&2&0&0&1\\ 0&1&-1&0&1&-1\\ 0&0&1&-\frac14&-\frac14&\frac34
+  \end{array}\right)
+  \xrightarrow[r_1-2r_3]{r_2+r_3}
+  \left(\begin{array}{ccc|ccc}
+  1&1&0&\frac12&\frac12&-\frac12\\ 0&1&0&-\frac14&\frac34&-\frac14\\ 0&0&1&-\frac14&-\frac14&\frac34
+  \end{array}\right)
+  \]
+  \[
+  \xrightarrow{r_1-r_2}
+  \left(\begin{array}{ccc|ccc}
+  1&0&0&\frac34&-\frac14&-\frac14\\ 0&1&0&-\frac14&\frac34&-\frac14\\ 0&0&1&-\frac14&-\frac14&\frac34
+  \end{array}\right).
+  \]
+  故
+  \[
+  A^{-1}=\frac14\begin{pmatrix}3&-1&-1\\-1&3&-1\\-1&-1&3\end{pmatrix}.
+  \]
+
+\item 以 $\alpha_1,\alpha_2,\alpha_3,\alpha_4$ 为列作矩阵并作初等行变换：
+  \[
+  \begin{pmatrix}1&1&1&1\\1&2&3&0\\1&3&5&-1\end{pmatrix}
+  \xrightarrow[r_3-r_1]{r_2-r_1}
+  \begin{pmatrix}1&1&1&1\\0&1&2&-1\\0&2&4&-2\end{pmatrix}
+  \xrightarrow{r_3-2r_2}
+  \begin{pmatrix}1&1&1&1\\0&1&2&-1\\0&0&0&0\end{pmatrix}.
+  \]
+  故秩为 $2$，$\{\alpha_1,\alpha_2\}$ 为一个极大线性无关组。继续化为行最简形：
+  \[
+  \xrightarrow{r_1-r_2}
+  \begin{pmatrix}1&0&-1&2\\0&1&2&-1\\0&0&0&0\end{pmatrix},
+  \]
+  由此读出
+  \[
+  \alpha_3=-\alpha_1+2\alpha_2,\qquad \alpha_4=2\alpha_1-\alpha_2.
+  \]
+  （验证：$-\alpha_1+2\alpha_2=(1,3,5)=\alpha_3$，$2\alpha_1-\alpha_2=(1,0,-1)=\alpha_4$。）
+\end{enumerate}
+
+\end{document}
diff --git a/exam/math-analysis-final-B.tex b/exam/math-analysis-final-B.tex
new file mode 100644
index 0000000..2bb7704
--- /dev/null
+++ b/exam/math-analysis-final-B.tex
@@ -0,0 +1,294 @@
+% !TEX program = xelatex
+\documentclass[12pt]{ctexart}
+
+\usepackage[a4paper,margin=2.3cm,top=2.6cm]{geometry}
+\usepackage{amsmath,amssymb,amsthm}
+\usepackage{enumitem}
+\usepackage{array}
+\usepackage{fancyhdr}
+\usepackage{xcolor}
+
+\setlist[enumerate]{itemsep=10pt,topsep=6pt,leftmargin=2.2em}
+
+\pagestyle{fancy}
+\fancyhf{}
+\lhead{\small 数学分析（上）期末考试 · B 卷}
+\rhead{\small 第 \thepage 页}
+\cfoot{}
+\renewcommand{\headrulewidth}{0.4pt}
+
+\newcommand{\bigsection}[2]{%
+  \vspace{6pt}%
+  {\noindent\bfseries\large #1}\hfill{\normalsize（本大题共 #2）}\par
+  \vspace{2pt}\hrule height0.4pt\vspace{8pt}}
+
+\newcommand{\blank}[1][3cm]{\underline{\hspace{#1}}}
+
+\newcommand{\optgrid}[4]{%
+  \par\smallskip\noindent
+  \begin{tabular}{@{}p{0.45\textwidth}p{0.45\textwidth}@{}}
+  (A)~#1 & (B)~#2 \\[2pt]
+  (C)~#3 & (D)~#4
+  \end{tabular}}
+
+\linespread{1.15}
+
+\begin{document}
+
+%==================== 封面信息 ====================
+\begin{center}
+  {\Large\bfseries 数学分析（上册）期末考试试卷（B 卷）}\\[4pt]
+  {\small 教材：华东师范大学数学系《数学分析》（第 5 版）\;\;|\;\;
+  范围：导数与微分、微分中值定理及其应用、实数的完备性、不定积分、定积分、
+  定积分应用、反常积分；多元函数的极限与连续、多元函数微分学}\\[10pt]
+\end{center}
+
+\noindent
+\begin{tabular}{@{}p{4.5cm}p{4.5cm}p{4.5cm}@{}}
+姓名：\blank[3cm] & 学号：\blank[3cm] & 班级：\blank[3cm]
+\end{tabular}
+
+\vspace{6pt}
+\noindent\textbf{满分 100 分\qquad 考试时间 120 分钟\qquad 闭卷}
+
+\vspace{8pt}
+\noindent
+\renewcommand{\arraystretch}{1.4}
+\begin{tabular}{|c|c|c|c|c|c|c|c|}
+\hline
+题号 & 一 & 二 & 三 & 四 & 五 & 六 & 总分 \\\hline
+满分 & 15 & 10 & 15 & 36 & 12 & 12 & 100 \\\hline
+得分 & & & & & & & \\\hline
+\end{tabular}
+
+\vspace{14pt}
+
+%==================== 一、选择题 ====================
+\bigsection{一、选择题}{5 小题，每题 3 分，共 15 分。每题只有一个正确选项}
+
+\begin{enumerate}[label=\arabic*.]
+\item 下列函数中，在 $x=0$ 处可导的是（\qquad）
+  \optgrid{$|x|$}{$x|x|$}{$\sqrt{|x|}$}{$\sqrt[3]{x}$}
+
+\item 函数 $f(x)=\ln x$ 在 $[1,e]$ 上满足拉格朗日中值定理，其中值点 $\xi=$（\qquad）
+  \optgrid{$1$}{$e-1$}{$\dfrac{e+1}{2}$}{$\sqrt{e}$}
+
+\item 反常积分 $\displaystyle\int_{0}^{1}\frac{1}{x^{p}}\,\mathrm{d}x$ 收敛的充要条件是（\qquad）
+  \optgrid{$p>1$}{$p<1$}{$p\geq 1$}{$p>0$}
+
+\item 数列 $\{a_{n}\}$ 收敛的充要条件是（\qquad）
+  \optgrid{$\{a_{n}\}$ 单调}{$\{a_{n}\}$ 有界}{$\{a_{n}\}$ 是柯西列}{$\{a_{n}\}$ 有收敛子列}
+
+\item 设二元函数 $z=f(x,y)$ 在点 $P_{0}$ 处两个偏导数都存在，则在 $P_{0}$ 处（\qquad）
+  \optgrid{$f$ 必连续}{$f$ 必可微}{$f$ 不一定连续}{$f$ 必取得极值}
+\end{enumerate}
+
+%==================== 二、判断题 ====================
+\bigsection{二、判断题}{5 小题，每题 2 分，共 10 分。正确打 “$\checkmark$”，错误打 “$\times$”}
+
+\begin{enumerate}[label=\arabic*.]
+\item 若 $f$ 在点 $x_{0}$ 连续，则 $f$ 在点 $x_{0}$ 必可导。\hfill（\qquad）
+\item 若 $f$ 在 $[a,b]$ 上可积，则 $f$ 在 $[a,b]$ 上必有界。\hfill（\qquad）
+\item 若 $f$ 在 $[a,b]$ 上连续，则存在 $\xi\in[a,b]$ 使
+  $\displaystyle\int_{a}^{b}f(x)\,\mathrm{d}x=f(\xi)(b-a)$。\hfill（\qquad）
+\item 反常积分 $\displaystyle\int_{1}^{+\infty}\frac{1}{x}\,\mathrm{d}x$ 收敛。\hfill（\qquad）
+\item 若二元函数在某点可微，则它在该点的两个偏导数都存在。\hfill（\qquad）
+\end{enumerate}
+
+%==================== 三、填空题 ====================
+\bigsection{三、填空题}{5 小题，每题 3 分，共 15 分}
+
+\begin{enumerate}[label=\arabic*.]
+\item 设 $f(x)=\ln(1+x^{2})$，则 $f'(x)=\blank[3.5cm]$。
+\item $\displaystyle\int \cos x\,\mathrm{d}x=\blank[4cm]$。
+\item $\displaystyle\int_{0}^{\pi}\sin x\,\mathrm{d}x=\blank[3cm]$。
+\item 反常积分 $\displaystyle\int_{1}^{+\infty}\frac{1}{x^{2}}\,\mathrm{d}x=\blank[3cm]$。
+\item 设 $z=x^{2}+xy+y^{2}$，则 $\dfrac{\partial z}{\partial x}=\blank[3.5cm]$。
+\end{enumerate}
+
+%==================== 四、计算题 ====================
+\bigsection{四、计算题}{6 小题，每题 6 分，共 36 分。要求写出主要计算步骤}
+
+\begin{enumerate}[label=\arabic*.]
+\item 求极限 $\displaystyle\lim_{x\to 0}\frac{1-\cos x}{x^{2}}$。
+
+\item 求不定积分 $\displaystyle\int \ln x\,\mathrm{d}x$。
+
+\item 计算定积分 $\displaystyle\int_{0}^{1} x\,e^{x^{2}}\,\mathrm{d}x$。
+
+\item 求函数 $f(x)=\dfrac{x}{1+x^{2}}$ 的单调区间与极值。
+
+\item 设 $z=x^{3}+y^{3}-3xy$，求一阶偏导数 $z_{x},z_{y}$ 及全部二阶偏导数
+  $z_{xx},z_{yy},z_{xy}$。
+
+\item 计算反常积分 $\displaystyle\int_{0}^{1}\frac{1}{\sqrt{1-x^{2}}}\,\mathrm{d}x$。
+\end{enumerate}
+
+%==================== 五、证明题 ====================
+\bigsection{五、证明题}{2 小题，每题 6 分，共 12 分}
+
+\begin{enumerate}[label=\arabic*.]
+\item 证明：当 $x>0$ 时，$e^{x}>1+x$。
+
+\item 设 $a_{1}=\sqrt{2}$，$a_{n+1}=\sqrt{2+a_{n}}\ (n=1,2,\dots)$。
+  利用单调有界定理证明数列 $\{a_{n}\}$ 收敛，并求其极限。
+\end{enumerate}
+
+%==================== 六、应用题 ====================
+\bigsection{六、应用题}{2 小题，每题 6 分，共 12 分}
+
+\begin{enumerate}[label=\arabic*.]
+\item 求由曲线 $y=\sqrt{x}$、直线 $x=4$ 及 $x$ 轴所围平面图形的面积 $A$，
+  并求该图形绕 $x$ 轴旋转一周所得旋转体的体积 $V$。
+
+\item 用长为 $20\ \mathrm{m}$ 的篱笆，靠一面墙围成一块矩形场地（靠墙一侧不用篱笆）。
+  问矩形的长、宽各为多少时围成的面积最大？最大面积是多少？
+\end{enumerate}
+
+\vspace{8pt}
+\begin{center}\small —— 试卷结束，参考答案见后 ——\end{center}
+
+%==================== 参 考 答 案 ====================
+\clearpage
+\begin{center}
+  {\Large\bfseries 参考答案与评分标准（B 卷）}\\[2pt]
+  {\small 数学分析（上册）期末考试}
+\end{center}
+\vspace{6pt}\hrule\vspace{12pt}
+
+\noindent\textbf{一、选择题}（每题 3 分）\par\vspace{4pt}
+\begin{center}
+\renewcommand{\arraystretch}{1.3}
+\begin{tabular}{|c|c|c|c|c|c|}
+\hline
+题号 & 1 & 2 & 3 & 4 & 5 \\\hline
+答案 & B & B & B & C & C \\\hline
+\end{tabular}
+\end{center}
+\noindent\small 简析：1.\,$x|x|$ 在 $0$ 处左右导数均为 $0$，可导；其余三者在 $0$ 处不可导。
+2.\,$\dfrac{1}{\xi}=\dfrac{\ln e-\ln 1}{e-1}=\dfrac{1}{e-1}\Rightarrow\xi=e-1\in(1,e)$。
+3.\,瑕点在 $x=0$，$p$-积分当且仅当 $p<1$ 收敛。
+4.\,实数系中数列收敛 $\Leftrightarrow$ 为柯西列（柯西收敛准则）。
+5.\,偏导数存在不能保证连续（更不能保证可微）。\normalsize
+
+\vspace{10pt}
+\noindent\textbf{二、判断题}（每题 2 分）\par\vspace{4pt}
+\begin{center}
+\renewcommand{\arraystretch}{1.3}
+\begin{tabular}{|c|c|c|c|c|c|}
+\hline
+题号 & 1 & 2 & 3 & 4 & 5 \\\hline
+答案 & $\times$ & $\checkmark$ & $\checkmark$ & $\times$ & $\checkmark$ \\\hline
+\end{tabular}
+\end{center}
+\noindent\small 简析：1.\,连续未必可导，反例 $|x|$ 在 $0$ 处。
+2.\,可积的必要条件是有界。3.\,积分第一中值定理。
+4.\,$\int_{1}^{+\infty}\frac1x\mathrm{d}x$ 发散（$p=1$）。
+5.\,可微 $\Rightarrow$ 偏导数存在。\normalsize
+
+\vspace{10pt}
+\noindent\textbf{三、填空题}（每题 3 分）\par\vspace{4pt}
+\begin{enumerate}[label=\arabic*.,itemsep=4pt]
+\item $\dfrac{2x}{1+x^{2}}$ \qquad
+\item $\sin x+C$ \qquad
+\item $2$（$[-\cos x]_{0}^{\pi}=1+1=2$）
+\item $1$（$[-x^{-1}]_{1}^{+\infty}=0-(-1)=1$）
+\item $2x+y$
+\end{enumerate}
+
+\vspace{6pt}
+\noindent\textbf{四、计算题}（每题 6 分）
+
+\begin{enumerate}[label=\textbf{\arabic*.},itemsep=10pt]
+\item 由 $1-\cos x=\dfrac{x^{2}}{2}+o(x^{2})$，得
+  $\displaystyle\lim_{x\to0}\frac{1-\cos x}{x^{2}}=\frac12$。
+  （或用洛必达：$\lim\dfrac{\sin x}{2x}=\dfrac12$。）
+
+\item 用分部积分，取 $u=\ln x,\ \mathrm{d}v=\mathrm{d}x$，则 $v=x$：
+  \[
+  \int\ln x\,\mathrm{d}x=x\ln x-\int x\cdot\frac1x\,\mathrm{d}x=x\ln x-x+C .
+  \]
+
+\item 令 $u=x^{2}$，$\mathrm{d}u=2x\,\mathrm{d}x$：
+  \[
+  \int_{0}^{1}x\,e^{x^{2}}\,\mathrm{d}x=\frac12\int_{0}^{1}e^{u}\,\mathrm{d}u
+  =\frac12\big(e^{u}\big)\Big|_{0}^{1}=\frac{e-1}{2}.
+  \]
+
+\item $f'(x)=\dfrac{(1+x^{2})-x\cdot 2x}{(1+x^{2})^{2}}=\dfrac{1-x^{2}}{(1+x^{2})^{2}}$。
+  令 $f'(x)=0$ 得 $x=\pm 1$。
+  \[
+  \begin{array}{c|ccccc}
+   x & (-\infty,-1) & -1 & (-1,1) & 1 & (1,+\infty)\\\hline
+   f'(x) & - & 0 & + & 0 & -\\
+   f(x) & \searrow & \text{极小} & \nearrow & \text{极大} & \searrow
+  \end{array}
+  \]
+  单调增区间 $(-1,1)$，单调减区间 $(-\infty,-1)$ 与 $(1,+\infty)$；
+  极小值 $f(-1)=-\dfrac12$，极大值 $f(1)=\dfrac12$。
+
+\item 一阶偏导：$z_{x}=3x^{2}-3y,\qquad z_{y}=3y^{2}-3x$。\\
+  二阶偏导：
+  \[
+  z_{xx}=6x,\quad z_{yy}=6y,\quad z_{xy}=z_{yx}=-3.
+  \]
+
+\item 瑕点在 $x=1$：
+  \[
+  \int_{0}^{1}\frac{\mathrm{d}x}{\sqrt{1-x^{2}}}
+  =\lim_{b\to 1^{-}}\big[\arcsin x\big]_{0}^{b}
+  =\lim_{b\to1^{-}}\arcsin b=\frac{\pi}{2}.
+  \]
+\end{enumerate}
+
+\vspace{6pt}
+\noindent\textbf{五、证明题}（每题 6 分）
+
+\begin{enumerate}[label=\textbf{\arabic*.},itemsep=12pt]
+\item 令 $g(x)=e^{x}-1-x$，则 $g(0)=0$，且当 $x>0$ 时
+  $g'(x)=e^{x}-1>0$，故 $g$ 在 $[0,+\infty)$ 上单调递增。
+  于是当 $x>0$ 时 $g(x)>g(0)=0$，即 $e^{x}>1+x$。$\qquad\blacksquare$
+
+\item \textbf{有界：} 用归纳法证 $0<a_{n}<2$。$a_{1}=\sqrt2<2$；
+  设 $a_{n}<2$，则 $a_{n+1}=\sqrt{2+a_{n}}<\sqrt{2+2}=2$。故对一切 $n$ 有 $0<a_{n}<2$，
+  即 $\{a_{n}\}$ 有上界。\\[2pt]
+  \textbf{单调递增：} 由
+  $a_{n+1}^{2}-a_{n}^{2}=(2+a_{n})-a_{n}^{2}=-(a_{n}-2)(a_{n}+1)$，
+  而 $0<a_{n}<2$ 时 $(a_{n}-2)<0,\ (a_{n}+1)>0$，故 $a_{n+1}^{2}-a_{n}^{2}>0$；
+  又 $a_{n},a_{n+1}>0$，所以 $a_{n+1}>a_{n}$，数列单调递增。\\[2pt]
+  \textbf{求极限：} 由\textbf{单调有界定理}，$\{a_{n}\}$ 收敛，设
+  $\displaystyle\lim_{n\to\infty}a_{n}=L$。在 $a_{n+1}=\sqrt{2+a_{n}}$ 两边取极限得
+  $L=\sqrt{2+L}$，即 $L^{2}-L-2=0$，$(L-2)(L+1)=0$。
+  因 $L>0$，故 $L=2$，即 $\displaystyle\lim_{n\to\infty}a_{n}=2$。$\qquad\blacksquare$
+\end{enumerate}
+
+\vspace{6pt}
+\noindent\textbf{六、应用题}（每题 6 分）
+
+\begin{enumerate}[label=\textbf{\arabic*.},itemsep=12pt]
+\item 在 $[0,4]$ 上 $y=\sqrt{x}\geq 0$，面积
+  \[
+  A=\int_{0}^{4}\sqrt{x}\,\mathrm{d}x=\Big[\frac23 x^{3/2}\Big]_{0}^{4}
+  =\frac23\cdot 8=\frac{16}{3}.
+  \]
+  绕 $x$ 轴旋转（圆盘法）：
+  \[
+  V=\pi\int_{0}^{4}(\sqrt{x})^{2}\,\mathrm{d}x=\pi\int_{0}^{4}x\,\mathrm{d}x
+  =\pi\Big[\frac{x^{2}}{2}\Big]_{0}^{4}=8\pi.
+  \]
+
+\item 设垂直于墙的两条边长为 $x$（$0<x<10$），则平行于墙的一边长为 $20-2x$，
+  面积
+  \[
+  S(x)=x(20-2x)=20x-2x^{2}.
+  \]
+  $S'(x)=20-4x=0\Rightarrow x=5$；当 $x<5$ 时 $S'>0$，$x>5$ 时 $S'<0$，
+  故 $x=5$ 为最大值点。此时平行墙的一边长 $20-2\cdot5=10$，最大面积
+  \[
+  S(5)=5\times 10=50\ (\mathrm{m}^{2}).
+  \]
+  即矩形宽（垂直墙）$5\,\mathrm{m}$、长（平行墙）$10\,\mathrm{m}$ 时面积最大，
+  为 $50\,\mathrm{m}^{2}$。
+\end{enumerate}
+
+\end{document}
diff --git a/exam/math-analysis-final.tex b/exam/math-analysis-final.tex
new file mode 100644
index 0000000..5c1b77c
--- /dev/null
+++ b/exam/math-analysis-final.tex
@@ -0,0 +1,314 @@
+% !TEX program = xelatex
+\documentclass[12pt]{ctexart}
+
+\usepackage[a4paper,margin=2.3cm,top=2.6cm]{geometry}
+\usepackage{amsmath,amssymb,amsthm}
+\usepackage{enumitem}
+\usepackage{array}
+\usepackage{fancyhdr}
+\usepackage{tikz}
+\usepackage{xcolor}
+
+\definecolor{ink}{HTML}{211C16}
+\definecolor{accent}{HTML}{8A2B2B}
+
+\setlist[enumerate]{itemsep=10pt,topsep=6pt,leftmargin=2.2em}
+
+% 页眉页脚
+\pagestyle{fancy}
+\fancyhf{}
+\lhead{\small 数学分析（上）期末考试}
+\rhead{\small 第 \thepage 页}
+\cfoot{}
+\renewcommand{\headrulewidth}{0.4pt}
+
+% 题型大节标题
+\newcommand{\bigsection}[2]{%
+  \vspace{6pt}%
+  {\noindent\bfseries\large #1}\hfill{\normalsize（本大题共 #2）}\par
+  \vspace{2pt}\hrule height0.4pt\vspace{8pt}}
+
+\newcommand{\blank}[1][3cm]{\underline{\hspace{#1}}}
+
+\theoremstyle{definition}
+\newtheorem*{solution}{解}
+\newtheorem*{proofx}{证明}
+
+\linespread{1.15}
+
+\begin{document}
+
+%==================== 封面信息 ====================
+\begin{center}
+  {\Large\bfseries 数学分析（上册）期末考试试卷}\\[4pt]
+  {\small 适用范围：导数与微分、微分中值定理、实数完备性、不定积分、定积分、
+  定积分应用、反常积分；多元函数的极限与连续、多元函数微分学}\\[10pt]
+\end{center}
+
+\noindent
+\begin{tabular}{@{}p{4.5cm}p{4.5cm}p{4.5cm}@{}}
+姓名：\blank[3cm] & 学号：\blank[3cm] & 班级：\blank[3cm]
+\end{tabular}
+
+\vspace{6pt}
+\noindent\textbf{满分 100 分\qquad 考试时间 120 分钟\qquad 闭卷}
+
+\vspace{8pt}
+\noindent
+\renewcommand{\arraystretch}{1.4}
+\begin{tabular}{|c|c|c|c|c|c|c|c|}
+\hline
+题号 & 一 & 二 & 三 & 四 & 五 & 六 & 总分 \\\hline
+满分 & 15 & 10 & 15 & 36 & 12 & 12 & 100 \\\hline
+得分 & & & & & & & \\\hline
+\end{tabular}
+
+\vspace{14pt}
+
+%==================== 一、选择题 ====================
+\bigsection{一、选择题}{5 小题，每题 3 分，共 15 分。每题只有一个正确选项}
+
+\newcommand{\optgrid}[4]{%
+  \par\smallskip\noindent
+  \begin{tabular}{@{}p{0.45\textwidth}p{0.45\textwidth}@{}}
+  (A)~#1 & (B)~#2 \\[2pt]
+  (C)~#3 & (D)~#4
+  \end{tabular}}
+
+\begin{enumerate}[label=\arabic*.]
+\item 函数 $f(x)=|x|$ 在 $x=0$ 处（\qquad）
+  \optgrid{连续且可导}{连续但不可导}{不连续}{可导但不连续}
+
+\item 函数 $f(x)=x^{3}-3x$ 的单调递减区间是（\qquad）
+  \optgrid{$(-\infty,-1)$}{$(-1,1)$}{$(1,+\infty)$}{$(-\infty,+\infty)$}
+
+\item 反常积分 $\displaystyle\int_{1}^{+\infty}\frac{1}{x^{p}}\,\mathrm{d}x$ 收敛的充要条件是（\qquad）
+  \optgrid{$p>0$}{$p\geq 1$}{$p>1$}{$p<1$}
+
+\item 设 $S$ 为非空有上界的实数集，则它的上确界 $\sup S$（\qquad）
+  \optgrid{一定属于 $S$}{一定不属于 $S$}{可能属于也可能不属于 $S$}{不一定存在}
+
+\item 设二元函数 $z=f(x,y)$ 在点 $P_{0}$ 处可微，则在 $P_{0}$ 处必有（\qquad）
+  \optgrid{两个偏导数存在且连续}{两个偏导数存在}{取得极值}{$f$ 不一定连续}
+\end{enumerate}
+
+%==================== 二、判断题 ====================
+\bigsection{二、判断题}{5 小题，每题 2 分，共 10 分。正确打 “$\checkmark$”，错误打 “$\times$”}
+
+\begin{enumerate}[label=\arabic*.]
+\item 若 $f$ 在点 $x_{0}$ 可导，则 $f$ 在点 $x_{0}$ 连续。\hfill（\qquad）
+\item 若 $f'(x_{0})=0$，则 $x_{0}$ 一定是 $f$ 的极值点。\hfill（\qquad）
+\item 闭区间 $[a,b]$ 上的连续函数一定在 $[a,b]$ 上可积。\hfill（\qquad）
+\item 若反常积分 $\displaystyle\int_{a}^{+\infty}f(x)\,\mathrm{d}x$ 收敛，则必有 $\displaystyle\lim_{x\to+\infty}f(x)=0$。\hfill（\qquad）
+\item 若二元函数在某点处两个偏导数都存在，则该函数在该点必连续。\hfill（\qquad）
+\end{enumerate}
+
+%==================== 三、填空题 ====================
+\bigsection{三、填空题}{5 小题，每题 3 分，共 15 分}
+
+\begin{enumerate}[label=\arabic*.]
+\item 设 $f(x)=\arctan x$，则 $f'(x)=\blank[3.5cm]$。
+\item $\displaystyle\int \frac{1}{1+x^{2}}\,\mathrm{d}x=\blank[4cm]$。
+\item $\displaystyle\int_{-1}^{1} x^{3}\cos x\,\mathrm{d}x=\blank[3cm]$。
+\item 反常积分 $\displaystyle\int_{0}^{1}\frac{1}{\sqrt{x}}\,\mathrm{d}x=\blank[3cm]$。
+\item 设 $z=x^{y}\ (x>0)$，则 $\dfrac{\partial z}{\partial x}=\blank[3.5cm]$。
+\end{enumerate}
+
+%==================== 四、计算题 ====================
+\bigsection{四、计算题}{6 小题，每题 6 分，共 36 分。要求写出主要计算步骤}
+
+\begin{enumerate}[label=\arabic*.]
+\item 求极限 $\displaystyle\lim_{x\to 0}\frac{e^{x}-1-x}{x^{2}}$。
+
+\item 求不定积分 $\displaystyle\int x\ln x\,\mathrm{d}x$。
+
+\item 计算定积分 $\displaystyle\int_{0}^{1} x\sqrt{1-x^{2}}\,\mathrm{d}x$。
+
+\item 求函数 $f(x)=x^{3}-3x^{2}+1$ 的单调区间与极值。
+
+\item 设 $z=x^{2}e^{y}+y^{2}$，求一阶偏导数 $z_{x},z_{y}$ 及全部二阶偏导数
+  $z_{xx},z_{yy},z_{xy}$。
+
+\item 计算反常积分 $\displaystyle\int_{0}^{+\infty}\frac{1}{1+x^{2}}\,\mathrm{d}x$。
+\end{enumerate}
+
+%==================== 五、证明题 ====================
+\bigsection{五、证明题}{2 小题，每题 6 分，共 12 分}
+
+\begin{enumerate}[label=\arabic*.]
+\item 利用拉格朗日中值定理证明：当 $x>0$ 时，
+  \[
+  \frac{x}{1+x}<\ln(1+x)<x .
+  \]
+
+\item 设数列 $\{a_{n}\}$ 单调递增且有上界。利用实数的确界原理证明：
+  $\{a_{n}\}$ 收敛，且 $\displaystyle\lim_{n\to\infty}a_{n}=\sup_{n}a_{n}$。
+\end{enumerate}
+
+%==================== 六、应用题 ====================
+\bigsection{六、应用题}{2 小题，每题 6 分，共 12 分}
+
+\begin{enumerate}[label=\arabic*.]
+\item 求由曲线 $y=x^{2}$ 与直线 $y=x$ 所围平面图形的面积 $A$，
+  并求该图形绕 $x$ 轴旋转一周所得旋转体的体积 $V$。
+
+\item 要制作一个容积为 $16\pi\ \mathrm{cm}^{3}$ 的有盖圆柱形罐头。设底面半径为 $r$、
+  高为 $h$，问 $r,h$ 各为多少时，所用材料（即罐头表面积）最省？并求最小表面积。
+\end{enumerate}
+
+\vspace{8pt}
+\begin{center}\small —— 试卷结束，参考答案见后 ——\end{center}
+
+%==================== 参 考 答 案 ====================
+\clearpage
+\begin{center}
+  {\Large\bfseries 参考答案与评分标准}\\[2pt]
+  {\small 数学分析（上册）期末考试}
+\end{center}
+\vspace{6pt}\hrule\vspace{12pt}
+
+\noindent\textbf{一、选择题}（每题 3 分）\par\vspace{4pt}
+\begin{center}
+\renewcommand{\arraystretch}{1.3}
+\begin{tabular}{|c|c|c|c|c|c|}
+\hline
+题号 & 1 & 2 & 3 & 4 & 5 \\\hline
+答案 & B & B & C & C & B \\\hline
+\end{tabular}
+\end{center}
+\noindent\small 简析：1.\,$|x|$ 在 $0$ 处连续但左右导数 $\mp1$ 不等，不可导。
+2.\,$f'(x)=3x^{2}-3<0\Leftrightarrow x\in(-1,1)$。
+3.\,$p$-积分在 $+\infty$ 处当且仅当 $p>1$ 收敛。
+4.\,确界存在但未必是 $S$ 中元素（如 $S=(0,1)$，$\sup S=1\notin S$）。
+5.\,可微 $\Rightarrow$ 偏导存在且 $f$ 连续，但偏导未必连续。\normalsize
+
+\vspace{10pt}
+\noindent\textbf{二、判断题}（每题 2 分）\par\vspace{4pt}
+\begin{center}
+\renewcommand{\arraystretch}{1.3}
+\begin{tabular}{|c|c|c|c|c|c|}
+\hline
+题号 & 1 & 2 & 3 & 4 & 5 \\\hline
+答案 & $\checkmark$ & $\times$ & $\checkmark$ & $\times$ & $\times$ \\\hline
+\end{tabular}
+\end{center}
+\noindent\small 简析：2.\,反例 $f(x)=x^{3}$，$f'(0)=0$ 但 $0$ 非极值点。
+4.\,收敛不蕴含被积函数趋于 $0$（可构造在越来越窄区间上的尖峰）。
+5.\,偏导存在不能保证连续，更不能保证可微。\normalsize
+
+\vspace{10pt}
+\noindent\textbf{三、填空题}（每题 3 分）\par\vspace{4pt}
+\begin{enumerate}[label=\arabic*.,itemsep=4pt]
+\item $\dfrac{1}{1+x^{2}}$ \qquad
+\item $\arctan x+C$ \qquad
+\item $0$（被积函数为奇函数，对称区间积分为 $0$）
+\item $2$\qquad（$\int_{0}^{1}x^{-1/2}\mathrm{d}x=\big[2\sqrt{x}\big]_{0}^{1}=2$）
+\item $y\,x^{\,y-1}$
+\end{enumerate}
+
+\vspace{6pt}
+\noindent\textbf{四、计算题}（每题 6 分）
+
+\begin{enumerate}[label=\textbf{\arabic*.},itemsep=10pt]
+\item 由泰勒展开 $e^{x}=1+x+\dfrac{x^{2}}{2}+o(x^{2})$，故
+  \[
+  \frac{e^{x}-1-x}{x^{2}}=\frac{\tfrac{1}{2}x^{2}+o(x^{2})}{x^{2}}\to\frac{1}{2}.
+  \]
+  （或对 $\frac{0}{0}$ 型连用两次洛必达：$\lim\frac{e^{x}-1}{2x}=\lim\frac{e^{x}}{2}=\tfrac12$。）
+
+\item 用分部积分，取 $u=\ln x,\ \mathrm{d}v=x\,\mathrm{d}x$，则 $v=\dfrac{x^{2}}{2}$：
+  \[
+  \int x\ln x\,\mathrm{d}x=\frac{x^{2}}{2}\ln x-\int\frac{x^{2}}{2}\cdot\frac{1}{x}\,\mathrm{d}x
+  =\frac{x^{2}}{2}\ln x-\frac{x^{2}}{4}+C .
+  \]
+
+\item 令 $u=1-x^{2}$，$\mathrm{d}u=-2x\,\mathrm{d}x$；当 $x:0\to1$ 时 $u:1\to0$：
+  \[
+  \int_{0}^{1}x\sqrt{1-x^{2}}\,\mathrm{d}x
+  =\frac12\int_{0}^{1}\sqrt{u}\,\mathrm{d}u
+  =\frac12\cdot\frac{2}{3}u^{3/2}\Big|_{0}^{1}=\frac{1}{3}.
+  \]
+
+\item $f'(x)=3x^{2}-6x=3x(x-2)$。令 $f'(x)=0$ 得 $x=0,2$。
+  \[
+  \begin{array}{c|ccccc}
+   x & (-\infty,0) & 0 & (0,2) & 2 & (2,+\infty)\\\hline
+   f'(x) & + & 0 & - & 0 & +\\
+   f(x) & \nearrow & \text{极大} & \searrow & \text{极小} & \nearrow
+  \end{array}
+  \]
+  单调增区间 $(-\infty,0)$ 与 $(2,+\infty)$，单调减区间 $(0,2)$；
+  极大值 $f(0)=1$，极小值 $f(2)=-3$。
+
+\item 一阶偏导：$z_{x}=2x\,e^{y},\qquad z_{y}=x^{2}e^{y}+2y$。\\
+  二阶偏导：
+  \[
+  z_{xx}=2e^{y},\quad z_{yy}=x^{2}e^{y}+2,\quad z_{xy}=z_{yx}=2x\,e^{y}.
+  \]
+
+\item $\displaystyle\int_{0}^{+\infty}\frac{\mathrm{d}x}{1+x^{2}}
+  =\lim_{b\to+\infty}\big[\arctan x\big]_{0}^{b}
+  =\lim_{b\to+\infty}\arctan b=\frac{\pi}{2}.$
+\end{enumerate}
+
+\vspace{6pt}
+\noindent\textbf{五、证明题}（每题 6 分）
+
+\begin{enumerate}[label=\textbf{\arabic*.},itemsep=12pt]
+\item 设 $g(t)=\ln(1+t)$，它在 $[0,x]$ 上连续、在 $(0,x)$ 内可导，
+  $g'(t)=\dfrac{1}{1+t}$。由拉格朗日中值定理，存在 $\xi\in(0,x)$ 使
+  \[
+  \ln(1+x)-\ln 1=g'(\xi)\,(x-0)=\frac{x}{1+\xi}.
+  \]
+  因 $0<\xi<x$，故 $1<1+\xi<1+x$，从而
+  $\dfrac{1}{1+x}<\dfrac{1}{1+\xi}<1$，两边乘以 $x>0$ 得
+  \[
+  \frac{x}{1+x}<\frac{x}{1+\xi}=\ln(1+x)<x. \qquad\blacksquare
+  \]
+
+\item 因 $\{a_{n}\}$ 有上界，由\textbf{确界原理}，数集 $\{a_{n}\}$ 存在上确界，
+  记 $a=\sup_{n}a_{n}$。对任意 $\varepsilon>0$，由上确界的定义，
+  $a-\varepsilon$ 不是上界，故存在 $N$ 使 $a_{N}>a-\varepsilon$。
+  又 $\{a_{n}\}$ 单调递增，且 $a$ 是上界，故当 $n>N$ 时
+  \[
+  a-\varepsilon<a_{N}\leq a_{n}\leq a<a+\varepsilon,
+  \]
+  即 $|a_{n}-a|<\varepsilon$。由 $\varepsilon$ 的任意性，
+  $\displaystyle\lim_{n\to\infty}a_{n}=a=\sup_{n}a_{n}$，即 $\{a_{n}\}$ 收敛。
+  $\qquad\blacksquare$
+\end{enumerate}
+
+\vspace{6pt}
+\noindent\textbf{六、应用题}（每题 6 分）
+
+\begin{enumerate}[label=\textbf{\arabic*.},itemsep=12pt]
+\item 两曲线交点：由 $x^{2}=x$ 得 $x=0,1$，且在 $[0,1]$ 上 $x\geq x^{2}$。\\
+  面积
+  \[
+  A=\int_{0}^{1}(x-x^{2})\,\mathrm{d}x
+  =\Big[\frac{x^{2}}{2}-\frac{x^{3}}{3}\Big]_{0}^{1}
+  =\frac12-\frac13=\frac{1}{6}.
+  \]
+  绕 $x$ 轴旋转用垫圈法，外半径 $x$、内半径 $x^{2}$：
+  \[
+  V=\pi\int_{0}^{1}\big[x^{2}-(x^{2})^{2}\big]\mathrm{d}x
+  =\pi\int_{0}^{1}(x^{2}-x^{4})\mathrm{d}x
+  =\pi\Big[\frac{x^{3}}{3}-\frac{x^{5}}{5}\Big]_{0}^{1}
+  =\frac{2\pi}{15}.
+  \]
+
+\item 由容积 $\pi r^{2}h=16\pi$ 得 $h=\dfrac{16}{r^{2}}$。
+  有盖圆柱表面积
+  \[
+  S(r)=2\pi r^{2}+2\pi r h=2\pi r^{2}+\frac{32\pi}{r}\quad(r>0).
+  \]
+  求导：$S'(r)=4\pi r-\dfrac{32\pi}{r^{2}}=0\Rightarrow r^{3}=8\Rightarrow r=2$。
+  当 $0<r<2$ 时 $S'<0$，$r>2$ 时 $S'>0$，故 $r=2$ 为极小也是最小值点。
+  此时 $h=\dfrac{16}{4}=4$，最小表面积
+  \[
+  S(2)=2\pi\cdot4+\frac{32\pi}{2}=8\pi+16\pi=24\pi\ (\mathrm{cm}^{2}).
+  \]
+  即底半径 $r=2\,\mathrm{cm}$、高 $h=4\,\mathrm{cm}$ 时用料最省，最小表面积为 $24\pi\,\mathrm{cm}^{2}$。
+\end{enumerate}
+
+\end{document}
diff --git a/lib/course/courseRegistry.ts b/lib/course/courseRegistry.ts
new file mode 100644
index 0000000..0ce4828
--- /dev/null
+++ b/lib/course/courseRegistry.ts
@@ -0,0 +1,47 @@
+import mathAnalysisCourse from "@/content/courses/math-analysis/course.json";
+import mathAnalysisVolume1 from "@/content/courses/math-analysis/volume-1.json";
+import mathAnalysisVolume2 from "@/content/courses/math-analysis/volume-2.json";
+import gaodengShuxueCourse from "@/content/courses/gaodeng-shuxue/course.json";
+import gaodengShuxueVolume1 from "@/content/courses/gaodeng-shuxue/volume-1.json";
+import gaodengShuxueVolume2 from "@/content/courses/gaodeng-shuxue/volume-2.json";
+import { chapterRegistry as mathAnalysisChapterRegistry } from "./chapterRegistry";
+import { gaodengChapterRegistry } from "./gaodengChapterRegistry";
+import type { ChapterRegistryEntry } from "./chapterRegistry";
+import type { Course, Volume } from "./types";
+
+export interface RegisteredCourse {
+  course: Course;
+  volumes: Volume[];
+  chapterRegistry: Record<string, ChapterRegistryEntry>;
+}
+
+export const courseRegistry: Record<string, RegisteredCourse> = {
+  "math-analysis": {
+    course: mathAnalysisCourse as unknown as Course,
+    volumes: [mathAnalysisVolume1 as unknown as Volume, mathAnalysisVolume2 as unknown as Volume],
+    chapterRegistry: mathAnalysisChapterRegistry,
+  },
+  "gaodeng-shuxue": {
+    course: gaodengShuxueCourse as unknown as Course,
+    volumes: [gaodengShuxueVolume1 as unknown as Volume, gaodengShuxueVolume2 as unknown as Volume],
+    chapterRegistry: gaodengChapterRegistry,
+  },
+};
+
+export const REGISTERED_COURSE_IDS = Object.keys(courseRegistry) as Array<keyof typeof courseRegistry>;
+
+export function getRegisteredCourse(courseId: string): RegisteredCourse | undefined {
+  return courseRegistry[courseId];
+}
+
+export function listRegisteredCourses(): Course[] {
+  return REGISTERED_COURSE_IDS.map((id) => courseRegistry[id].course);
+}
+
+export function getVolumesForCourse(courseId: string): Volume[] {
+  const entry = getRegisteredCourse(courseId);
+  if (!entry) {
+    throw new Error(`unknown course id: ${courseId}`);
+  }
+  return entry.volumes;
+}
diff --git a/lib/course/gaodengChapterRegistry.ts b/lib/course/gaodengChapterRegistry.ts
new file mode 100644
index 0000000..3ba15bf
--- /dev/null
+++ b/lib/course/gaodengChapterRegistry.ts
@@ -0,0 +1,103 @@
+import gdFunctionLimitChapter from "@/content/courses/gaodeng-shuxue/chapters/gd-function-limit.json";
+import gdFunctionLimitDiagrams from "@/content/courses/gaodeng-shuxue/diagrams/gd-function-limit.json";
+import gdFunctionLimitExercises from "@/content/courses/gaodeng-shuxue/exercises/gd-function-limit.json";
+
+import gdDerivativeChapter from "@/content/courses/gaodeng-shuxue/chapters/gd-derivative.json";
+import gdDerivativeDiagrams from "@/content/courses/gaodeng-shuxue/diagrams/gd-derivative.json";
+import gdDerivativeExercises from "@/content/courses/gaodeng-shuxue/exercises/gd-derivative.json";
+
+import gdMeanValueChapter from "@/content/courses/gaodeng-shuxue/chapters/gd-mean-value.json";
+import gdMeanValueDiagrams from "@/content/courses/gaodeng-shuxue/diagrams/gd-mean-value.json";
+import gdMeanValueExercises from "@/content/courses/gaodeng-shuxue/exercises/gd-mean-value.json";
+
+import gdIndefiniteIntegralChapter from "@/content/courses/gaodeng-shuxue/chapters/gd-indefinite-integral.json";
+import gdIndefiniteIntegralDiagrams from "@/content/courses/gaodeng-shuxue/diagrams/gd-indefinite-integral.json";
+import gdIndefiniteIntegralExercises from "@/content/courses/gaodeng-shuxue/exercises/gd-indefinite-integral.json";
+
+import gdDefiniteIntegralChapter from "@/content/courses/gaodeng-shuxue/chapters/gd-definite-integral.json";
+import gdDefiniteIntegralDiagrams from "@/content/courses/gaodeng-shuxue/diagrams/gd-definite-integral.json";
+import gdDefiniteIntegralExercises from "@/content/courses/gaodeng-shuxue/exercises/gd-definite-integral.json";
+
+import gdOdeChapter from "@/content/courses/gaodeng-shuxue/chapters/gd-ode.json";
+import gdOdeDiagrams from "@/content/courses/gaodeng-shuxue/diagrams/gd-ode.json";
+import gdOdeExercises from "@/content/courses/gaodeng-shuxue/exercises/gd-ode.json";
+
+import gdVectorsChapter from "@/content/courses/gaodeng-shuxue/chapters/gd-vectors.json";
+import gdVectorsDiagrams from "@/content/courses/gaodeng-shuxue/diagrams/gd-vectors.json";
+import gdVectorsExercises from "@/content/courses/gaodeng-shuxue/exercises/gd-vectors.json";
+
+import gdMultivariableDiffChapter from "@/content/courses/gaodeng-shuxue/chapters/gd-multivariable-diff.json";
+import gdMultivariableDiffDiagrams from "@/content/courses/gaodeng-shuxue/diagrams/gd-multivariable-diff.json";
+import gdMultivariableDiffExercises from "@/content/courses/gaodeng-shuxue/exercises/gd-multivariable-diff.json";
+
+import gdMultipleIntegralsChapter from "@/content/courses/gaodeng-shuxue/chapters/gd-multiple-integrals.json";
+import gdMultipleIntegralsDiagrams from "@/content/courses/gaodeng-shuxue/diagrams/gd-multiple-integrals.json";
+import gdMultipleIntegralsExercises from "@/content/courses/gaodeng-shuxue/exercises/gd-multiple-integrals.json";
+
+import gdLineSurfaceChapter from "@/content/courses/gaodeng-shuxue/chapters/gd-line-surface.json";
+import gdLineSurfaceDiagrams from "@/content/courses/gaodeng-shuxue/diagrams/gd-line-surface.json";
+import gdLineSurfaceExercises from "@/content/courses/gaodeng-shuxue/exercises/gd-line-surface.json";
+
+import gdSeriesChapter from "@/content/courses/gaodeng-shuxue/chapters/gd-series.json";
+import gdSeriesDiagrams from "@/content/courses/gaodeng-shuxue/diagrams/gd-series.json";
+import gdSeriesExercises from "@/content/courses/gaodeng-shuxue/exercises/gd-series.json";
+
+import type { ChapterRegistryEntry } from "./chapterRegistry";
+
+export const gaodengChapterRegistry: Record<string, ChapterRegistryEntry> = {
+  "ch-gd-function-limit": {
+    chapter: gdFunctionLimitChapter as unknown as Record<string, unknown>,
+    exercises: gdFunctionLimitExercises as { exercises: unknown[] },
+    diagrams: gdFunctionLimitDiagrams as { diagrams: unknown[] },
+  },
+  "ch-gd-derivative": {
+    chapter: gdDerivativeChapter as unknown as Record<string, unknown>,
+    exercises: gdDerivativeExercises as { exercises: unknown[] },
+    diagrams: gdDerivativeDiagrams as { diagrams: unknown[] },
+  },
+  "ch-gd-mean-value": {
+    chapter: gdMeanValueChapter as unknown as Record<string, unknown>,
+    exercises: gdMeanValueExercises as { exercises: unknown[] },
+    diagrams: gdMeanValueDiagrams as { diagrams: unknown[] },
+  },
+  "ch-gd-indefinite-integral": {
+    chapter: gdIndefiniteIntegralChapter as unknown as Record<string, unknown>,
+    exercises: gdIndefiniteIntegralExercises as { exercises: unknown[] },
+    diagrams: gdIndefiniteIntegralDiagrams as { diagrams: unknown[] },
+  },
+  "ch-gd-definite-integral": {
+    chapter: gdDefiniteIntegralChapter as unknown as Record<string, unknown>,
+    exercises: gdDefiniteIntegralExercises as { exercises: unknown[] },
+    diagrams: gdDefiniteIntegralDiagrams as { diagrams: unknown[] },
+  },
+  "ch-gd-ode": {
+    chapter: gdOdeChapter as unknown as Record<string, unknown>,
+    exercises: gdOdeExercises as { exercises: unknown[] },
+    diagrams: gdOdeDiagrams as { diagrams: unknown[] },
+  },
+  "ch-gd-vectors": {
+    chapter: gdVectorsChapter as unknown as Record<string, unknown>,
+    exercises: gdVectorsExercises as { exercises: unknown[] },
+    diagrams: gdVectorsDiagrams as { diagrams: unknown[] },
+  },
+  "ch-gd-multivariable-diff": {
+    chapter: gdMultivariableDiffChapter as unknown as Record<string, unknown>,
+    exercises: gdMultivariableDiffExercises as { exercises: unknown[] },
+    diagrams: gdMultivariableDiffDiagrams as { diagrams: unknown[] },
+  },
+  "ch-gd-multiple-integrals": {
+    chapter: gdMultipleIntegralsChapter as unknown as Record<string, unknown>,
+    exercises: gdMultipleIntegralsExercises as { exercises: unknown[] },
+    diagrams: gdMultipleIntegralsDiagrams as { diagrams: unknown[] },
+  },
+  "ch-gd-line-surface": {
+    chapter: gdLineSurfaceChapter as unknown as Record<string, unknown>,
+    exercises: gdLineSurfaceExercises as { exercises: unknown[] },
+    diagrams: gdLineSurfaceDiagrams as { diagrams: unknown[] },
+  },
+  "ch-gd-series": {
+    chapter: gdSeriesChapter as unknown as Record<string, unknown>,
+    exercises: gdSeriesExercises as { exercises: unknown[] },
+    diagrams: gdSeriesDiagrams as { diagrams: unknown[] },
+  },
+};
diff --git a/lib/course/loadCourse.ts b/lib/course/loadCourse.ts
index efc9d2f..ec39a4b 100644
--- a/lib/course/loadCourse.ts
+++ b/lib/course/loadCourse.ts
@@ -1,10 +1,14 @@
-import course from "@/content/courses/math-analysis/course.json";
-import volume1 from "@/content/courses/math-analysis/volume-1.json";
-import volume2 from "@/content/courses/math-analysis/volume-2.json";
-import { chapterRegistry } from "./chapterRegistry";
+import { getRegisteredCourse, getVolumesForCourse } from "./courseRegistry";
 import type { ChapterContent, CourseBundle, DiagramSpec, Exercise, Volume, VolumeChapter } from "./types";
 
+const DEFAULT_COURSE_ID = "math-analysis";
 const DEFAULT_CHAPTER_ID = "ch-sequence-limit";
+const DEFAULT_GD_CHAPTER_ID = "ch-gd-function-limit";
+
+const DEFAULT_CHAPTER_BY_COURSE: Record<string, string> = {
+  "math-analysis": DEFAULT_CHAPTER_ID,
+  "gaodeng-shuxue": DEFAULT_GD_CHAPTER_ID,
+};
 
 function adaptChapter(raw: Record<string, unknown>, volumeChapter: VolumeChapter): ChapterContent {
   if ("id" in raw) {
@@ -16,7 +20,7 @@ function adaptChapter(raw: Record<string, unknown>, volumeChapter: VolumeChapter
     number: volumeChapter.number,
     title: volumeChapter.title,
     status: volumeChapter.status,
-    overview: "",
+    overview: typeof raw.overview === "string" ? raw.overview : "",
   } as unknown as ChapterContent;
 }
 
@@ -27,7 +31,10 @@ function adaptExercise(raw: unknown): Exercise {
     : typeof e.knowledgePointId === "string"
       ? [e.knowledgePointId]
       : [];
-  const prompt = typeof e.prompt === "string" ? e.prompt : typeof e.problem === "string" ? e.problem : "";
+  const prompt =
+    typeof e.prompt === "string" ? e.prompt :
+    typeof e.problem === "string" ? e.problem :
+    typeof e.problemStatement === "string" ? e.problemStatement : "";
   const gradingRubric = Array.isArray(e.gradingRubric)
     ? (e.gradingRubric as unknown[]).map((r) =>
         typeof r === "string" ? r : typeof (r as Record<string, unknown>).criterion === "string" ? ((r as Record<string, unknown>).criterion as string) : JSON.stringify(r)
@@ -49,30 +56,63 @@ function adaptDiagram(raw: unknown): DiagramSpec {
   } as unknown as DiagramSpec;
 }
 
-export function loadMathAnalysisCourse(chapterId?: string): CourseBundle {
-  const targetId = chapterId ?? DEFAULT_CHAPTER_ID;
+function findVolumeChapter(courseId: string, chapterId: string): { volume: Volume; volumeChapter: VolumeChapter } | undefined {
+  const registered = getRegisteredCourse(courseId);
+  if (!registered) return undefined;
 
-  const vol1Chapter = (volume1 as unknown as Volume).chapters.find((c) => c.id === targetId);
-  const vol2Chapter = (volume2 as unknown as Volume).chapters.find((c) => c.id === targetId);
-  const volumeChapter = vol1Chapter ?? vol2Chapter;
-  const volume = vol1Chapter ? (volume1 as unknown as Volume) : (volume2 as unknown as Volume);
+  for (const volume of registered.volumes) {
+    const volumeChapter = volume.chapters.find((c) => c.id === chapterId);
+    if (volumeChapter) {
+      return { volume, volumeChapter };
+    }
+  }
+  return undefined;
+}
 
-  if (!volumeChapter) {
-    return loadMathAnalysisCourse(DEFAULT_CHAPTER_ID);
+export function loadCourse(courseId: string = DEFAULT_COURSE_ID, chapterId?: string): CourseBundle {
+  const registered = getRegisteredCourse(courseId);
+  if (!registered) {
+    return loadCourse(DEFAULT_COURSE_ID, DEFAULT_CHAPTER_ID);
   }
 
-  const entry = chapterRegistry[targetId];
+  const fallbackChapterId = DEFAULT_CHAPTER_BY_COURSE[courseId];
+  const targetId = chapterId ?? fallbackChapterId;
+  if (!targetId) {
+    throw new Error(`chapterId is required for course ${courseId}`);
+  }
+
+  const located = findVolumeChapter(courseId, targetId);
+  if (!located) {
+    if (fallbackChapterId && targetId !== fallbackChapterId) {
+      return loadCourse(DEFAULT_COURSE_ID, fallbackChapterId);
+    }
+    throw new Error(`chapter ${targetId} not found in course ${courseId}`);
+  }
+
+  const { volume, volumeChapter } = located;
+  const entry = registered.chapterRegistry[targetId];
   if (!entry) {
-    return loadMathAnalysisCourse(DEFAULT_CHAPTER_ID);
+    if (fallbackChapterId && targetId !== fallbackChapterId) {
+      return loadCourse(DEFAULT_COURSE_ID, fallbackChapterId);
+    }
+    throw new Error(`chapter content not registered for ${targetId} in course ${courseId}`);
   }
 
   const chapter = adaptChapter(entry.chapter, volumeChapter);
   const exercises = (entry.exercises.exercises as unknown[]).map(adaptExercise);
   const diagrams = (entry.diagrams.diagrams as unknown[]).map(adaptDiagram);
 
-  return { course: course as CourseBundle["course"], volume, chapter, exercises, diagrams };
+  return { course: registered.course, volume, chapter, exercises, diagrams };
+}
+
+export function loadMathAnalysisCourse(chapterId?: string): CourseBundle {
+  return loadCourse(DEFAULT_COURSE_ID, chapterId ?? DEFAULT_CHAPTER_ID);
+}
+
+export function loadGaodengShuxueCourse(chapterId?: string): CourseBundle {
+  return loadCourse("gaodeng-shuxue", chapterId ?? DEFAULT_GD_CHAPTER_ID);
 }
 
-export function getAllVolumes(): Volume[] {
-  return [volume1 as unknown as Volume, volume2 as unknown as Volume];
+export function getAllVolumes(courseId: string = DEFAULT_COURSE_ID): Volume[] {
+  return getVolumesForCourse(courseId);
 }
diff --git a/lib/course/types.ts b/lib/course/types.ts
index 3fb83fb..abdd1d2 100644
--- a/lib/course/types.ts
+++ b/lib/course/types.ts
@@ -72,6 +72,7 @@ export interface ChapterContent {
 
 export interface Exercise {
   id: string;
+  title?: string;
   sourceType: string;
   sourceRef: string;
   knowledgePointIds: string[];
diff --git a/lib/diagrams/engine.ts b/lib/diagrams/engine.ts
new file mode 100644
index 0000000..07e9852
--- /dev/null
+++ b/lib/diagrams/engine.ts
@@ -0,0 +1,241 @@
+// 图示渲染引擎 —— 纯函数，无 DOM 依赖。
+// 负责：数学表达式求值、数据坐标↔像素坐标映射、曲线采样成 SVG path、
+// 以及把 LaTeX 标注转成可直接放进 SVG <text> 的 Unicode。
+//
+// 设计目标：内容 JSON 里的 parameters（expr / 端点 / 区间 / 阈值等）能被
+// 程序化地画成正确的图，而不是退化成一段说明文字。
+
+/* ----------------------------------------------------------------
+   配色（与 globals.css 主题一致：暖纸张 + 墨黑 + 暗红 + 金 + teal）
+----------------------------------------------------------------- */
+export const PALETTE = {
+  ink: "#211c16",
+  inkSoft: "#6c6151",
+  inkFaint: "#b7ab92",
+  accent: "#8a2b2b",
+  accentDeep: "#5f1d1d",
+  gold: "#9c7a2d",
+  curve: "#2f6f68",
+  curve2: "#9c7a2d",
+  curve3: "#8a2b2b",
+  paperSunk: "#efe7d6",
+  paperPage: "#fbf7ee",
+} as const;
+
+export const CURVE_COLORS = [PALETTE.curve, PALETTE.curve2, PALETTE.accent, PALETTE.ink];
+
+/* ----------------------------------------------------------------
+   表达式求值：tokenize → shunting-yard(RPN) → eval
+   支持 + - * / ^、一元负号、括号、变量 x，
+   函数 sin cos tan asin acos atan sinh cosh tanh exp ln log sqrt abs sign，
+   常量 pi e。
+----------------------------------------------------------------- */
+const FUNCS: Record<string, (x: number) => number> = {
+  sin: Math.sin, cos: Math.cos, tan: Math.tan,
+  asin: Math.asin, acos: Math.acos, atan: Math.atan,
+  sinh: Math.sinh, cosh: Math.cosh, tanh: Math.tanh,
+  exp: Math.exp, ln: Math.log, log: (x) => Math.log(x) / Math.LN10,
+  sqrt: Math.sqrt, abs: Math.abs, sign: Math.sign,
+};
+const CONSTS: Record<string, number> = { pi: Math.PI, e: Math.E };
+
+type Tok =
+  | { t: "num"; v: number }
+  | { t: "id"; v: string }
+  | { t: "op"; v: string }
+  | { t: "lp" } | { t: "rp" } | { t: "comma" };
+
+function tokenize(s: string): Tok[] {
+  const out: Tok[] = [];
+  let i = 0;
+  while (i < s.length) {
+    const c = s[i];
+    if (c === " " || c === "\t") { i++; continue; }
+    if (/[0-9.]/.test(c)) {
+      let j = i + 1;
+      while (j < s.length && /[0-9.]/.test(s[j])) j++;
+      out.push({ t: "num", v: parseFloat(s.slice(i, j)) });
+      i = j; continue;
+    }
+    if (/[a-zA-Z_]/.test(c)) {
+      let j = i + 1;
+      while (j < s.length && /[a-zA-Z0-9_]/.test(s[j])) j++;
+      out.push({ t: "id", v: s.slice(i, j) });
+      i = j; continue;
+    }
+    if (c === "(") { out.push({ t: "lp" }); i++; continue; }
+    if (c === ")") { out.push({ t: "rp" }); i++; continue; }
+    if (c === ",") { out.push({ t: "comma" }); i++; continue; }
+    if ("+-*/^".includes(c)) { out.push({ t: "op", v: c }); i++; continue; }
+    i++; // 忽略未知字符
+  }
+  return out;
+}
+
+type RPN = Array<
+  | { k: "num"; v: number }
+  | { k: "var" }
+  | { k: "fn"; name: string }
+  | { k: "op"; v: string }
+  | { k: "neg" }
+>;
+
+const prec = (o: string) => (o === "+" || o === "-" ? 1 : o === "*" || o === "/" ? 2 : o === "^" ? 4 : 0);
+
+function toRPN(toks: Tok[]): RPN {
+  const out: RPN = [];
+  type S = { s: "op"; v: string } | { s: "neg" } | { s: "fn"; name: string } | { s: "lp" };
+  const stack: S[] = [];
+  const flush = (t: S) => {
+    if (t.s === "op") out.push({ k: "op", v: t.v });
+    else if (t.s === "neg") out.push({ k: "neg" });
+    else if (t.s === "fn") out.push({ k: "fn", name: t.name });
+  };
+  let prevValue = false;
+  for (const tk of toks) {
+    if (tk.t === "num") { out.push({ k: "num", v: tk.v }); prevValue = true; continue; }
+    if (tk.t === "id") {
+      const name = tk.v.toLowerCase();
+      if (name === "x") { out.push({ k: "var" }); prevValue = true; }
+      else if (name in CONSTS) { out.push({ k: "num", v: CONSTS[name] }); prevValue = true; }
+      else if (name in FUNCS) { stack.push({ s: "fn", name }); prevValue = false; }
+      else { out.push({ k: "num", v: NaN }); prevValue = true; }
+      continue;
+    }
+    if (tk.t === "op") {
+      if (!prevValue && tk.v === "-") { stack.push({ s: "neg" }); continue; }
+      if (!prevValue && tk.v === "+") { continue; }
+      while (stack.length) {
+        const top = stack[stack.length - 1];
+        if (top.s === "op" && (prec(top.v) > prec(tk.v) || (prec(top.v) === prec(tk.v) && tk.v !== "^"))) { flush(stack.pop()!); }
+        else if (top.s === "neg" && 3 >= prec(tk.v)) { flush(stack.pop()!); }
+        else break;
+      }
+      stack.push({ s: "op", v: tk.v }); prevValue = false; continue;
+    }
+    if (tk.t === "lp") { stack.push({ s: "lp" }); prevValue = false; continue; }
+    if (tk.t === "rp") {
+      while (stack.length && stack[stack.length - 1].s !== "lp") flush(stack.pop()!);
+      stack.pop();
+      if (stack.length && stack[stack.length - 1].s === "fn") flush(stack.pop()!);
+      prevValue = true; continue;
+    }
+    if (tk.t === "comma") {
+      while (stack.length && stack[stack.length - 1].s !== "lp") flush(stack.pop()!);
+      prevValue = false; continue;
+    }
+  }
+  while (stack.length) { const t = stack.pop()!; if (t.s !== "lp") flush(t); }
+  return out;
+}
+
+function evalRPN(rpn: RPN, x: number): number {
+  const st: number[] = [];
+  for (const it of rpn) {
+    if (it.k === "num") st.push(it.v);
+    else if (it.k === "var") st.push(x);
+    else if (it.k === "neg") st.push(-(st.pop() ?? NaN));
+    else if (it.k === "fn") { const a = st.pop() ?? NaN; const f = FUNCS[it.name]; st.push(f ? f(a) : NaN); }
+    else if (it.k === "op") {
+      const b = st.pop() ?? NaN, a = st.pop() ?? NaN;
+      st.push(it.v === "+" ? a + b : it.v === "-" ? a - b : it.v === "*" ? a * b : it.v === "/" ? a / b : it.v === "^" ? Math.pow(a, b) : NaN);
+    }
+  }
+  return st.pop() ?? NaN;
+}
+
+/** 把表达式字符串编译成 (x) => y 的函数；非法表达式返回恒 NaN。 */
+export function compile(expr: string): (x: number) => number {
+  let rpn: RPN;
+  try { rpn = toRPN(tokenize(expr)); } catch { return () => NaN; }
+  return (x) => { try { return evalRPN(rpn, x); } catch { return NaN; } };
+}
+
+/* ----------------------------------------------------------------
+   坐标映射 + 曲线采样
+----------------------------------------------------------------- */
+export interface Frame { xMin: number; xMax: number; yMin: number; yMax: number; }
+export interface Box { x0: number; y0: number; w: number; h: number; }
+
+export function makeScales(frame: Frame, box: Box) {
+  const sx = (x: number) => box.x0 + ((x - frame.xMin) / (frame.xMax - frame.xMin)) * box.w;
+  const sy = (y: number) => box.y0 + box.h - ((y - frame.yMin) / (frame.yMax - frame.yMin)) * box.h;
+  return { sx, sy };
+}
+
+/** 采样函数得到 y 值范围，用于在内容未给定 y 区间时自动取景。 */
+export function autoYRange(fn: (x: number) => number, xMin: number, xMax: number, samples = 200): [number, number] {
+  let lo = Infinity, hi = -Infinity;
+  for (let i = 0; i <= samples; i++) {
+    const y = fn(xMin + (i / samples) * (xMax - xMin));
+    if (isFinite(y)) { if (y < lo) lo = y; if (y > hi) hi = y; }
+  }
+  if (!isFinite(lo) || !isFinite(hi)) return [-1, 1];
+  if (lo === hi) { lo -= 1; hi += 1; }
+  const pad = (hi - lo) * 0.15;
+  return [lo - pad, hi + pad];
+}
+
+/** 把函数采样成 SVG path（"d" 属性）；在出界或不连续处断笔，避免渐近线被连成竖线。 */
+export function plotPath(fn: (x: number) => number, frame: Frame, box: Box, samples = 260): string {
+  const { sx, sy } = makeScales(frame, box);
+  const span = frame.yMax - frame.yMin;
+  let d = "";
+  let pen = false;
+  let prevY = NaN;
+  for (let i = 0; i <= samples; i++) {
+    const x = frame.xMin + (i / samples) * (frame.xMax - frame.xMin);
+    const y = fn(x);
+    const outOfView = !isFinite(y) || y < frame.yMin - span || y > frame.yMax + span;
+    const jump = isFinite(prevY) && isFinite(y) && Math.abs(y - prevY) > span * 1.5;
+    if (outOfView || jump) { pen = false; prevY = y; continue; }
+    const yc = Math.min(frame.yMax + span * 0.02, Math.max(frame.yMin - span * 0.02, y));
+    const px = sx(x).toFixed(1), py = sy(yc).toFixed(1);
+    d += `${pen ? "L" : "M"}${px} ${py} `;
+    pen = true;
+    prevY = y;
+  }
+  return d.trim();
+}
+
+/* ----------------------------------------------------------------
+   参数安全读取（parameters 是 Record<string,unknown>）
+----------------------------------------------------------------- */
+export const asNum = (v: unknown, def = 0): number => (typeof v === "number" && isFinite(v) ? v : def);
+export const asStr = (v: unknown, def = ""): string => (typeof v === "string" ? v : def);
+export const asArr = (v: unknown): unknown[] => (Array.isArray(v) ? v : []);
+export const asObj = (v: unknown): Record<string, unknown> => (v && typeof v === "object" && !Array.isArray(v) ? (v as Record<string, unknown>) : {});
+
+/* ----------------------------------------------------------------
+   LaTeX 标注 → 可直接放进 SVG <text> 的 Unicode
+   （SVG 内无法跑 KaTeX，这里做常用符号的轻量映射）
+----------------------------------------------------------------- */
+const TEX_SYMBOLS: Array<[RegExp, string]> = [
+  [/\\varepsilon/g, "ε"], [/\\epsilon/g, "ε"], [/\\delta/g, "δ"], [/\\Delta/g, "Δ"],
+  [/\\infty/g, "∞"], [/\\cdots/g, "⋯"], [/\\dots/g, "…"], [/\\ldots/g, "…"],
+  [/\\leq?/g, "≤"], [/\\geq?/g, "≥"], [/\\neq/g, "≠"], [/\\to/g, "→"], [/\\pm/g, "±"],
+  [/\\times/g, "×"], [/\\cdot/g, "·"], [/\\approx/g, "≈"], [/\\in/g, "∈"],
+  [/\\alpha/g, "α"], [/\\beta/g, "β"], [/\\gamma/g, "γ"], [/\\theta/g, "θ"],
+  [/\\lambda/g, "λ"], [/\\mu/g, "μ"], [/\\pi/g, "π"], [/\\rho/g, "ρ"], [/\\sigma/g, "σ"],
+  [/\\sum/g, "Σ"], [/\\int/g, "∫"], [/\\sqrt/g, "√"], [/\\cos/g, "cos"], [/\\sin/g, "sin"],
+  [/\\left/g, ""], [/\\right/g, ""], [/\\,/g, " "],
+];
+const SUP: Record<string, string> = { "0": "⁰", "1": "¹", "2": "²", "3": "³", "4": "⁴", "5": "⁵", "6": "⁶", "7": "⁷", "8": "⁸", "9": "⁹", "-": "⁻", "+": "⁺", n: "ⁿ" };
+const SUB: Record<string, string> = { "0": "₀", "1": "₁", "2": "₂", "3": "₃", "4": "₄", "5": "₅", "6": "₆", "7": "₇", "8": "₈", "9": "₉", "-": "₋", "+": "₊", n: "ₙ", k: "ₖ", i: "ᵢ", j: "ⱼ", x: "ₓ", a: "ₐ" };
+
+export function texLabel(raw: string): string {
+  if (!raw) return "";
+  let s = raw.replace(/\$/g, "");
+  for (const [re, rep] of TEX_SYMBOLS) s = s.replace(re, rep);
+  // 上标：^2、^{-1}、^- ；下标：_0、_{n}、_n
+  s = s.replace(/\^\{([^}]*)\}/g, (_, g: string) => mapScript(g, SUP));
+  s = s.replace(/\^(\S)/g, (_, g: string) => mapScript(g, SUP));
+  s = s.replace(/_\{([^}]*)\}/g, (_, g: string) => mapScript(g, SUB));
+  s = s.replace(/_(\S)/g, (_, g: string) => mapScript(g, SUB));
+  s = s.replace(/[{}]/g, "");
+  return s.trim();
+}
+
+function mapScript(g: string, table: Record<string, string>): string {
+  return g.split("").map((ch) => table[ch] ?? ch).join("");
+}
diff --git a/package.json b/package.json
index 4863f1c..c5047ce 100644
--- a/package.json
+++ b/package.json
@@ -15,6 +15,7 @@
     "validate:vision-grading": "node scripts/validate-vision-grading.mjs",
     "validate:progress-state": "node scripts/validate-progress-state.mjs",
     "validate:mastery-state": "node scripts/validate-mastery-state.mjs",
+    "validate:wx-diagrams": "node scripts/build-wx-data.js && node scripts/validate-wx-diagrams.mjs",
     "validate:all": "node scripts/validate-all.mjs"
   },
   "dependencies": {
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diff --git a/scripts/build-wx-data.js b/scripts/build-wx-data.js
new file mode 100644
index 0000000..cde3928
--- /dev/null
+++ b/scripts/build-wx-data.js
@@ -0,0 +1,243 @@
+#!/usr/bin/env node
+// Bundles all course content JSON into wx-miniprogram/data/all-chapters.js
+// Run: node scripts/build-wx-data.js
+
+const fs = require('fs');
+const path = require('path');
+
+const CONTENT_BASE = path.join(__dirname, '../content/courses/math-analysis');
+const OUTPUT_FILE = path.join(__dirname, '../wx-miniprogram/data/all-chapters.js');
+
+function readJson(filePath) {
+  try {
+    return JSON.parse(fs.readFileSync(filePath, 'utf-8'));
+  } catch (e) {
+    console.warn('  [warn] Could not read:', filePath, '-', e.message);
+    return null;
+  }
+}
+
+function adaptGradingRubric(rubric) {
+  if (!Array.isArray(rubric)) return [];
+  return rubric.map(item => {
+    if (typeof item === 'string') return item;
+    if (item && typeof item === 'object') {
+      const pts = item.points != null ? '[' + item.points + '分] ' : '';
+      return pts + (item.criterion || '');
+    }
+    return String(item);
+  });
+}
+
+function getPrompt(ex) {
+  return ex.problem || ex.prompt || ex.problemStatement || '';
+}
+
+function adaptExercise(ex) {
+  const kpIds = Array.isArray(ex.knowledgePointIds)
+    ? ex.knowledgePointIds
+    : ex.knowledgePointId
+    ? [ex.knowledgePointId]
+    : [];
+
+  return {
+    id: ex.id,
+    title: ex.title || null,
+    difficulty: ex.difficulty || 'basic',
+    type: ex.type || 'computation',
+    prompt: getPrompt(ex),
+    hints: Array.isArray(ex.hints) ? ex.hints : [],
+    gradingRubric: adaptGradingRubric(ex.gradingRubric),
+    commonMistakes: Array.isArray(ex.commonMistakes) ? ex.commonMistakes : [],
+    knowledgePointIds: kpIds,
+    knowledgePointId: ex.knowledgePointId || kpIds[0] || null,
+  };
+}
+
+const DIAGRAM_TYPE_LABELS = {
+  'number-line': '数轴图示',
+  'sequence-on-number-line': '数列数轴',
+  'two-panel-sequence-plot': '数列对比',
+  'subsequence-highlight': '子列图示',
+  'monotone-sequence-plot': '单调数列',
+  'bounded-strip': '有界性图示',
+  'cartesian-epsilon-delta': 'ε-δ 图示',
+  'function-plot-asymptote': '渐近线图示',
+  'piecewise-function-plot': '分段函数',
+  'multi-curve-plot': '函数曲线',
+  'function-plot': '函数曲线',
+  'area-under-curve': '面积图示',
+  'region-2d': '平面区域',
+  geometric: '几何图示',
+  table: '表格图示',
+};
+
+function getDiagramDisplayKind(type) {
+  if (type === 'table') return 'table';
+  if (type.includes('sequence') || type === 'bounded-strip' || type === 'subsequence-highlight') return 'sequence';
+  if (type === 'number-line') return 'number-line';
+  if (type.includes('function') || type.includes('curve') || type.includes('epsilon') || type.includes('asymptote')) return 'cartesian';
+  if (type === 'geometric' || type === 'region-2d') return 'geometric';
+  return 'concept';
+}
+
+function adaptDiagram(diagram) {
+  const type = diagram.type || 'concept';
+  return {
+    id: diagram.id,
+    title: diagram.title || '教学图示',
+    type,
+    typeLabel: DIAGRAM_TYPE_LABELS[type] || '教学图示',
+    displayKind: getDiagramDisplayKind(type),
+    description: diagram.description || '',
+    parameters: diagram.parameters || {},
+    renderHints: diagram.renderHints || {},
+    teacherNotes: Array.isArray(diagram.teacherNotes) ? diagram.teacherNotes : [],
+    studentPrompt: diagram.studentPrompt || '',
+    knowledgePointIds: Array.isArray(diagram.knowledgePointIds) ? diagram.knowledgePointIds : [],
+  };
+}
+
+function getDiagramsForKnowledgePoint(kp, allDiagrams) {
+  const explicitIds = Array.isArray(kp.diagramIds) ? kp.diagramIds : [];
+  const byId = new Map(allDiagrams.map(diagram => [diagram.id, diagram]));
+  const result = [];
+  const seen = new Set();
+
+  for (const id of explicitIds) {
+    const diagram = byId.get(id);
+    if (diagram && !seen.has(diagram.id)) {
+      result.push(diagram);
+      seen.add(diagram.id);
+    }
+  }
+
+  for (const diagram of allDiagrams) {
+    if (diagram.knowledgePointIds.includes(kp.id) && !seen.has(diagram.id)) {
+      result.push(diagram);
+      seen.add(diagram.id);
+    }
+  }
+
+  return result;
+}
+
+function buildData() {
+  const output = { volumes: [], chapters: {} };
+  const volumeFiles = ['volume-1.json', 'volume-2.json'];
+
+  for (const vf of volumeFiles) {
+    const volume = readJson(path.join(CONTENT_BASE, vf));
+    if (!volume) continue;
+    console.log('Processing volume:', volume.title);
+
+    const volMeta = {
+      id: volume.id,
+      courseId: volume.courseId,
+      title: volume.title,
+      chapters: [],
+    };
+
+    for (const ch of volume.chapters) {
+      volMeta.chapters.push({
+        id: ch.id,
+        number: ch.number,
+        title: ch.title,
+        status: ch.status,
+      });
+
+      // Read chapter content
+      const chapterFilePath = ch.chapterFile
+        ? path.join(CONTENT_BASE, ch.chapterFile)
+        : null;
+      const chapterData = chapterFilePath ? readJson(chapterFilePath) : null;
+
+      // Read exercises
+      const exFilePath = ch.exercisesFile
+        ? path.join(CONTENT_BASE, ch.exercisesFile)
+        : null;
+      const exerciseData = exFilePath ? readJson(exFilePath) : null;
+      const allExercises = exerciseData && exerciseData.exercises
+        ? exerciseData.exercises.map(adaptExercise)
+        : [];
+
+      // Read teaching diagrams
+      const diagramFilePath = ch.diagramFile
+        ? path.join(CONTENT_BASE, ch.diagramFile)
+        : null;
+      const diagramData = diagramFilePath ? readJson(diagramFilePath) : null;
+      const allDiagrams = diagramData && Array.isArray(diagramData.diagrams)
+        ? diagramData.diagrams.map(adaptDiagram)
+        : [];
+
+      // Build KP list
+      let kps = [];
+      if (chapterData && Array.isArray(chapterData.knowledgePoints)) {
+        kps = chapterData.knowledgePoints.map(kp => {
+          // Match exercises to this KP
+          const kpExercises = allExercises.filter(ex =>
+            ex.knowledgePointIds.includes(kp.id) ||
+            ex.knowledgePointId === kp.id
+          );
+          return {
+            id: kp.id,
+            title: kp.title,
+            learningGoals: Array.isArray(kp.learningGoals) ? kp.learningGoals : [],
+            coreExplanation: kp.coreExplanation || '',
+            socraticQuestions: Array.isArray(kp.socraticQuestions) ? kp.socraticQuestions : [],
+            commonMistakes: Array.isArray(kp.commonMistakes) ? kp.commonMistakes : [],
+            diagramIds: Array.isArray(kp.diagramIds) ? kp.diagramIds : [],
+            diagrams: getDiagramsForKnowledgePoint(kp, allDiagrams),
+            exercises: kpExercises,
+          };
+        });
+      }
+
+      // Get overview — try new-format (id present) or old-format field
+      const overview = chapterData
+        ? (chapterData.overview || '')
+        : '';
+
+      output.chapters[ch.id] = {
+        id: ch.id,
+        number: ch.number,
+        title: ch.title,
+        status: ch.status,
+        courseId: volume.courseId,
+        volumeId: volume.id,
+        overview,
+        knowledgePoints: kps,
+      };
+
+      const exCount = kps.reduce((s, k) => s + k.exercises.length, 0);
+      const diagramCount = kps.reduce((s, k) => s + k.diagrams.length, 0);
+      console.log(
+        '  ch' + ch.number + ' ' + ch.title +
+        ' — ' + kps.length + ' KPs, ' + exCount + ' exercises, ' + diagramCount + ' diagrams'
+      );
+    }
+
+    output.volumes.push(volMeta);
+  }
+
+  const totalChapters = Object.keys(output.chapters).length;
+  const totalKps = Object.values(output.chapters)
+    .reduce((s, ch) => s + ch.knowledgePoints.length, 0);
+  const totalExercises = Object.values(output.chapters)
+    .reduce((s, ch) => s + ch.knowledgePoints
+      .reduce((ss, kp) => ss + kp.exercises.length, 0), 0);
+
+  fs.mkdirSync(path.dirname(OUTPUT_FILE), { recursive: true });
+  const js =
+    '// Auto-generated by scripts/build-wx-data.js — do not edit manually\n' +
+    '// Run: node scripts/build-wx-data.js\n' +
+    'module.exports = ' + JSON.stringify(output, null, 2) + ';\n';
+  fs.writeFileSync(OUTPUT_FILE, js, 'utf-8');
+
+  const sizeKb = Math.round(fs.statSync(OUTPUT_FILE).size / 1024);
+  console.log('\nDone!');
+  console.log('  ' + totalChapters + ' chapters, ' + totalKps + ' KPs, ' + totalExercises + ' exercises');
+  console.log('  Output: ' + OUTPUT_FILE + ' (' + sizeKb + ' KB)');
+}
+
+buildData();
diff --git a/scripts/fetch-fonts.mjs b/scripts/fetch-fonts.mjs
new file mode 100644
index 0000000..21bd250
--- /dev/null
+++ b/scripts/fetch-fonts.mjs
@@ -0,0 +1,58 @@
+// 一次性脚本：从 Google Fonts 抓取拉丁字体 woff2 并自托管到 public/fonts，
+// 生成 app/fonts.css（@font-face 指向本地文件）。
+// 目的：中国大陆访客不再依赖运行时访问 fonts.gstatic.com。
+// 运行：node scripts/fetch-fonts.mjs
+import { mkdir, writeFile } from "node:fs/promises";
+import { join } from "node:path";
+
+const OUT_DIR = join(process.cwd(), "public", "fonts");
+const CSS_OUT = join(process.cwd(), "app", "fonts.css");
+const KEEP_SUBSETS = new Set(["latin", "latin-ext"]);
+const UA =
+  "Mozilla/5.0 (Windows NT 10.0; Win64; x64) AppleWebKit/537.36 (KHTML, like Gecko) Chrome/120.0 Safari/537.36";
+
+const FAMILIES = [
+  { name: "Spectral", url: "https://fonts.googleapis.com/css2?family=Spectral:ital,wght@0,400;0,500;0,600;0,700;1,400;1,500&display=swap" },
+  { name: "Source Serif 4", url: "https://fonts.googleapis.com/css2?family=Source+Serif+4:ital,wght@0,400;0,500;0,600;1,400&display=swap" },
+  { name: "IBM Plex Mono", url: "https://fonts.googleapis.com/css2?family=IBM+Plex+Mono:wght@400;500&display=swap" },
+];
+
+const slug = (s) => s.toLowerCase().replace(/[^a-z0-9]+/g, "-").replace(/^-|-$/g, "");
+
+async function run() {
+  await mkdir(OUT_DIR, { recursive: true });
+  const faceBlocks = [];
+
+  for (const fam of FAMILIES) {
+    const res = await fetch(fam.url, { headers: { "User-Agent": UA } });
+    const css = await res.text();
+    const re = /\/\*\s*([\w-]+)\s*\*\/\s*@font-face\s*\{([^}]*)\}/g;
+    let m;
+    while ((m = re.exec(css))) {
+      const subset = m[1];
+      if (!KEEP_SUBSETS.has(subset)) continue;
+      const body = m[2];
+      const family = (body.match(/font-family:\s*'([^']+)'/) || [])[1] || fam.name;
+      const style = (body.match(/font-style:\s*(\w+)/) || [])[1] || "normal";
+      const weight = (body.match(/font-weight:\s*(\d+)/) || [])[1] || "400";
+      const url = (body.match(/src:\s*url\(([^)]+)\)/) || [])[1];
+      const range = (body.match(/unicode-range:\s*([^;]+);/) || [])[1];
+      if (!url) continue;
+
+      const file = `${slug(family)}-${weight}-${style}-${subset}.woff2`;
+      const buf = Buffer.from(await (await fetch(url, { headers: { "User-Agent": UA } })).arrayBuffer());
+      await writeFile(join(OUT_DIR, file), buf);
+      console.log(`saved ${file} (${(buf.length / 1024).toFixed(1)} KB)`);
+
+      faceBlocks.push(
+        `@font-face {\n  font-family: '${family}';\n  font-style: ${style};\n  font-weight: ${weight};\n  font-display: swap;\n  src: url('/fonts/${file}') format('woff2');\n  unicode-range: ${range};\n}`,
+      );
+    }
+  }
+
+  const header = "/* 自托管字体 —— 由 scripts/fetch-fonts.mjs 生成，请勿手改。\n   中文走本地宋体/思源回退（见 globals.css 字体栈）。 */\n\n";
+  await writeFile(CSS_OUT, header + faceBlocks.join("\n\n") + "\n");
+  console.log(`\n${faceBlocks.length} @font-face -> app/fonts.css`);
+}
+
+run().catch((e) => { console.error(e); process.exit(1); });
diff --git a/scripts/validate-all.mjs b/scripts/validate-all.mjs
index 358139b..81fc546 100644
--- a/scripts/validate-all.mjs
+++ b/scripts/validate-all.mjs
@@ -9,6 +9,7 @@ const commands = [
   ["run", "validate:vision-grading"],
   ["run", "validate:progress-state"],
   ["run", "validate:mastery-state"],
+  ["run", "validate:wx-diagrams"],
   ["run", "build"]
 ];
 
diff --git a/scripts/validate-wx-diagrams.mjs b/scripts/validate-wx-diagrams.mjs
new file mode 100644
index 0000000..191737c
--- /dev/null
+++ b/scripts/validate-wx-diagrams.mjs
@@ -0,0 +1,50 @@
+import fs from "node:fs";
+import path from "node:path";
+import { createRequire } from "node:module";
+
+const require = createRequire(import.meta.url);
+const root = process.cwd();
+const dataPath = path.join(root, "wx-miniprogram/data/all-chapters.js");
+const studyJsonPath = path.join(root, "wx-miniprogram/pages/study/study.json");
+const studyWxmlPath = path.join(root, "wx-miniprogram/pages/study/study.wxml");
+const componentPath = path.join(root, "wx-miniprogram/components/diagram-card/diagram-card.js");
+
+function assert(condition, message) {
+  if (!condition) {
+    throw new Error(message);
+  }
+}
+
+assert(fs.existsSync(dataPath), "wx data bundle is missing; run scripts/build-wx-data.js first");
+
+const data = require(dataPath);
+const sequenceChapter = data.chapters["ch-sequence-limit"];
+assert(sequenceChapter, "sequence-limit chapter missing from wx data");
+
+const epsilonKp = sequenceChapter.knowledgePoints.find((kp) => kp.id === "epsilon-n-definition");
+assert(epsilonKp, "epsilon-n-definition KP missing from wx data");
+assert(Array.isArray(epsilonKp.diagrams), "knowledge point diagrams must be an array");
+assert(
+  epsilonKp.diagrams.some((diagram) => diagram.id === "epsilon-neighborhood-on-number-line"),
+  "epsilon-neighborhood-on-number-line diagram missing from epsilon-n-definition"
+);
+assert(
+  epsilonKp.diagrams.every((diagram) => diagram.title && diagram.type && diagram.displayKind),
+  "each wx diagram must include title, type, and displayKind"
+);
+
+const functionChapter = data.chapters["ch-function-limit"];
+const functionKp = functionChapter?.knowledgePoints.find((kp) => kp.id === "x-to-x0-limit-definition");
+assert(functionKp?.diagrams?.length > 0, "function-limit definition KP should include epsilon-delta diagrams");
+
+const studyJson = JSON.parse(fs.readFileSync(studyJsonPath, "utf-8"));
+assert(
+  studyJson.usingComponents?.["diagram-card"] === "/components/diagram-card/diagram-card",
+  "study page must register diagram-card component"
+);
+
+const studyWxml = fs.readFileSync(studyWxmlPath, "utf-8");
+assert(studyWxml.includes("<diagram-card"), "study page must render diagram-card");
+assert(fs.existsSync(componentPath), "diagram-card component JS file is missing");
+
+console.log("[validate:wx-diagrams] ok");
diff --git a/wx-miniprogram/app.js b/wx-miniprogram/app.js
new file mode 100644
index 0000000..38cd81f
--- /dev/null
+++ b/wx-miniprogram/app.js
@@ -0,0 +1,23 @@
+let allChapters = { volumes: [], chapters: {} };
+try {
+  allChapters = require('./data/all-chapters');
+} catch (e) {
+  console.error('[math-analysis] Data not built. Run: node scripts/build-wx-data.js');
+}
+
+App({
+  globalData: {
+    volumes: allChapters.volumes,
+    chapters: allChapters.chapters,
+    currentKp: null,   // { chapterId, kpId } — set when entering study page
+  },
+  onLaunch() {
+    const onboarded = wx.getStorageSync('ma_onboarded');
+    if (!onboarded) {
+      // Delay so the app frame finishes mounting before redirect
+      setTimeout(() => {
+        wx.redirectTo({ url: '/pages/onboarding/onboarding' });
+      }, 100);
+    }
+  }
+});
diff --git a/wx-miniprogram/app.json b/wx-miniprogram/app.json
new file mode 100644
index 0000000..2493d12
--- /dev/null
+++ b/wx-miniprogram/app.json
@@ -0,0 +1,20 @@
+{
+  "pages": [
+    "pages/index/index",
+    "pages/onboarding/onboarding",
+    "pages/chapter/chapter",
+    "pages/study/study",
+    "pages/chat/chat",
+    "pages/settings/settings"
+  ],
+  "window": {
+    "backgroundTextStyle": "light",
+    "navigationBarBackgroundColor": "#f3ecdd",
+    "navigationBarTitleText": "数学分析",
+    "navigationBarTextStyle": "black",
+    "backgroundColor": "#f3ecdd"
+  },
+  "style": "v2",
+  "sitemapLocation": "sitemap.json",
+  "lazyCodeLoading": "requiredComponents"
+}
diff --git a/wx-miniprogram/app.wxss b/wx-miniprogram/app.wxss
new file mode 100644
index 0000000..98101f5
--- /dev/null
+++ b/wx-miniprogram/app.wxss
@@ -0,0 +1,118 @@
+/* Global design tokens — matches web app editorial palette */
+page {
+  --paper: #f3ecdd;
+  --paper-page: #fbf7ee;
+  --ink: #211c16;
+  --ink-soft: #4a3728;
+  --ink-faint: #8f7d6a;
+  --accent: #8a2b2b;
+  --accent-deep: #6b1e1e;
+  --accent-pale: #f7ede8;
+  --rule: #d9cebd;
+  --gold: #9a7a1e;
+  --shadow: 0 1px 4px rgba(33,28,22,0.10);
+  --radius: 6rpx;
+  --serif: Georgia, 'Times New Roman', serif;
+  --sans: -apple-system, 'PingFang SC', 'Microsoft YaHei', sans-serif;
+  --mono: 'Courier New', Courier, monospace;
+
+  background: var(--paper);
+  color: var(--ink);
+  font-family: var(--sans);
+  font-size: 30rpx;
+  line-height: 1.7;
+}
+
+/* Typography */
+.eyebrow {
+  font-size: 22rpx;
+  letter-spacing: 0.12em;
+  text-transform: uppercase;
+  color: var(--accent);
+  font-weight: 600;
+  margin: 0 0 4rpx;
+}
+
+.section-title {
+  font-size: 28rpx;
+  font-weight: 700;
+  color: var(--ink);
+  margin: 0 0 16rpx;
+}
+
+/* Shared card */
+.card {
+  background: var(--paper-page);
+  border: 1rpx solid var(--rule);
+  border-radius: var(--radius);
+  padding: 28rpx 32rpx;
+  margin-bottom: 20rpx;
+  box-shadow: var(--shadow);
+}
+
+/* Difficulty pills */
+.difficulty-pill {
+  display: inline-block;
+  padding: 2rpx 14rpx;
+  border-radius: 20rpx;
+  font-size: 20rpx;
+  font-weight: 600;
+  letter-spacing: 0.04em;
+}
+.difficulty-pill.basic { background: #e8f5e9; color: #2e7d32; }
+.difficulty-pill.medium { background: #fff3e0; color: #e65100; }
+.difficulty-pill.advanced { background: #fce4ec; color: #880e4f; }
+
+/* Status badge */
+.status-badge {
+  font-size: 20rpx;
+  padding: 2rpx 12rpx;
+  border-radius: 20rpx;
+  font-weight: 600;
+}
+.status-badge.draft { background: #fff9c4; color: #f57f17; }
+.status-badge.sample-ready { background: #e8f5e9; color: #2e7d32; }
+.status-badge.planned { background: #f3e5f5; color: #6a1b9a; }
+
+/* Buttons */
+.btn {
+  display: inline-flex;
+  align-items: center;
+  justify-content: center;
+  padding: 18rpx 32rpx;
+  border-radius: var(--radius);
+  border: 1.5rpx solid var(--rule);
+  background: var(--paper-page);
+  color: var(--ink);
+  font-size: 28rpx;
+  font-weight: 500;
+}
+.btn-primary {
+  background: var(--accent);
+  border-color: var(--accent-deep);
+  color: #fff;
+  font-weight: 600;
+}
+.btn-ghost {
+  background: transparent;
+  border-color: var(--rule);
+  color: var(--ink-soft);
+}
+
+/* Loading */
+.loading-wrap {
+  display: flex;
+  align-items: center;
+  justify-content: center;
+  padding: 80rpx 0;
+  color: var(--ink-faint);
+  font-size: 28rpx;
+}
+
+/* Empty state */
+.empty-state {
+  text-align: center;
+  padding: 80rpx 40rpx;
+  color: var(--ink-faint);
+  font-size: 28rpx;
+}
diff --git a/wx-miniprogram/components/diagram-card/diagram-card.js b/wx-miniprogram/components/diagram-card/diagram-card.js
new file mode 100644
index 0000000..a718e18
--- /dev/null
+++ b/wx-miniprogram/components/diagram-card/diagram-card.js
@@ -0,0 +1,139 @@
+function clamp(value, min, max) {
+  return Math.max(min, Math.min(max, value));
+}
+
+function toPercent(value, min, max) {
+  if (max === min) return 50;
+  return clamp(Math.round(((value - min) / (max - min)) * 100), 4, 96);
+}
+
+function getDiagramTypeGroup(type, displayKind) {
+  if (displayKind) return displayKind;
+  if (type === 'table') return 'table';
+  if (type === 'number-line') return 'number-line';
+  if (type && (type.includes('sequence') || type === 'bounded-strip' || type === 'subsequence-highlight')) return 'sequence';
+  if (type && (type.includes('function') || type.includes('epsilon') || type.includes('curve') || type.includes('asymptote'))) return 'cartesian';
+  if (type === 'geometric' || type === 'region-2d') return 'geometric';
+  return 'concept';
+}
+
+function getNumberLineView(parameters) {
+  const axisMin = Number(parameters.axisMin ?? -1);
+  const axisMax = Number(parameters.axisMax ?? 1);
+  const epsilon = parameters.epsilon || {};
+  const limitPoint = parameters.limitPoint || {};
+  const highlight = parameters.highlightInterval || {};
+  const from = Number(highlight.from ?? (Number(limitPoint.x ?? 0) - Number(epsilon.value ?? 0.35)));
+  const to = Number(highlight.to ?? (Number(limitPoint.x ?? 0) + Number(epsilon.value ?? 0.35)));
+
+  return {
+    axisMin,
+    axisMax,
+    intervalLeft: toPercent(from, axisMin, axisMax),
+    intervalWidth: Math.max(8, toPercent(to, axisMin, axisMax) - toPercent(from, axisMin, axisMax)),
+    markers: [
+      { label: epsilon.leftEndpointLabel || 'a-ε', left: toPercent(from, axisMin, axisMax), tone: 'edge' },
+      { label: limitPoint.symbol || 'a', left: toPercent(Number(limitPoint.x ?? 0), axisMin, axisMax), tone: 'limit' },
+      { label: epsilon.rightEndpointLabel || 'a+ε', left: toPercent(to, axisMin, axisMax), tone: 'edge' },
+    ],
+  };
+}
+
+function getSequenceTerms(parameters) {
+  const rawTerms =
+    parameters.terms ||
+    parameters.tailTerms ||
+    parameters.originalSequence ||
+    (parameters.panels && parameters.panels[0] && parameters.panels[0].terms) ||
+    [];
+  if (!Array.isArray(rawTerms)) return [];
+
+  const ys = rawTerms.map((term) => Number(term.y ?? term.x ?? 0));
+  const minY = Math.min(...ys, -1);
+  const maxY = Math.max(...ys, 1);
+  const maxN = Math.max(...rawTerms.map((term, index) => Number(term.n ?? index + 1)), 1);
+
+  return rawTerms.slice(0, 12).map((term, index) => {
+    const n = Number(term.n ?? index + 1);
+    const y = Number(term.y ?? term.x ?? 0);
+    return {
+      n,
+      label: term.inside === false ? '外' : term.selected ? '子' : String(n),
+      left: toPercent(n, 1, maxN),
+      top: 100 - toPercent(y, minY, maxY),
+      tone: term.inside === false ? 'outside' : term.selected ? 'selected' : 'inside',
+    };
+  });
+}
+
+function getCartesianView(parameters) {
+  const curves = Array.isArray(parameters.curves) ? parameters.curves : [];
+  const panels = Array.isArray(parameters.panels) ? parameters.panels : [];
+  const labels = curves.length
+    ? curves.map((curve) => curve.label || curve.expr).filter(Boolean)
+    : panels.map((panel) => panel.title).filter(Boolean);
+
+  const bands = [];
+  if (parameters.epsilonBand) bands.push(parameters.epsilonBand.symbol || 'ε 带');
+  if (parameters.deltaInterval) bands.push(parameters.deltaInterval.symbol || 'δ 区间');
+  if (parameters.asymptote) bands.push((parameters.asymptote.symbol || 'A') + ' 渐近线');
+  if (parameters.threshold) bands.push((parameters.threshold.symbol || 'M') + ' 门槛');
+
+  return {
+    labels: labels.slice(0, 4),
+    bands,
+  };
+}
+
+function getTableView(parameters) {
+  const columns = Array.isArray(parameters.columns) ? parameters.columns : [];
+  const rows = Array.isArray(parameters.rows) ? parameters.rows : [];
+  return {
+    columns,
+    rows: rows.slice(0, 8),
+  };
+}
+
+function deriveDiagramView(diagram) {
+  const safeDiagram = diagram || {};
+  const parameters = safeDiagram.parameters || {};
+  const kind = getDiagramTypeGroup(safeDiagram.type || '', safeDiagram.displayKind);
+
+  return {
+    kind,
+    typeLabel: safeDiagram.typeLabel || '教学图示',
+    numberLine: getNumberLineView(parameters),
+    sequenceTerms: getSequenceTerms(parameters),
+    cartesian: getCartesianView(parameters),
+    table: getTableView(parameters),
+    notesPreview: Array.isArray(safeDiagram.teacherNotes) ? safeDiagram.teacherNotes.slice(0, 2) : [],
+  };
+}
+
+Component({
+  properties: {
+    diagram: {
+      type: Object,
+      value: {},
+    },
+  },
+  data: {
+    view: deriveDiagramView({}),
+    notesOpen: false,
+  },
+  observers: {
+    diagram(diagram) {
+      this.setData({
+        view: deriveDiagramView(diagram),
+        notesOpen: false,
+      });
+    },
+  },
+  methods: {
+    toggleNotes() {
+      this.setData({ notesOpen: !this.data.notesOpen });
+    },
+  },
+});
+
+module.exports = { deriveDiagramView };
diff --git a/wx-miniprogram/components/diagram-card/diagram-card.json b/wx-miniprogram/components/diagram-card/diagram-card.json
new file mode 100644
index 0000000..f154458
--- /dev/null
+++ b/wx-miniprogram/components/diagram-card/diagram-card.json
@@ -0,0 +1,6 @@
+{
+  "component": true,
+  "usingComponents": {
+    "math-text": "/components/math-text/math-text"
+  }
+}
diff --git a/wx-miniprogram/components/diagram-card/diagram-card.wxml b/wx-miniprogram/components/diagram-card/diagram-card.wxml
new file mode 100644
index 0000000..b30af68
--- /dev/null
+++ b/wx-miniprogram/components/diagram-card/diagram-card.wxml
@@ -0,0 +1,85 @@
+<view class="diagram-card">
+  <view class="diagram-head">
+    <view>
+      <text class="diagram-type">{{view.typeLabel}}</text>
+      <text class="diagram-title">{{diagram.title}}</text>
+    </view>
+  </view>
+
+  <view class="diagram-visual {{view.kind}}">
+    <view wx:if="{{view.kind === 'number-line'}}" class="number-line-wrap">
+      <view class="number-axis" />
+      <view class="number-interval" style="left:{{view.numberLine.intervalLeft}}%;width:{{view.numberLine.intervalWidth}}%;" />
+      <view
+        wx:for="{{view.numberLine.markers}}"
+        wx:key="label"
+        class="number-marker {{item.tone}}"
+        style="left:{{item.left}}%;"
+      >
+        <view class="number-tick" />
+        <text class="number-label">{{item.label}}</text>
+      </view>
+    </view>
+
+    <view wx:elif="{{view.kind === 'sequence'}}" class="sequence-wrap">
+      <view class="plot-axis x" />
+      <view class="plot-axis y" />
+      <view
+        wx:for="{{view.sequenceTerms}}"
+        wx:key="n"
+        class="sequence-dot {{item.tone}}"
+        style="left:{{item.left}}%;top:{{item.top}}%;"
+      >
+        <text>{{item.label}}</text>
+      </view>
+    </view>
+
+    <view wx:elif="{{view.kind === 'cartesian'}}" class="cartesian-wrap">
+      <view class="plot-axis x" />
+      <view class="plot-axis y" />
+      <view class="epsilon-band" />
+      <view class="curve-line one" />
+      <view class="curve-line two" />
+      <view class="cartesian-tags">
+        <text wx:for="{{view.cartesian.bands}}" wx:key="*this" class="diagram-chip">{{item}}</text>
+        <text wx:for="{{view.cartesian.labels}}" wx:key="*this" class="diagram-chip muted">{{item}}</text>
+      </view>
+    </view>
+
+    <view wx:elif="{{view.kind === 'table'}}" class="diagram-table">
+      <view class="diagram-table-row head">
+        <text wx:for="{{view.table.columns}}" wx:key="*this">{{item}}</text>
+      </view>
+      <view wx:for="{{view.table.rows}}" wx:key="*this" class="diagram-table-row">
+        <text wx:for="{{item}}" wx:key="*this">{{item}}</text>
+      </view>
+    </view>
+
+    <view wx:else class="concept-wrap">
+      <view class="concept-rule" />
+      <text class="concept-label">结构示意</text>
+    </view>
+  </view>
+
+  <view class="diagram-desc" wx:if="{{diagram.description}}">
+    <math-text text="{{diagram.description}}" size="small" />
+  </view>
+
+  <view class="diagram-prompt" wx:if="{{diagram.studentPrompt}}">
+    <text class="prompt-label">想一想</text>
+    <math-text text="{{diagram.studentPrompt}}" size="small" />
+  </view>
+
+  <view wx:if="{{diagram.teacherNotes.length}}" class="diagram-notes">
+    <view class="diagram-notes-head" bindtap="toggleNotes">
+      <text>教学提示</text>
+      <text>{{notesOpen ? '收起 ▲' : '展开 ▼'}}</text>
+    </view>
+    <view wx:if="{{notesOpen}}" class="diagram-notes-body">
+      <view wx:for="{{diagram.teacherNotes}}" wx:key="*this" class="diagram-note">
+        <text class="note-dot">·</text>
+        <math-text text="{{item}}" size="small" />
+      </view>
+    </view>
+  </view>
+</view>
diff --git a/wx-miniprogram/components/diagram-card/diagram-card.wxss b/wx-miniprogram/components/diagram-card/diagram-card.wxss
new file mode 100644
index 0000000..31c5d8e
--- /dev/null
+++ b/wx-miniprogram/components/diagram-card/diagram-card.wxss
@@ -0,0 +1,264 @@
+.diagram-card {
+  background: var(--paper-page);
+  border: 1rpx solid var(--rule);
+  border-left: 4rpx solid var(--gold);
+  border-radius: 0 var(--radius) var(--radius) 0;
+  margin-bottom: 20rpx;
+  overflow: hidden;
+}
+
+.diagram-head {
+  padding: 24rpx 28rpx 14rpx;
+}
+
+.diagram-type {
+  display: block;
+  font-size: 20rpx;
+  color: var(--gold);
+  font-weight: 700;
+  letter-spacing: 0.12em;
+  text-transform: uppercase;
+  margin-bottom: 6rpx;
+}
+
+.diagram-title {
+  display: block;
+  color: var(--ink);
+  font-size: 30rpx;
+  font-weight: 700;
+  line-height: 1.4;
+}
+
+.diagram-visual {
+  position: relative;
+  min-height: 220rpx;
+  margin: 0 28rpx 20rpx;
+  background: #f3ecdd;
+  border: 1rpx solid var(--rule);
+  border-radius: var(--radius);
+  overflow: hidden;
+}
+
+.number-line-wrap,
+.sequence-wrap,
+.cartesian-wrap,
+.concept-wrap {
+  position: relative;
+  width: 100%;
+  height: 220rpx;
+}
+
+.number-axis {
+  position: absolute;
+  left: 30rpx;
+  right: 30rpx;
+  top: 106rpx;
+  height: 2rpx;
+  background: var(--ink-soft);
+}
+
+.number-interval {
+  position: absolute;
+  top: 88rpx;
+  height: 38rpx;
+  background: rgba(138, 43, 43, 0.14);
+  border: 1rpx solid rgba(138, 43, 43, 0.28);
+}
+
+.number-marker {
+  position: absolute;
+  top: 70rpx;
+  transform: translateX(-50%);
+  text-align: center;
+}
+
+.number-tick {
+  width: 2rpx;
+  height: 62rpx;
+  margin: 0 auto 6rpx;
+  background: var(--ink-soft);
+}
+
+.number-marker.limit .number-tick { background: var(--accent); }
+.number-marker.edge .number-tick { background: var(--gold); }
+.number-label { font-size: 22rpx; color: var(--ink-soft); }
+
+.plot-axis.x {
+  position: absolute;
+  left: 28rpx;
+  right: 24rpx;
+  bottom: 42rpx;
+  height: 2rpx;
+  background: var(--rule);
+}
+
+.plot-axis.y {
+  position: absolute;
+  left: 42rpx;
+  top: 24rpx;
+  bottom: 28rpx;
+  width: 2rpx;
+  background: var(--rule);
+}
+
+.sequence-dot {
+  position: absolute;
+  width: 34rpx;
+  height: 34rpx;
+  margin-left: -17rpx;
+  margin-top: -17rpx;
+  border-radius: 50%;
+  background: var(--accent);
+  color: #fff;
+  display: flex;
+  align-items: center;
+  justify-content: center;
+  font-size: 18rpx;
+  font-weight: 700;
+}
+
+.sequence-dot.outside { background: var(--gold); }
+.sequence-dot.selected { background: #2f6f68; }
+
+.epsilon-band {
+  position: absolute;
+  left: 44rpx;
+  right: 22rpx;
+  top: 74rpx;
+  height: 72rpx;
+  background: rgba(138, 43, 43, 0.10);
+  border-top: 1rpx dashed var(--accent);
+  border-bottom: 1rpx dashed var(--accent);
+}
+
+.curve-line {
+  position: absolute;
+  left: 46rpx;
+  right: 28rpx;
+  height: 54rpx;
+  border-top: 5rpx solid #2f6f68;
+  border-radius: 50%;
+  transform: rotate(-7deg);
+}
+
+.curve-line.one { top: 86rpx; }
+.curve-line.two {
+  top: 122rpx;
+  border-color: var(--gold);
+  opacity: 0.85;
+  transform: rotate(8deg);
+}
+
+.cartesian-tags {
+  position: absolute;
+  left: 58rpx;
+  right: 18rpx;
+  bottom: 12rpx;
+  display: flex;
+  gap: 8rpx;
+  flex-wrap: wrap;
+}
+
+.diagram-chip {
+  display: inline-flex;
+  padding: 3rpx 12rpx;
+  border-radius: 20rpx;
+  background: var(--accent-pale);
+  color: var(--accent);
+  font-size: 20rpx;
+  font-weight: 600;
+}
+
+.diagram-chip.muted {
+  background: #efe7d6;
+  color: var(--ink-soft);
+}
+
+.diagram-table {
+  padding: 12rpx;
+}
+
+.diagram-table-row {
+  display: grid;
+  grid-template-columns: repeat(2, minmax(0, 1fr));
+  border-bottom: 1rpx solid var(--rule);
+}
+
+.diagram-table-row text {
+  padding: 12rpx;
+  font-size: 22rpx;
+  color: var(--ink);
+  word-break: break-all;
+}
+
+.diagram-table-row.head {
+  background: var(--accent-pale);
+  font-weight: 700;
+  color: var(--accent);
+}
+
+.concept-rule {
+  position: absolute;
+  left: 46rpx;
+  right: 46rpx;
+  top: 96rpx;
+  height: 4rpx;
+  background: linear-gradient(90deg, var(--accent), var(--gold));
+}
+
+.concept-label {
+  position: absolute;
+  left: 0;
+  right: 0;
+  top: 120rpx;
+  text-align: center;
+  color: var(--ink-faint);
+  font-size: 24rpx;
+}
+
+.diagram-desc,
+.diagram-prompt {
+  padding: 0 28rpx 20rpx;
+}
+
+.diagram-prompt {
+  border-top: 1rpx solid var(--rule);
+  padding-top: 18rpx;
+}
+
+.prompt-label {
+  display: block;
+  color: var(--accent);
+  font-size: 20rpx;
+  font-weight: 700;
+  letter-spacing: 0.12em;
+  margin-bottom: 8rpx;
+}
+
+.diagram-notes {
+  border-top: 1rpx solid var(--rule);
+}
+
+.diagram-notes-head {
+  display: flex;
+  justify-content: space-between;
+  padding: 18rpx 28rpx;
+  color: var(--ink-soft);
+  font-size: 24rpx;
+  font-weight: 700;
+}
+
+.diagram-notes-body {
+  padding: 0 28rpx 18rpx;
+}
+
+.diagram-note {
+  display: flex;
+  gap: 10rpx;
+  margin-top: 10rpx;
+}
+
+.note-dot {
+  color: var(--gold);
+  flex-shrink: 0;
+}
diff --git a/wx-miniprogram/components/math-text/math-text.js b/wx-miniprogram/components/math-text/math-text.js
new file mode 100644
index 0000000..46b3abc
--- /dev/null
+++ b/wx-miniprogram/components/math-text/math-text.js
@@ -0,0 +1,35 @@
+const { parseText } = require('../../utils/parser');
+
+Component({
+  options: {
+    addGlobalClass: true,  // lets parent pages override styles
+    styleIsolation: 'apply-shared',
+  },
+  properties: {
+    text: { type: String, value: '' },
+    size: { type: String, value: 'normal' }, // normal | small | large
+    color: { type: String, value: '' },      // override text color
+  },
+  data: {
+    nodes: [],
+    inlineStyle: '',
+  },
+  observers: {
+    text(val) {
+      this.setData({ nodes: parseText(val || '') });
+    },
+    color(val) {
+      this.setData({ inlineStyle: val ? 'color:' + val + ';' : '' });
+    },
+  },
+  lifetimes: {
+    attached() {
+      if (this.data.text) {
+        this.setData({ nodes: parseText(this.data.text) });
+      }
+      if (this.data.color) {
+        this.setData({ inlineStyle: 'color:' + this.data.color + ';' });
+      }
+    },
+  },
+});
diff --git a/wx-miniprogram/components/math-text/math-text.json b/wx-miniprogram/components/math-text/math-text.json
new file mode 100644
index 0000000..a89ef4d
--- /dev/null
+++ b/wx-miniprogram/components/math-text/math-text.json
@@ -0,0 +1,4 @@
+{
+  "component": true,
+  "usingComponents": {}
+}
diff --git a/wx-miniprogram/components/math-text/math-text.wxml b/wx-miniprogram/components/math-text/math-text.wxml
new file mode 100644
index 0000000..2b92f7a
--- /dev/null
+++ b/wx-miniprogram/components/math-text/math-text.wxml
@@ -0,0 +1 @@
+<rich-text nodes="{{nodes}}" class="math-text math-text--{{size}}" style="{{inlineStyle}}" />
diff --git a/wx-miniprogram/components/math-text/math-text.wxss b/wx-miniprogram/components/math-text/math-text.wxss
new file mode 100644
index 0000000..6e886bc
--- /dev/null
+++ b/wx-miniprogram/components/math-text/math-text.wxss
@@ -0,0 +1,10 @@
+.math-text {
+  display: block;
+  line-height: 1.8;
+  color: #211c16;
+  font-family: -apple-system, 'PingFang SC', sans-serif;
+}
+
+.math-text--normal { font-size: 30rpx; }
+.math-text--small  { font-size: 26rpx; }
+.math-text--large  { font-size: 34rpx; }
diff --git a/wx-miniprogram/config.example.js b/wx-miniprogram/config.example.js
new file mode 100644
index 0000000..216e42b
--- /dev/null
+++ b/wx-miniprogram/config.example.js
@@ -0,0 +1,6 @@
+// Copy this file to config.js and fill in your API key.
+module.exports = {
+  DEEPSEEK_API_KEY: 'sk-YOUR_DEEPSEEK_API_KEY_HERE',
+  DEEPSEEK_BASE_URL: 'https://api.deepseek.com/v1',
+  DEEPSEEK_MODEL: 'deepseek-chat',
+};
diff --git a/wx-miniprogram/pages/chapter/chapter.js b/wx-miniprogram/pages/chapter/chapter.js
new file mode 100644
index 0000000..be12ac2
--- /dev/null
+++ b/wx-miniprogram/pages/chapter/chapter.js
@@ -0,0 +1,59 @@
+const app = getApp();
+const { loadKpProgress } = require('../../utils/progress');
+
+Page({
+  data: {
+    chapter: null,
+    loading: true,
+  },
+  onLoad(options) {
+    this._load(options.chapterId);
+  },
+  onShow() {
+    // Refresh progress badges when returning from study page
+    if (this.data.chapter) {
+      this._refreshProgress();
+    }
+  },
+  _load(chapterId) {
+    const chapter = app.globalData.chapters[chapterId];
+    if (!chapter) {
+      wx.showToast({ title: '章节不存在', icon: 'error' });
+      return;
+    }
+    wx.setNavigationBarTitle({ title: chapter.title });
+    this.setData({ chapter: this._enrich(chapter), loading: false });
+  },
+  _enrich(chapter) {
+    const kps = chapter.knowledgePoints.map(kp => {
+      const prog = loadKpProgress(chapter.id, kp.id);
+      return {
+        ...kp,
+        studied: !!prog.studied,
+        bestScore: prog.bestExScore != null ? prog.bestExScore : null,
+        exercisesAttempted: prog.exercisesAttempted || 0,
+        diagrams: Array.isArray(kp.diagrams) ? kp.diagrams : [],
+      };
+    });
+    const studiedCount = kps.filter(k => k.studied).length;
+    const total = kps.length;
+    const diagramCount = kps.reduce((sum, kp) => sum + kp.diagrams.length, 0);
+    const progressPct = total > 0 ? Math.round(studiedCount / total * 100) : 0;
+    return {
+      ...chapter,
+      knowledgePoints: kps,
+      studiedCount,
+      diagramCount,
+      progressPct,
+      isComplete: studiedCount === total && total > 0,
+    };
+  },
+  _refreshProgress() {
+    const chapter = app.globalData.chapters[this.data.chapter.id];
+    if (chapter) this.setData({ chapter: this._enrich(chapter) });
+  },
+  goToStudy(e) {
+    const { kpid, chapterid } = e.currentTarget.dataset;
+    wx.navigateTo({ url: '/pages/study/study?chapterId=' + chapterid + '&kpId=' + kpid });
+  },
+});
diff --git a/wx-miniprogram/pages/chapter/chapter.json b/wx-miniprogram/pages/chapter/chapter.json
new file mode 100644
index 0000000..48fb7bb
--- /dev/null
+++ b/wx-miniprogram/pages/chapter/chapter.json
@@ -0,0 +1,6 @@
+{
+  "navigationBarTitleText": "章节详情",
+  "usingComponents": {
+    "math-text": "/components/math-text/math-text"
+  }
+}
diff --git a/wx-miniprogram/pages/chapter/chapter.wxml b/wx-miniprogram/pages/chapter/chapter.wxml
new file mode 100644
index 0000000..a54fa5a
--- /dev/null
+++ b/wx-miniprogram/pages/chapter/chapter.wxml
@@ -0,0 +1,66 @@
+<view class="page">
+  <view wx:if="{{loading}}" class="loading-wrap"><text>加载中…</text></view>
+
+  <block wx:elif="{{chapter}}">
+    <!-- Chapter header -->
+    <view class="chapter-header">
+      <text class="ch-eyebrow">第 {{chapter.number}} 章</text>
+      <text class="ch-title">{{chapter.title}}</text>
+      <view wx:if="{{chapter.overview}}" class="ch-overview">
+        <math-text text="{{chapter.overview}}" size="small" />
+      </view>
+      <view class="ch-progress-row">
+        <text class="ch-meta">{{chapter.knowledgePoints.length}} 个知识点 · {{chapter.diagramCount}} 张图示</text>
+        <text wx:if="{{chapter.isComplete}}" class="ch-complete-badge">✓ 已完成</text>
+        <text wx:elif="{{chapter.studiedCount > 0}}" class="ch-studied">
+          {{chapter.studiedCount}}/{{chapter.knowledgePoints.length}} 已学
+        </text>
+      </view>
+      <view wx:if="{{chapter.studiedCount > 0}}" class="ch-progress-bar-track">
+        <view
+          class="ch-progress-bar-fill {{chapter.isComplete ? 'complete' : ''}}"
+          style="width:{{chapter.progressPct}}%;"
+        />
+      </view>
+    </view>
+
+    <!-- KP list -->
+    <view class="kp-section">
+      <view class="section-header-row">
+        <text class="section-title">知识点</text>
+        <text wx:if="{{chapter.studiedCount === 0}}" class="section-hint">点击开始学习</text>
+      </view>
+
+      <view class="kp-list">
+        <view
+          wx:for="{{chapter.knowledgePoints}}"
+          wx:key="id"
+          class="kp-row {{item.studied ? 'is-studied' : ''}}"
+          bindtap="goToStudy"
+          data-kpid="{{item.id}}"
+          data-chapterid="{{chapter.id}}"
+        >
+          <view class="kp-index-wrap">
+            <text wx:if="{{item.studied}}" class="kp-check">✓</text>
+            <text wx:else class="kp-index">{{index + 1}}</text>
+          </view>
+          <view class="kp-info">
+            <text class="kp-title">{{item.title}}</text>
+            <view class="kp-goals" wx:if="{{item.learningGoals.length}}">
+              <text class="kp-goal-first">{{item.learningGoals[0]}}</text>
+            </view>
+            <view class="kp-stats-row">
+              <text wx:if="{{item.exercises.length}}" class="kp-ex-count">{{item.exercises.length}} 题</text>
+              <text wx:else class="kp-ex-count kp-ex-none">暂无练习</text>
+              <text wx:if="{{item.diagrams.length}}" class="kp-diagram-count">{{item.diagrams.length}} 图</text>
+              <text wx:if="{{item.bestScore != null}}" class="kp-score {{item.bestScore >= 80 ? 'good' : 'ok'}}">
+                最高 {{item.bestScore}} 分
+              </text>
+            </view>
+          </view>
+          <text class="kp-arrow">›</text>
+        </view>
+      </view>
+    </view>
+  </block>
+</view>
diff --git a/wx-miniprogram/pages/chapter/chapter.wxss b/wx-miniprogram/pages/chapter/chapter.wxss
new file mode 100644
index 0000000..2777195
--- /dev/null
+++ b/wx-miniprogram/pages/chapter/chapter.wxss
@@ -0,0 +1,136 @@
+.page { min-height: 100vh; background: var(--paper); padding-bottom: 60rpx; }
+
+/* Chapter header */
+.chapter-header {
+  background: var(--paper-page);
+  border-bottom: 1rpx solid var(--rule);
+  padding: 48rpx 40rpx 36rpx;
+}
+.ch-eyebrow {
+  display: block;
+  font-size: 22rpx;
+  letter-spacing: 0.14em;
+  text-transform: uppercase;
+  color: var(--accent);
+  font-weight: 600;
+  margin-bottom: 8rpx;
+}
+.ch-title {
+  display: block;
+  font-size: 44rpx;
+  font-weight: 800;
+  color: var(--ink);
+  line-height: 1.3;
+  margin-bottom: 16rpx;
+  font-family: var(--serif);
+}
+.ch-overview {
+  background: var(--paper);
+  border-left: 3rpx solid var(--accent);
+  padding: 16rpx 20rpx;
+  margin-bottom: 20rpx;
+  border-radius: 0 var(--radius) var(--radius) 0;
+}
+.ch-progress-row {
+  display: flex;
+  align-items: center;
+  justify-content: space-between;
+}
+.ch-meta { font-size: 24rpx; color: var(--ink-faint); }
+.ch-studied { font-size: 24rpx; color: var(--accent); font-weight: 700; }
+.ch-complete-badge {
+  font-size: 22rpx;
+  font-weight: 700;
+  color: #2e7d32;
+  background: #e8f5e9;
+  padding: 2rpx 14rpx;
+  border-radius: 20rpx;
+}
+.ch-progress-bar-track {
+  height: 6rpx;
+  background: var(--rule);
+  border-radius: 3rpx;
+  overflow: hidden;
+  margin-top: 14rpx;
+}
+.ch-progress-bar-fill {
+  height: 100%;
+  background: var(--accent);
+  border-radius: 3rpx;
+  transition: width 0.4s;
+}
+.ch-progress-bar-fill.complete { background: #2e7d32; }
+
+/* KP section */
+.kp-section { padding: 32rpx 40rpx 0; }
+.section-header-row {
+  display: flex;
+  align-items: center;
+  justify-content: space-between;
+  padding-bottom: 16rpx;
+  border-bottom: 1rpx solid var(--rule);
+  margin-bottom: 8rpx;
+}
+.section-title {
+  font-size: 24rpx;
+  font-weight: 700;
+  color: var(--ink-soft);
+  letter-spacing: 0.06em;
+}
+.section-hint { font-size: 22rpx; color: var(--gold); font-weight: 600; }
+
+/* KP list */
+.kp-row {
+  display: flex;
+  align-items: flex-start;
+  padding: 24rpx 0;
+  border-bottom: 1rpx solid var(--rule);
+  gap: 20rpx;
+}
+.kp-row:last-child { border-bottom: none; }
+.kp-row.is-studied .kp-title { color: var(--ink-soft); }
+
+.kp-index-wrap {
+  width: 52rpx;
+  height: 52rpx;
+  border-radius: 50%;
+  display: flex;
+  align-items: center;
+  justify-content: center;
+  flex-shrink: 0;
+  margin-top: 4rpx;
+  background: var(--accent-pale);
+}
+.kp-index { font-size: 22rpx; font-weight: 700; color: var(--accent); }
+.kp-check { font-size: 26rpx; color: #2e7d32; font-weight: 900; }
+.kp-row.is-studied .kp-index-wrap { background: #e8f5e9; }
+
+.kp-info { flex: 1; min-width: 0; }
+.kp-title {
+  display: block;
+  font-size: 30rpx;
+  font-weight: 600;
+  color: var(--ink);
+  line-height: 1.4;
+  margin-bottom: 8rpx;
+}
+.kp-goal-first {
+  font-size: 24rpx;
+  color: var(--ink-faint);
+  line-height: 1.5;
+  margin-bottom: 8rpx;
+  display: -webkit-box;
+  -webkit-line-clamp: 2;
+  -webkit-box-orient: vertical;
+  overflow: hidden;
+  display: block;
+}
+.kp-stats-row { display: flex; align-items: center; gap: 14rpx; flex-wrap: wrap; }
+.kp-ex-count { font-size: 22rpx; color: var(--accent); font-weight: 600; }
+.kp-ex-none { color: var(--ink-faint); }
+.kp-diagram-count { font-size: 22rpx; color: var(--gold); font-weight: 700; }
+.kp-score { font-size: 22rpx; font-weight: 700; }
+.kp-score.good { color: #2e7d32; }
+.kp-score.ok { color: #f57f17; }
+
+.kp-arrow { font-size: 40rpx; color: var(--ink-faint); flex-shrink: 0; margin-top: 8rpx; }
diff --git a/wx-miniprogram/pages/chat/chat.js b/wx-miniprogram/pages/chat/chat.js
new file mode 100644
index 0000000..74f24f8
--- /dev/null
+++ b/wx-miniprogram/pages/chat/chat.js
@@ -0,0 +1,147 @@
+const app = getApp();
+const { chatRequest } = require('../../utils/api');
+const { saveChat, loadChat } = require('../../utils/progress');
+
+function buildOpeningMessage(kp) {
+  if (!kp) return '你好！我是你的数学分析 AI 助教。有什么想问的？';
+  const goal = kp.learningGoals && kp.learningGoals.length ? kp.learningGoals[0] : '';
+  return '你好！我们今天学习「' + kp.title + '」。' +
+    (goal ? '本节核心目标：' + goal + '。' : '') +
+    '\n\n这个知识点你目前哪里还不太清楚？或者想从哪里开始？';
+}
+
+function nowTs() { return Date.now(); }
+
+function fmtTime(ts) {
+  if (!ts) return '';
+  const d = new Date(ts);
+  const h = d.getHours().toString().padStart(2, '0');
+  const m = d.getMinutes().toString().padStart(2, '0');
+  return h + ':' + m;
+}
+
+Page({
+  data: {
+    kp: null,
+    kpTitle: '',
+    chapterId: '',
+    kpId: '',
+    messages: [],
+    inputText: '',
+    sending: false,
+    hasError: false,
+    suggestions: [],
+    showSuggestions: false,
+    scrollTop: 0,
+    _lastScrollTop: 0,
+  },
+  onLoad(options) {
+    const { chapterId, kpId } = options;
+    const chapter = app.globalData.chapters[chapterId];
+    const kp = chapter && chapter.knowledgePoints.find(k => k.id === kpId);
+    const title = kp ? kp.title : 'AI 老师';
+    wx.setNavigationBarTitle({ title: 'AI 老师 · ' + title });
+
+    // Try to restore previous chat session for this KP
+    const saved = loadChat(chapterId, kpId);
+    const messages = (saved && saved.length > 0)
+      ? saved.map(m => ({ ...m, timeLabel: fmtTime(m.ts) }))
+      : [{ role: 'assistant', content: buildOpeningMessage(kp), ts: nowTs(), timeLabel: fmtTime(nowTs()) }];
+
+    // Build quick-reply suggestions from KP learning goals
+    const suggestions = kp && kp.learningGoals && kp.learningGoals.length
+      ? kp.learningGoals.slice(0, 3).map(g => '「' + g + '」是什么意思？')
+      : [];
+
+    this.setData({
+      kp: kp || null,
+      kpTitle: title,
+      chapterId,
+      kpId,
+      messages,
+      suggestions,
+      showSuggestions: suggestions.length > 0 && messages.length <= 1,
+    });
+    this._scrollToBottom(false);
+  },
+  onInputChange(e) {
+    this.setData({ inputText: e.detail.value });
+  },
+  sendSuggestion(e) {
+    const text = e.currentTarget.dataset.text;
+    if (!text) return;
+    this.setData({ inputText: text, showSuggestions: false });
+    // Send immediately
+    setTimeout(() => this.sendMessage(), 50);
+  },
+  sendMessage() {
+    const { inputText, messages, kp, sending } = this.data;
+    if (sending || !inputText.trim()) return;
+
+    const ts = nowTs();
+    const userMsg = { role: 'user', content: inputText.trim(), ts, timeLabel: fmtTime(ts) };
+    const newMessages = [...messages, userMsg];
+    wx.vibrateShort({ type: 'light' });
+    this.setData({ messages: newMessages, inputText: '', sending: true, hasError: false, showSuggestions: false });
+    this._scrollToBottom(true);
+    this._sendToApi(newMessages, kp);
+  },
+  _sendToApi(messages, kp) {
+    const { chapterId, kpId } = this.data;
+    chatRequest(messages, kp, {
+      onSuccess: (reply) => {
+        const replyTs = nowTs();
+        const updated = [
+          ...this.data.messages,
+          { role: 'assistant', content: reply, ts: replyTs, timeLabel: fmtTime(replyTs) },
+        ];
+        this.setData({ messages: updated, sending: false, hasError: false });
+        saveChat(chapterId, kpId, updated);
+        this._scrollToBottom(true);
+      },
+      onError: (msg) => {
+        this.setData({ sending: false, hasError: true, lastErrorMsg: msg });
+        this._scrollToBottom(true);
+      },
+    });
+  },
+  retryLastMessage() {
+    const { messages, kp, sending } = this.data;
+    if (sending) return;
+    // Remove any trailing error-placeholder messages and retry
+    const userMessages = messages.filter(m => m.role === 'user');
+    if (!userMessages.length) return;
+    this.setData({ sending: true, hasError: false });
+    this._sendToApi(messages, kp);
+  },
+  clearChat() {
+    wx.showModal({
+      title: '重置对话',
+      content: '清除本次对话记录，重新开始？',
+      success: (res) => {
+        if (!res.confirm) return;
+        const opening = buildOpeningMessage(this.data.kp);
+        const ts = nowTs();
+        const messages = [{ role: 'assistant', content: opening, ts, timeLabel: fmtTime(ts) }];
+        this.setData({ messages, inputText: '', sending: false });
+        saveChat(this.data.chapterId, this.data.kpId, messages);
+        this._scrollToBottom(false);
+      },
+    });
+  },
+  _scrollToBottom(animate) {
+    // Use query to get actual scroll height
+    const query = this.createSelectorQuery();
+    query.select('.messages-inner').boundingClientRect();
+    query.select('.messages-area').boundingClientRect();
+    query.exec((res) => {
+      if (!res[0] || !res[1]) return;
+      const innerHeight = res[0].height;
+      const areaHeight = res[1].height;
+      const newTop = Math.max(0, innerHeight - areaHeight + 100);
+      if (newTop !== this.data._lastScrollTop) {
+        this.setData({ scrollTop: newTop, _lastScrollTop: newTop });
+      }
+    });
+  },
+});
diff --git a/wx-miniprogram/pages/chat/chat.json b/wx-miniprogram/pages/chat/chat.json
new file mode 100644
index 0000000..a8785bb
--- /dev/null
+++ b/wx-miniprogram/pages/chat/chat.json
@@ -0,0 +1,6 @@
+{
+  "navigationBarTitleText": "AI 老师",
+  "usingComponents": {
+    "math-text": "/components/math-text/math-text"
+  }
+}
diff --git a/wx-miniprogram/pages/chat/chat.wxml b/wx-miniprogram/pages/chat/chat.wxml
new file mode 100644
index 0000000..bb90646
--- /dev/null
+++ b/wx-miniprogram/pages/chat/chat.wxml
@@ -0,0 +1,99 @@
+<view class="chat-page">
+  <!-- Context strip -->
+  <view class="context-strip" wx:if="{{kp}}">
+    <text class="context-label">知识点：</text>
+    <text class="context-kp">{{kpTitle}}</text>
+    <text class="context-clear" bindtap="clearChat">重置</text>
+  </view>
+
+  <!-- Messages scroll area -->
+  <scroll-view
+    class="messages-area"
+    scroll-y
+    scroll-with-animation
+    scroll-top="{{scrollTop}}"
+    enhanced
+    show-scrollbar="{{false}}"
+  >
+    <view class="messages-inner">
+      <view
+        wx:for="{{messages}}"
+        wx:key="{{index}}"
+        class="msg-row {{item.role === 'user' ? 'is-user' : 'is-ai'}}"
+      >
+        <view wx:if="{{item.role === 'assistant'}}" class="avatar ai-avatar">
+          <text>📚</text>
+        </view>
+
+        <view class="bubble-col {{item.role === 'user' ? 'bubble-col-user' : ''}}">
+          <view class="bubble {{item.role === 'user' ? 'bubble-user' : 'bubble-ai'}}">
+            <math-text
+              text="{{item.content}}"
+              size="normal"
+              color="{{item.role === 'user' ? '#fff' : ''}}"
+            />
+          </view>
+          <text wx:if="{{item.timeLabel}}" class="msg-time">{{item.timeLabel}}</text>
+        </view>
+
+        <view wx:if="{{item.role === 'user'}}" class="avatar user-avatar">
+          <text>你</text>
+        </view>
+      </view>
+
+      <!-- Typing indicator -->
+      <view wx:if="{{sending}}" class="msg-row is-ai">
+        <view class="avatar ai-avatar"><text>📚</text></view>
+        <view class="bubble bubble-ai thinking">
+          <text>思考中</text><text class="typing-dots">...</text>
+        </view>
+      </view>
+
+      <!-- Error state with retry -->
+      <view wx:if="{{hasError}}" class="error-row">
+        <text class="error-msg">⚠ {{lastErrorMsg}}</text>
+        <view class="retry-btn" bindtap="retryLastMessage"><text>重试</text></view>
+      </view>
+
+      <!-- Spacer so last message isn't hidden by input bar -->
+      <view style="height:16rpx;" />
+    </view>
+  </scroll-view>
+
+  <!-- Suggestion chips -->
+  <view wx:if="{{showSuggestions && suggestions.length}}" class="suggestions-wrap">
+    <scroll-view class="suggestions-scroll" scroll-x enhanced show-scrollbar="{{false}}">
+      <view class="suggestions-inner">
+        <view
+          wx:for="{{suggestions}}"
+          wx:key="*this"
+          class="suggestion-chip"
+          bindtap="sendSuggestion"
+          data-text="{{item}}"
+        >
+          <text>{{item}}</text>
+        </view>
+      </view>
+    </scroll-view>
+  </view>
+
+  <!-- Input area -->
+  <view class="input-area">
+    <textarea
+      class="chat-input"
+      placeholder="问一个问题…"
+      value="{{inputText}}"
+      bindinput="onInputChange"
+      auto-height
+      maxlength="500"
+      confirm-type="send"
+      bindconfirm="sendMessage"
+      adjust-position
+    />
+    <button
+      class="send-btn {{(!inputText || sending) ? 'is-disabled' : ''}}"
+      bindtap="sendMessage"
+      disabled="{{!inputText || sending}}"
+    >发送</button>
+  </view>
+</view>
diff --git a/wx-miniprogram/pages/chat/chat.wxss b/wx-miniprogram/pages/chat/chat.wxss
new file mode 100644
index 0000000..ae0d680
--- /dev/null
+++ b/wx-miniprogram/pages/chat/chat.wxss
@@ -0,0 +1,203 @@
+.chat-page {
+  display: flex;
+  flex-direction: column;
+  height: 100vh;
+  background: var(--paper);
+}
+
+/* Context strip */
+.context-strip {
+  background: var(--accent-pale);
+  border-bottom: 1rpx solid #f2d4cd;
+  padding: 12rpx 32rpx;
+  display: flex;
+  align-items: center;
+  flex-shrink: 0;
+  gap: 8rpx;
+}
+.context-label { font-size: 20rpx; color: var(--accent); font-weight: 600; flex-shrink: 0; }
+.context-kp {
+  font-size: 20rpx;
+  color: var(--accent-deep);
+  font-weight: 700;
+  flex: 1;
+  overflow: hidden;
+  text-overflow: ellipsis;
+  white-space: nowrap;
+}
+.context-clear {
+  font-size: 20rpx;
+  color: var(--ink-faint);
+  flex-shrink: 0;
+  padding: 4rpx 12rpx;
+  border: 1rpx solid var(--rule);
+  border-radius: 20rpx;
+}
+
+/* Messages — height:0 + min-height:0 forces scroll-view to fill flex space */
+.messages-area {
+  flex: 1;
+  height: 0;
+  min-height: 0;
+}
+.messages-inner { padding: 24rpx 28rpx; }
+
+/* Message rows */
+.msg-row {
+  display: flex;
+  align-items: flex-end;
+  gap: 14rpx;
+  margin-bottom: 28rpx;
+}
+.msg-row.is-user { flex-direction: row-reverse; }
+
+/* Avatars */
+.avatar {
+  width: 60rpx;
+  height: 60rpx;
+  border-radius: 50%;
+  display: flex;
+  align-items: center;
+  justify-content: center;
+  flex-shrink: 0;
+}
+.ai-avatar { background: var(--accent-pale); font-size: 30rpx; }
+.user-avatar {
+  background: var(--accent);
+  color: #fff;
+  font-size: 20rpx;
+  font-weight: 700;
+}
+
+/* Bubble column (bubble + timestamp) */
+.bubble-col { display: flex; flex-direction: column; max-width: 74%; }
+.bubble-col-user { align-items: flex-end; }
+.msg-time {
+  font-size: 18rpx;
+  color: var(--ink-faint);
+  margin-top: 6rpx;
+  padding: 0 4rpx;
+}
+
+/* Bubbles */
+.bubble {
+  padding: 20rpx 24rpx;
+  border-radius: 20rpx;
+  line-height: 1.7;
+}
+.bubble-ai {
+  background: var(--paper-page);
+  border: 1rpx solid var(--rule);
+  border-bottom-left-radius: 4rpx;
+}
+.bubble-user {
+  background: var(--accent);
+  border-bottom-right-radius: 4rpx;
+}
+.thinking {
+  display: flex;
+  align-items: center;
+  font-size: 26rpx;
+  color: var(--ink-faint);
+  font-style: italic;
+  padding: 16rpx 20rpx;
+}
+.typing-dots {
+  display: inline-block;
+  animation: blink 1.2s step-start infinite;
+  letter-spacing: 0.1em;
+  margin-left: 2rpx;
+}
+@keyframes blink {
+  0%, 100% { opacity: 1; }
+  33% { opacity: 0.2; }
+  66% { opacity: 0.6; }
+}
+
+/* Suggestion chips */
+.suggestions-wrap {
+  background: var(--paper-page);
+  border-top: 1rpx solid var(--rule);
+  padding: 16rpx 0;
+  flex-shrink: 0;
+}
+.suggestions-scroll { width: 100%; }
+.suggestions-inner {
+  display: flex;
+  gap: 12rpx;
+  padding: 0 24rpx;
+  white-space: nowrap;
+}
+.suggestion-chip {
+  display: inline-flex;
+  align-items: center;
+  flex-shrink: 0;
+  padding: 12rpx 24rpx;
+  border: 1.5rpx solid var(--rule);
+  border-radius: 30rpx;
+  font-size: 24rpx;
+  color: var(--ink-soft);
+  background: var(--paper);
+  max-width: 500rpx;
+  overflow: hidden;
+  text-overflow: ellipsis;
+}
+
+/* Error + retry */
+.error-row {
+  display: flex;
+  align-items: center;
+  justify-content: space-between;
+  padding: 16rpx 24rpx;
+  background: #fff0f0;
+  border: 1rpx solid #ffc9c9;
+  border-radius: var(--radius);
+  margin-bottom: 16rpx;
+  gap: 16rpx;
+}
+.error-msg { font-size: 24rpx; color: #c62828; flex: 1; line-height: 1.5; }
+.retry-btn {
+  flex-shrink: 0;
+  padding: 10rpx 24rpx;
+  background: #c62828;
+  color: #fff;
+  border-radius: 30rpx;
+  font-size: 24rpx;
+  font-weight: 600;
+}
+
+/* Input bar */
+.input-area {
+  display: flex;
+  align-items: flex-end;
+  gap: 14rpx;
+  padding: 14rpx 24rpx calc(14rpx + env(safe-area-inset-bottom));
+  background: var(--paper-page);
+  border-top: 1rpx solid var(--rule);
+  flex-shrink: 0;
+}
+.chat-input {
+  flex: 1;
+  min-height: 72rpx;
+  max-height: 180rpx;
+  padding: 18rpx 22rpx;
+  background: var(--paper);
+  border: 1.5rpx solid var(--rule);
+  border-radius: 36rpx;
+  font-size: 28rpx;
+  color: var(--ink);
+  line-height: 1.6;
+}
+.send-btn {
+  padding: 18rpx 32rpx;
+  background: var(--accent);
+  color: #fff;
+  border-radius: 36rpx;
+  font-size: 28rpx;
+  font-weight: 600;
+  flex-shrink: 0;
+  border: none;
+  margin: 0;
+  line-height: 1.4;
+}
+.send-btn.is-disabled { opacity: 0.4; }
diff --git a/wx-miniprogram/pages/index/index.js b/wx-miniprogram/pages/index/index.js
new file mode 100644
index 0000000..5c50f28
--- /dev/null
+++ b/wx-miniprogram/pages/index/index.js
@@ -0,0 +1,98 @@
+const app = getApp();
+const { loadChapterProgress, loadKpProgress } = require('../../utils/progress');
+
+const STATUS_LABEL = {
+  'sample-ready': '完整',
+  draft: '草稿',
+  planned: '待整理',
+};
+
+Page({
+  data: {
+    volumes: [],
+    recentKp: null,   // { chapterId, kpId, chapterTitle, kpTitle, chapterNum }
+    stats: { chapters: 0, kps: 0, diagrams: 0, exercises: 0 },
+    loading: true,
+  },
+  onLoad() {
+    this._buildData();
+  },
+  onShow() {
+    this._buildData();
+  },
+  _buildData() {
+    const { volumes, chapters } = app.globalData;
+
+    // Find most recently studied KP
+    let recentKp = null;
+    let latestTs = 0;
+    for (const vol of volumes) {
+      for (const ch of vol.chapters) {
+        const chData = chapters[ch.id];
+        if (!chData) continue;
+        for (const kp of chData.knowledgePoints) {
+          const prog = loadKpProgress(ch.id, kp.id);
+          if (prog.studied && (prog.lastStudied || 0) > latestTs) {
+            latestTs = prog.lastStudied || 0;
+            recentKp = {
+              chapterId: ch.id,
+              kpId: kp.id,
+              chapterNum: ch.number,
+              chapterTitle: ch.title,
+              kpTitle: kp.title,
+            };
+          }
+        }
+      }
+    }
+
+    const enriched = volumes.map(vol => ({
+      ...vol,
+      chapters: vol.chapters.map(ch => {
+        const chData = chapters[ch.id];
+        const prog = chData ? loadChapterProgress(chData) : { studiedCount: 0, totalCount: 0, pct: 0 };
+        return {
+          ...ch,
+          statusLabel: STATUS_LABEL[ch.status] || ch.status,
+          studiedCount: prog.studiedCount,
+          totalCount: prog.totalCount,
+          pct: prog.pct,
+          hasProgress: prog.studiedCount > 0,
+        };
+      }),
+    }));
+
+    const stats = Object.values(chapters).reduce((acc, ch) => {
+      const kps = ch.knowledgePoints || [];
+      acc.chapters += 1;
+      acc.kps += kps.length;
+      acc.diagrams += kps.reduce((sum, kp) => sum + ((kp.diagrams || []).length), 0);
+      acc.exercises += kps.reduce((sum, kp) => sum + ((kp.exercises || []).length), 0);
+      return acc;
+    }, { chapters: 0, kps: 0, diagrams: 0, exercises: 0 });
+
+    this.setData({ volumes: enriched, recentKp, stats, loading: false });
+  },
+  goToChapter(e) {
+    wx.navigateTo({ url: '/pages/chapter/chapter?chapterId=' + e.currentTarget.dataset.id });
+  },
+  continueStudy() {
+    const { recentKp } = this.data;
+    if (!recentKp) return;
+    wx.navigateTo({
+      url: '/pages/study/study?chapterId=' + recentKp.chapterId + '&kpId=' + recentKp.kpId,
+    });
+  },
+  goToSettings() {
+    wx.navigateTo({ url: '/pages/settings/settings' });
+  },
+  onShareAppMessage() {
+    return {
+      title: '数学分析学习助手 — 22章完整讲义 · AI批改练习',
+      path: '/pages/index/index',
+    };
+  },
+  onShareTimeline() {
+    return { title: '数学分析：AI辅助的大学数学学习小程序' };
+  },
+});
diff --git a/wx-miniprogram/pages/index/index.json b/wx-miniprogram/pages/index/index.json
new file mode 100644
index 0000000..a7d9239
--- /dev/null
+++ b/wx-miniprogram/pages/index/index.json
@@ -0,0 +1,4 @@
+{
+  "navigationBarTitleText": "数学分析",
+  "usingComponents": {}
+}
diff --git a/wx-miniprogram/pages/index/index.wxml b/wx-miniprogram/pages/index/index.wxml
new file mode 100644
index 0000000..21d1144
--- /dev/null
+++ b/wx-miniprogram/pages/index/index.wxml
@@ -0,0 +1,73 @@
+<view class="page">
+  <!-- Header -->
+  <view class="hero">
+    <view class="hero-top">
+      <view>
+        <text class="hero-eyebrow">大学数学</text>
+        <text class="hero-title">数学分析</text>
+        <text class="hero-subtitle">{{stats.chapters}} 章 · {{stats.kps}} 知识点 · {{stats.diagrams}} 图示 · {{stats.exercises}} 练习 · AI 批改</text>
+      </view>
+      <view class="settings-btn" bindtap="goToSettings">
+        <text class="settings-icon">⚙</text>
+      </view>
+    </view>
+  </view>
+
+  <view wx:if="{{loading}}" class="loading-wrap">
+    <text>加载中…</text>
+  </view>
+
+  <view wx:else>
+    <!-- Continue learning card -->
+    <view wx:if="{{recentKp}}" class="continue-card" bindtap="continueStudy">
+      <view class="continue-body">
+        <text class="continue-eyebrow">继续学习</text>
+        <text class="continue-kp-title">{{recentKp.kpTitle}}</text>
+        <text class="continue-ch-title">第 {{recentKp.chapterNum}} 章 · {{recentKp.chapterTitle}}</text>
+      </view>
+      <text class="continue-arrow">›</text>
+    </view>
+
+    <!-- First-visit hint (no progress yet) -->
+    <view wx:elif="{{!recentKp}}" class="start-hint">
+      <text class="start-hint-text">从第 1 章开始，系统掌握数学分析 →</text>
+    </view>
+
+    <view wx:for="{{volumes}}" wx:key="id" class="volume-section">
+      <text class="volume-title">{{item.title}}</text>
+
+      <view class="chapter-list">
+        <view
+          wx:for="{{item.chapters}}"
+          wx:for-item="ch"
+          wx:key="id"
+          class="chapter-row"
+          bindtap="goToChapter"
+          data-id="{{ch.id}}"
+        >
+          <view class="chapter-num-wrap">
+            <text class="chapter-num">{{ch.number}}</text>
+          </view>
+          <view class="chapter-info">
+            <text class="chapter-name">{{ch.title}}</text>
+            <view class="chapter-meta-row">
+              <text class="chapter-status {{ch.status}}">{{ch.statusLabel}}</text>
+              <view wx:if="{{ch.hasProgress}}" class="progress-tag">
+                <text>{{ch.studiedCount}}/{{ch.totalCount}} 节</text>
+              </view>
+            </view>
+            <!-- Progress bar -->
+            <view wx:if="{{ch.hasProgress}}" class="progress-bar-track">
+              <view class="progress-bar-fill {{ch.pct >= 100 ? 'complete' : ''}}" style="width:{{ch.pct}}%;" />
+            </view>
+          </view>
+          <text class="chapter-arrow">›</text>
+        </view>
+      </view>
+    </view>
+
+    <view class="footer-note">
+      <text>数学符号以 LaTeX 格式显示 · AI 采用 DeepSeek 模型</text>
+    </view>
+  </view>
+</view>
diff --git a/wx-miniprogram/pages/index/index.wxss b/wx-miniprogram/pages/index/index.wxss
new file mode 100644
index 0000000..d98bf13
--- /dev/null
+++ b/wx-miniprogram/pages/index/index.wxss
@@ -0,0 +1,187 @@
+.page { min-height: 100vh; background: var(--paper); padding-bottom: 60rpx; }
+
+/* Hero */
+.hero {
+  background: var(--paper-page);
+  border-bottom: 1rpx solid var(--rule);
+  padding: 52rpx 40rpx 44rpx;
+}
+.hero-top { display: flex; align-items: flex-start; justify-content: space-between; }
+.hero-eyebrow {
+  display: block;
+  font-size: 22rpx;
+  letter-spacing: 0.14em;
+  text-transform: uppercase;
+  color: var(--accent);
+  font-weight: 600;
+  margin-bottom: 8rpx;
+}
+.hero-title {
+  display: block;
+  font-size: 52rpx;
+  font-weight: 800;
+  color: var(--ink);
+  line-height: 1.2;
+  margin-bottom: 10rpx;
+  font-family: var(--serif);
+}
+.hero-subtitle { display: block; font-size: 24rpx; color: var(--ink-faint); }
+
+.settings-btn {
+  padding: 16rpx;
+  background: var(--paper);
+  border: 1rpx solid var(--rule);
+  border-radius: 50%;
+  width: 64rpx;
+  height: 64rpx;
+  display: flex;
+  align-items: center;
+  justify-content: center;
+  flex-shrink: 0;
+}
+.settings-icon { font-size: 32rpx; }
+
+/* Continue learning card */
+.continue-card {
+  display: flex;
+  align-items: center;
+  margin: 28rpx 36rpx 0;
+  padding: 28rpx 32rpx;
+  background: var(--paper-page);
+  border: 1rpx solid var(--rule);
+  border-left: 4rpx solid var(--accent);
+  border-radius: 0 var(--radius) var(--radius) 0;
+  gap: 16rpx;
+}
+.continue-body { flex: 1; min-width: 0; }
+.continue-eyebrow {
+  display: block;
+  font-size: 20rpx;
+  color: var(--accent);
+  font-weight: 700;
+  letter-spacing: 0.1em;
+  text-transform: uppercase;
+  margin-bottom: 6rpx;
+}
+.continue-kp-title {
+  display: block;
+  font-size: 30rpx;
+  font-weight: 700;
+  color: var(--ink);
+  margin-bottom: 4rpx;
+  overflow: hidden;
+  text-overflow: ellipsis;
+  white-space: nowrap;
+}
+.continue-ch-title {
+  display: block;
+  font-size: 22rpx;
+  color: var(--ink-faint);
+}
+.continue-arrow { font-size: 40rpx; color: var(--ink-faint); flex-shrink: 0; }
+
+/* First-visit hint */
+.start-hint {
+  margin: 20rpx 36rpx 0;
+  padding: 20rpx 28rpx;
+  background: var(--paper-page);
+  border: 1rpx solid var(--rule);
+  border-left: 3rpx solid var(--gold);
+  border-radius: 0 var(--radius) var(--radius) 0;
+}
+.start-hint-text {
+  font-size: 26rpx;
+  color: var(--gold);
+  font-weight: 600;
+}
+
+/* Volume */
+.volume-section { padding: 32rpx 40rpx 0; }
+.volume-title {
+  display: block;
+  font-size: 24rpx;
+  font-weight: 700;
+  color: var(--ink-soft);
+  letter-spacing: 0.06em;
+  padding-bottom: 16rpx;
+  border-bottom: 1rpx solid var(--rule);
+  margin-bottom: 8rpx;
+}
+
+/* Chapter list */
+.chapter-row {
+  display: flex;
+  align-items: center;
+  padding: 24rpx 0;
+  border-bottom: 1rpx solid var(--rule);
+  gap: 20rpx;
+}
+.chapter-row:last-child { border-bottom: none; }
+.chapter-num-wrap {
+  width: 60rpx;
+  height: 60rpx;
+  border-radius: 50%;
+  background: var(--accent-pale);
+  display: flex;
+  align-items: center;
+  justify-content: center;
+  flex-shrink: 0;
+}
+.chapter-num { font-size: 24rpx; font-weight: 700; color: var(--accent); }
+.chapter-info { flex: 1; min-width: 0; }
+.chapter-name {
+  display: block;
+  font-size: 30rpx;
+  font-weight: 600;
+  color: var(--ink);
+  margin-bottom: 8rpx;
+  line-height: 1.4;
+}
+.chapter-meta-row {
+  display: flex;
+  align-items: center;
+  gap: 12rpx;
+  margin-bottom: 8rpx;
+}
+.chapter-status {
+  font-size: 20rpx;
+  padding: 2rpx 12rpx;
+  border-radius: 20rpx;
+  font-weight: 600;
+}
+.chapter-status.sample-ready { background: #e8f5e9; color: #2e7d32; }
+.chapter-status.draft { background: #fff9c4; color: #f57f17; }
+.chapter-status.planned { background: #f3f3f3; color: #9e9e9e; }
+
+.progress-tag {
+  font-size: 20rpx;
+  color: var(--accent);
+  font-weight: 600;
+}
+
+/* Progress bar */
+.progress-bar-track {
+  height: 6rpx;
+  background: var(--rule);
+  border-radius: 3rpx;
+  overflow: hidden;
+}
+.progress-bar-fill {
+  height: 100%;
+  background: var(--accent);
+  border-radius: 3rpx;
+  transition: width 0.3s;
+}
+.progress-bar-fill.complete { background: #2e7d32; }
+
+.chapter-arrow { font-size: 40rpx; color: var(--ink-faint); flex-shrink: 0; }
+
+.footer-note {
+  margin: 56rpx 40rpx 0;
+  padding: 18rpx 24rpx;
+  background: var(--paper-page);
+  border-radius: var(--radius);
+  border: 1rpx solid var(--rule);
+  text-align: center;
+}
+.footer-note text { font-size: 22rpx; color: var(--ink-faint); }
diff --git a/wx-miniprogram/pages/onboarding/onboarding.js b/wx-miniprogram/pages/onboarding/onboarding.js
new file mode 100644
index 0000000..b6c0d55
--- /dev/null
+++ b/wx-miniprogram/pages/onboarding/onboarding.js
@@ -0,0 +1,40 @@
+Page({
+  data: {
+    current: 0,
+    slides: [
+      {
+        icon: '∫',
+        title: '数学分析',
+        subtitle: '大学本科·完整讲义',
+        body: '22章覆盖实数到曲面积分，93个知识点，214道练习，体系完整、层次清晰。',
+      },
+      {
+        icon: '✎',
+        title: '系统练习',
+        subtitle: '做题·批改·追踪',
+        body: '每节附例题与练习，AI 即时批改并给出详细评分，学习进度一目了然。',
+      },
+      {
+        icon: '≈',
+        title: 'AI 答疑',
+        subtitle: '苏格拉底式对话',
+        body: '遇到不懂的知识点？AI 助教不给答案，而是引导你自己推导出来——真正学会，不是背会。',
+      },
+    ],
+  },
+  onChange(e) {
+    this.setData({ current: e.detail.current });
+  },
+  next() {
+    const { current, slides } = this.data;
+    if (current < slides.length - 1) this.setData({ current: current + 1 });
+  },
+  start() {
+    wx.setStorageSync('ma_onboarded', true);
+    wx.redirectTo({ url: '/pages/index/index' });
+  },
+  skip() {
+    wx.setStorageSync('ma_onboarded', true);
+    wx.redirectTo({ url: '/pages/index/index' });
+  },
+});
diff --git a/wx-miniprogram/pages/onboarding/onboarding.json b/wx-miniprogram/pages/onboarding/onboarding.json
new file mode 100644
index 0000000..ed205e3
--- /dev/null
+++ b/wx-miniprogram/pages/onboarding/onboarding.json
@@ -0,0 +1,4 @@
+{
+  "navigationBarTitleText": "",
+  "navigationStyle": "custom"
+}
diff --git a/wx-miniprogram/pages/onboarding/onboarding.wxml b/wx-miniprogram/pages/onboarding/onboarding.wxml
new file mode 100644
index 0000000..86bdbdc
--- /dev/null
+++ b/wx-miniprogram/pages/onboarding/onboarding.wxml
@@ -0,0 +1,49 @@
+<view class="page">
+  <!-- Skip button -->
+  <view class="skip-btn" bindtap="skip">
+    <text class="skip-text">跳过</text>
+  </view>
+
+  <!-- Slides -->
+  <swiper
+    class="swiper"
+    indicator-dots="{{false}}"
+    autoplay="{{false}}"
+    duration="300"
+    current="{{current}}"
+    bindchange="onChange"
+  >
+    <swiper-item wx:for="{{slides}}" wx:key="title">
+      <view class="slide">
+        <view class="slide-icon-wrap">
+          <text class="slide-icon">{{item.icon}}</text>
+        </view>
+        <text class="slide-title">{{item.title}}</text>
+        <text class="slide-subtitle">{{item.subtitle}}</text>
+        <text class="slide-body">{{item.body}}</text>
+      </view>
+    </swiper-item>
+  </swiper>
+
+  <!-- Dots -->
+  <view class="dots">
+    <view
+      wx:for="{{slides}}"
+      wx:key="index"
+      class="dot {{index === current ? 'dot-active' : ''}}"
+    />
+  </view>
+
+  <!-- CTA -->
+  <view class="cta-area">
+    <view wx:if="{{current < slides.length - 1}}" class="cta-btn cta-next" bindtap="next">
+      <text>下一步 ›</text>
+    </view>
+    <view wx:else class="cta-btn cta-start" bindtap="start">
+      <text>开始学习</text>
+    </view>
+  </view>
+
+  <!-- Decoration rule -->
+  <view class="bottom-rule" />
+</view>
diff --git a/wx-miniprogram/pages/onboarding/onboarding.wxss b/wx-miniprogram/pages/onboarding/onboarding.wxss
new file mode 100644
index 0000000..bb58b77
--- /dev/null
+++ b/wx-miniprogram/pages/onboarding/onboarding.wxss
@@ -0,0 +1,130 @@
+.page {
+  min-height: 100vh;
+  background: var(--paper);
+  display: flex;
+  flex-direction: column;
+  position: relative;
+  overflow: hidden;
+}
+
+/* Skip */
+.skip-btn {
+  position: absolute;
+  top: 64rpx;
+  right: 40rpx;
+  z-index: 10;
+  padding: 12rpx 24rpx;
+}
+.skip-text { font-size: 26rpx; color: var(--ink-faint); }
+
+/* Swiper */
+.swiper { flex: 1; width: 100%; min-height: 70vh; }
+
+.slide {
+  display: flex;
+  flex-direction: column;
+  align-items: center;
+  justify-content: center;
+  padding: 100rpx 64rpx 60rpx;
+  height: 100%;
+  box-sizing: border-box;
+}
+
+.slide-icon-wrap {
+  width: 160rpx;
+  height: 160rpx;
+  border-radius: 50%;
+  background: var(--accent-pale);
+  border: 2rpx solid #f2d4cd;
+  display: flex;
+  align-items: center;
+  justify-content: center;
+  margin-bottom: 48rpx;
+}
+.slide-icon {
+  font-size: 72rpx;
+  color: var(--accent);
+  font-family: var(--serif);
+  font-weight: 900;
+  line-height: 1;
+}
+
+.slide-title {
+  display: block;
+  font-size: 52rpx;
+  font-weight: 800;
+  color: var(--ink);
+  font-family: var(--serif);
+  text-align: center;
+  margin-bottom: 12rpx;
+  line-height: 1.2;
+}
+.slide-subtitle {
+  display: block;
+  font-size: 26rpx;
+  font-weight: 600;
+  color: var(--accent);
+  text-align: center;
+  letter-spacing: 0.05em;
+  margin-bottom: 36rpx;
+}
+.slide-body {
+  display: block;
+  font-size: 28rpx;
+  color: var(--ink-soft);
+  text-align: center;
+  line-height: 1.9;
+  max-width: 540rpx;
+}
+
+/* Dots */
+.dots {
+  display: flex;
+  justify-content: center;
+  gap: 14rpx;
+  padding: 0 0 32rpx;
+}
+.dot {
+  width: 14rpx;
+  height: 14rpx;
+  border-radius: 50%;
+  background: var(--rule);
+  transition: all 0.3s;
+}
+.dot-active {
+  background: var(--accent);
+  width: 32rpx;
+  border-radius: 7rpx;
+}
+
+/* CTA */
+.cta-area {
+  padding: 0 64rpx calc(60rpx + env(safe-area-inset-bottom));
+}
+.cta-btn {
+  border-radius: 60rpx;
+  display: flex;
+  align-items: center;
+  justify-content: center;
+  padding: 32rpx 0;
+  font-size: 32rpx;
+  font-weight: 700;
+}
+.cta-next {
+  background: var(--paper-page);
+  border: 1.5rpx solid var(--rule);
+  color: var(--ink);
+}
+.cta-start {
+  background: var(--accent);
+  color: #fff;
+}
+
+.bottom-rule {
+  position: absolute;
+  bottom: 0;
+  left: 0;
+  right: 0;
+  height: 2rpx;
+  background: var(--rule);
+}
diff --git a/wx-miniprogram/pages/settings/settings.js b/wx-miniprogram/pages/settings/settings.js
new file mode 100644
index 0000000..c7a5f59
--- /dev/null
+++ b/wx-miniprogram/pages/settings/settings.js
@@ -0,0 +1,104 @@
+const { loadApiKeyOverride, saveApiKeyOverride, loadChapterProgress, loadExerciseAttempts, clearAllProgress } = require('../../utils/progress');
+const defaultConfig = require('../../config');
+
+Page({
+  data: {
+    apiKey: '',
+    hasOverride: false,
+    saved: false,
+    stats: null,  // { kpStudied, kpTotal, exAttempted, avgScore }
+  },
+  onLoad() {
+    const override = loadApiKeyOverride();
+    this.setData({
+      apiKey: override || '',
+      hasOverride: !!override,
+    });
+    this._computeStats();
+  },
+  _computeStats() {
+    const app = getApp();
+    const { volumes, chapters } = app.globalData;
+    if (!volumes || !volumes.length) return;
+    let kpStudied = 0, kpTotal = 0, exAttempted = 0, scoreSum = 0, scoreCount = 0;
+    for (const vol of volumes) {
+      for (const ch of vol.chapters) {
+        const chData = chapters[ch.id];
+        if (!chData) continue;
+        const prog = loadChapterProgress(chData);
+        kpStudied += prog.studiedCount;
+        kpTotal += prog.totalCount;
+        if (prog.avgScore != null) { scoreSum += prog.avgScore; scoreCount++; }
+        for (const kp of chData.knowledgePoints) {
+          for (const ex of kp.exercises) {
+            if (loadExerciseAttempts(ex.id).length > 0) exAttempted++;
+          }
+        }
+      }
+    }
+    this.setData({
+      stats: {
+        kpStudied,
+        kpTotal,
+        exAttempted,
+        avgScore: scoreCount > 0 ? Math.round(scoreSum / scoreCount) : null,
+      },
+    });
+  },
+  onKeyInput(e) {
+    this.setData({ apiKey: e.detail.value, saved: false });
+  },
+  saveKey() {
+    const { apiKey } = this.data;
+    const trimmed = apiKey.trim();
+    saveApiKeyOverride(trimmed || null);
+    this.setData({
+      apiKey: trimmed,
+      hasOverride: !!trimmed,
+      saved: true,
+    });
+    wx.showToast({ title: trimmed ? '已保存' : '已重置为默认', icon: 'success', duration: 1500 });
+  },
+  resetKey() {
+    wx.showModal({
+      title: '重置 API Key',
+      content: '清除自定义 Key，使用内置默认 Key？',
+      success: (res) => {
+        if (!res.confirm) return;
+        saveApiKeyOverride(null);
+        this.setData({ apiKey: '', hasOverride: false, saved: false });
+        wx.showToast({ title: '已重置', icon: 'success', duration: 1500 });
+      },
+    });
+  },
+  resetProgress() {
+    wx.showModal({
+      title: '清空学习记录',
+      content: '将清除所有已学进度、练习记录和聊天记录（不影响 API Key）。此操作不可撤销。',
+      confirmText: '清空',
+      confirmColor: '#c62828',
+      success: (res) => {
+        if (!res.confirm) return;
+        clearAllProgress();
+        this.setData({ stats: null });
+        wx.showToast({ title: '已清空', icon: 'success', duration: 2000 });
+      },
+    });
+  },
+  maskKey(key) {
+    if (!key || key.length < 8) return key;
+    return key.slice(0, 5) + '·'.repeat(8) + key.slice(-4);
+  },
+  shareApp() {
+    wx.showShareMenu({ withShareTicket: false, menus: ['shareAppMessage', 'shareTimeline'] });
+  },
+  onShareAppMessage() {
+    return {
+      title: '数学分析学习助手 — 22章完整讲义 · AI批改练习',
+      path: '/pages/index/index',
+    };
+  },
+  onShareTimeline() {
+    return { title: '数学分析：AI辅助的大学数学学习小程序' };
+  },
+});
diff --git a/wx-miniprogram/pages/settings/settings.json b/wx-miniprogram/pages/settings/settings.json
new file mode 100644
index 0000000..ecfa0f3
--- /dev/null
+++ b/wx-miniprogram/pages/settings/settings.json
@@ -0,0 +1,4 @@
+{
+  "navigationBarTitleText": "设置",
+  "usingComponents": {}
+}
diff --git a/wx-miniprogram/pages/settings/settings.wxml b/wx-miniprogram/pages/settings/settings.wxml
new file mode 100644
index 0000000..9f57e68
--- /dev/null
+++ b/wx-miniprogram/pages/settings/settings.wxml
@@ -0,0 +1,109 @@
+<view class="page">
+
+  <!-- Learning stats -->
+  <view wx:if="{{stats && stats.kpStudied > 0}}" class="section">
+    <text class="section-title">学习统计</text>
+    <view class="stats-grid">
+      <view class="stat-cell">
+        <text class="stat-val">{{stats.kpStudied}}</text>
+        <text class="stat-lbl">已学知识点</text>
+      </view>
+      <view class="stat-cell">
+        <text class="stat-val">{{stats.exAttempted}}</text>
+        <text class="stat-lbl">已做练习</text>
+      </view>
+      <view class="stat-cell">
+        <text class="stat-val">{{stats.avgScore != null ? stats.avgScore : '--'}}</text>
+        <text class="stat-lbl">平均得分</text>
+      </view>
+      <view class="stat-cell">
+        <text class="stat-val">{{stats.kpTotal > 0 ? (stats.kpStudied * 100 / stats.kpTotal) | 0 : 0}}%</text>
+        <text class="stat-lbl">完成进度</text>
+      </view>
+    </view>
+  </view>
+
+  <view class="section">
+    <text class="section-title">AI 设置</text>
+
+    <view class="card">
+      <text class="field-label">DeepSeek API Key</text>
+      <text class="field-desc">
+        默认使用内置 Key（供学生免费使用）。如有自己的 Key 可在此替换，优先级更高。
+      </text>
+      <input
+        class="key-input"
+        placeholder="sk-xxxxxxxxxxxxxxxx（留空使用默认）"
+        value="{{apiKey}}"
+        bindinput="onKeyInput"
+        password="{{false}}"
+        maxlength="80"
+        confirm-type="done"
+      />
+      <view class="field-status" wx:if="{{hasOverride}}">
+        <text class="status-dot active" />
+        <text class="status-text">使用自定义 Key</text>
+      </view>
+      <view class="field-status" wx:else>
+        <text class="status-dot default" />
+        <text class="status-text">使用内置默认 Key</text>
+      </view>
+
+      <view class="btn-row">
+        <button class="btn btn-primary" bindtap="saveKey">保存</button>
+        <button class="btn btn-ghost" bindtap="resetKey" wx:if="{{hasOverride}}">重置默认</button>
+      </view>
+    </view>
+  </view>
+
+  <view class="section">
+    <text class="section-title">关于</text>
+    <view class="card about-card">
+      <view class="about-row">
+        <text class="about-key">版本</text>
+        <text class="about-val">1.1.0</text>
+      </view>
+      <view class="about-row">
+        <text class="about-key">AI 模型</text>
+        <text class="about-val">DeepSeek Chat</text>
+      </view>
+      <view class="about-row">
+        <text class="about-key">内容</text>
+        <text class="about-val">数学分析 22 章 · 93 知识点 · 214 练习</text>
+      </view>
+      <view class="about-row">
+        <text class="about-key">数学渲染</text>
+        <text class="about-val">LaTeX 符号格式显示</text>
+      </view>
+    </view>
+  </view>
+
+  <view class="section">
+    <text class="section-title">数据管理</text>
+    <view class="card">
+      <text class="field-desc">清空所有已学进度、练习评分记录、AI 聊天记录（API Key 不受影响）。</text>
+      <button class="btn btn-ghost danger-btn" bindtap="resetProgress">清空学习记录</button>
+    </view>
+  </view>
+
+  <view class="section">
+    <text class="section-title">分享</text>
+    <view class="card">
+      <button class="btn btn-ghost share-btn" open-type="share">
+        <text>分享给同学</text>
+      </button>
+    </view>
+  </view>
+
+  <view class="section">
+    <text class="section-title">域名配置说明</text>
+    <view class="card tips-card">
+      <text class="tip-text">
+        如遇「不在以下 request 合法域名列表」错误，需在微信公众平台 → 开发管理 → 服务器域名 → request 合法域名中添加：
+      </text>
+      <text class="domain-chip">https://api.deepseek.com</text>
+      <text class="tip-text">开发模式可在微信开发者工具中勾选「不校验合法域名」临时跳过。</text>
+    </view>
+  </view>
+
+</view>
diff --git a/wx-miniprogram/pages/settings/settings.wxss b/wx-miniprogram/pages/settings/settings.wxss
new file mode 100644
index 0000000..d2afc70
--- /dev/null
+++ b/wx-miniprogram/pages/settings/settings.wxss
@@ -0,0 +1,132 @@
+.page { background: var(--paper); min-height: 100vh; padding: 32rpx 36rpx 80rpx; }
+
+.section { margin-bottom: 40rpx; }
+.section-title {
+  display: block;
+  font-size: 24rpx;
+  font-weight: 700;
+  letter-spacing: 0.1em;
+  text-transform: uppercase;
+  color: var(--ink-faint);
+  margin-bottom: 16rpx;
+}
+
+/* Stats grid */
+.stats-grid {
+  display: grid;
+  grid-template-columns: 1fr 1fr;
+  gap: 16rpx;
+}
+.stat-cell {
+  background: var(--paper-page);
+  border: 1rpx solid var(--rule);
+  border-radius: var(--radius);
+  padding: 28rpx 24rpx;
+  text-align: center;
+}
+.stat-val {
+  display: block;
+  font-size: 52rpx;
+  font-weight: 900;
+  color: var(--accent);
+  line-height: 1.1;
+  margin-bottom: 8rpx;
+  font-family: var(--serif);
+}
+.stat-lbl {
+  display: block;
+  font-size: 22rpx;
+  color: var(--ink-faint);
+  font-weight: 500;
+}
+
+.card {
+  background: var(--paper-page);
+  border: 1rpx solid var(--rule);
+  border-radius: var(--radius);
+  padding: 28rpx 32rpx;
+}
+
+.field-label {
+  display: block;
+  font-size: 28rpx;
+  font-weight: 700;
+  color: var(--ink);
+  margin-bottom: 10rpx;
+}
+.field-desc {
+  display: block;
+  font-size: 24rpx;
+  color: var(--ink-faint);
+  line-height: 1.6;
+  margin-bottom: 20rpx;
+}
+.key-input {
+  width: 100%;
+  padding: 20rpx 24rpx;
+  background: var(--paper);
+  border: 1.5rpx solid var(--rule);
+  border-radius: var(--radius);
+  font-size: 26rpx;
+  color: var(--ink);
+  font-family: var(--mono);
+  box-sizing: border-box;
+  margin-bottom: 16rpx;
+}
+.field-status {
+  display: flex;
+  align-items: center;
+  gap: 10rpx;
+  margin-bottom: 20rpx;
+}
+.status-dot {
+  width: 14rpx;
+  height: 14rpx;
+  border-radius: 50%;
+  flex-shrink: 0;
+}
+.status-dot.active { background: #2e7d32; }
+.status-dot.default { background: var(--ink-faint); }
+.status-text { font-size: 24rpx; color: var(--ink-faint); }
+
+.btn-row { display: flex; gap: 16rpx; }
+.btn-row .btn { flex: 1; }
+
+/* Danger */
+.danger-btn { width: 100%; font-size: 28rpx; color: #c62828; border-color: #ffc9c9; }
+
+/* Share */
+.share-btn { width: 100%; font-size: 28rpx; }
+
+/* About */
+.about-row {
+  display: flex;
+  justify-content: space-between;
+  padding: 16rpx 0;
+  border-bottom: 1rpx solid var(--rule);
+  align-items: flex-start;
+  gap: 20rpx;
+}
+.about-row:last-child { border-bottom: none; }
+.about-key { font-size: 26rpx; color: var(--ink-faint); flex-shrink: 0; }
+.about-val { font-size: 26rpx; color: var(--ink); font-weight: 500; text-align: right; flex: 1; }
+
+/* Tips */
+.tips-card {}
+.tip-text {
+  display: block;
+  font-size: 24rpx;
+  color: var(--ink-faint);
+  line-height: 1.7;
+  margin-bottom: 12rpx;
+}
+.domain-chip {
+  display: inline-block;
+  font-family: var(--mono);
+  font-size: 24rpx;
+  color: var(--accent);
+  background: var(--accent-pale);
+  padding: 6rpx 16rpx;
+  border-radius: 8rpx;
+  margin-bottom: 16rpx;
+}
diff --git a/wx-miniprogram/pages/study/study.js b/wx-miniprogram/pages/study/study.js
new file mode 100644
index 0000000..f7d3e18
--- /dev/null
+++ b/wx-miniprogram/pages/study/study.js
@@ -0,0 +1,243 @@
+const app = getApp();
+const { gradeRequest } = require('../../utils/api');
+const {
+  markKpStudied,
+  saveExerciseAttempt,
+  getBestScore,
+  loadKpProgress,
+} = require('../../utils/progress');
+
+Page({
+  data: {
+    chapter: null,
+    kp: null,
+    chapterId: '',
+    kpId: '',
+    kpIndex: 0,
+    totalKps: 0,
+    // Progress
+    kpProgress: {},
+    // Collapsibles
+    showSocratic: false,
+    showMistakes: false,
+    // Tabs
+    activeTab: 'learn', // 'learn' | 'exercise'
+    // Exercise list — enriched with best score
+    exercisesWithScore: [],
+    exFilter: 'all', // 'all' | 'basic' | 'medium' | 'advanced' | 'todo'
+    filteredExercises: [],
+    // Exercise workspace
+    selectedExIndex: -1,
+    selectedEx: null,
+    answer: '',
+    hintLevel: 0,
+    gradingStatus: 'idle', // 'idle' | 'submitting' | 'success' | 'error'
+    gradingError: '',
+    gradeResult: null,
+    showRubric: false,
+  },
+
+  onLoad(options) {
+    const { chapterId, kpId } = options;
+    this._load(chapterId, kpId);
+  },
+
+  _normalizeKp(kp) {
+    return {
+      ...kp,
+      diagrams: Array.isArray(kp.diagrams) ? kp.diagrams : [],
+      exercises: Array.isArray(kp.exercises) ? kp.exercises : [],
+      learningGoals: Array.isArray(kp.learningGoals) ? kp.learningGoals : [],
+      socraticQuestions: Array.isArray(kp.socraticQuestions) ? kp.socraticQuestions : [],
+      commonMistakes: Array.isArray(kp.commonMistakes) ? kp.commonMistakes : [],
+    };
+  },
+
+  _load(chapterId, kpId) {
+    const rawChapter = app.globalData.chapters[chapterId];
+    const chapter = rawChapter
+      ? { ...rawChapter, knowledgePoints: rawChapter.knowledgePoints.map(kp => this._normalizeKp(kp)) }
+      : null;
+    if (!chapter) { wx.showToast({ title: '章节不存在', icon: 'error' }); return; }
+    const kpIndex = chapter.knowledgePoints.findIndex(k => k.id === kpId);
+    if (kpIndex < 0) { wx.showToast({ title: '知识点不存在', icon: 'error' }); return; }
+    const kp = chapter.knowledgePoints[kpIndex];
+    wx.setNavigationBarTitle({ title: kp.title });
+
+    // Mark as studied
+    markKpStudied(chapterId, kpId);
+    const kpProgress = loadKpProgress(chapterId, kpId);
+
+    // Enrich exercises with best score
+    const exercisesWithScore = kp.exercises.map(ex => ({
+      ...ex,
+      bestScore: getBestScore(ex.id),
+      diffLabel: ex.difficulty === 'basic' ? '基础' : ex.difficulty === 'medium' ? '中档' : '提升',
+    }));
+
+    this.setData({
+      chapter,
+      kp,
+      chapterId,
+      kpId,
+      kpIndex,
+      totalKps: chapter.knowledgePoints.length,
+      kpProgress,
+      exercisesWithScore,
+      filteredExercises: exercisesWithScore,
+      exFilter: 'all',
+      showSocratic: false,
+      showMistakes: false,
+      activeTab: 'learn',
+      selectedExIndex: -1,
+      selectedEx: null,
+      answer: '',
+      hintLevel: 0,
+      gradingStatus: 'idle',
+      gradingError: '',
+      gradeResult: null,
+      showRubric: false,
+    });
+  },
+
+  // ── Tab ──────────────────────────────────────────────────────
+  switchTab(e) {
+    this.setData({ activeTab: e.currentTarget.dataset.tab });
+  },
+
+  // ── Collapsibles ─────────────────────────────────────────────
+  toggleSocratic() { this.setData({ showSocratic: !this.data.showSocratic }); },
+  toggleMistakes() { this.setData({ showMistakes: !this.data.showMistakes }); },
+
+  // ── KP Navigation ────────────────────────────────────────────
+  goPrevKp() {
+    const { chapter, kpIndex } = this.data;
+    if (kpIndex <= 0) return;
+    wx.vibrateShort({ type: 'light' });
+    const prev = chapter.knowledgePoints[kpIndex - 1];
+    this._load(chapter.id, prev.id);
+    wx.pageScrollTo({ scrollTop: 0, duration: 150 });
+  },
+  goNextKp() {
+    const { chapter, kpIndex, totalKps } = this.data;
+    if (kpIndex >= totalKps - 1) {
+      // Reached end of chapter — show completion message
+      wx.vibrateShort({ type: 'medium' });
+      wx.showModal({
+        title: '🎉 本章学完了！',
+        content: '你已学完「' + chapter.title + '」的全部 ' + totalKps + ' 个知识点。继续下一章？',
+        confirmText: '返回目录',
+        cancelText: '继续复习',
+        success: (res) => {
+          if (res.confirm) wx.navigateBack();
+        },
+      });
+      return;
+    }
+    wx.vibrateShort({ type: 'light' });
+    const next = chapter.knowledgePoints[kpIndex + 1];
+    this._load(chapter.id, next.id);
+    wx.pageScrollTo({ scrollTop: 0, duration: 150 });
+  },
+
+  // ── Exercise filter ──────────────────────────────────────────
+  setExFilter(e) {
+    const filter = e.currentTarget.dataset.filter;
+    const { exercisesWithScore } = this.data;
+    let filtered;
+    if (filter === 'all') {
+      filtered = exercisesWithScore;
+    } else if (filter === 'todo') {
+      filtered = exercisesWithScore.filter(ex => ex.bestScore == null);
+    } else {
+      filtered = exercisesWithScore.filter(ex => ex.difficulty === filter);
+    }
+    this.setData({ exFilter: filter, filteredExercises: filtered });
+  },
+
+  // ── Exercises ────────────────────────────────────────────────
+  selectExercise(e) {
+    const id = e.currentTarget.dataset.id;
+    const index = this.data.kp.exercises.findIndex(ex => ex.id === id);
+    const ex = this.data.kp.exercises[index];
+    if (!ex || index < 0) return;
+    this.setData({
+      selectedExIndex: index,
+      selectedEx: ex,
+      answer: '',
+      hintLevel: 0,
+      gradingStatus: 'idle',
+      gradingError: '',
+      gradeResult: null,
+      showRubric: false,
+    });
+    wx.pageScrollTo({ scrollTop: 0, duration: 150 });
+  },
+  backToList() {
+    this.setData({ selectedExIndex: -1, selectedEx: null });
+    wx.pageScrollTo({ scrollTop: 0, duration: 150 });
+  },
+  onAnswerInput(e) {
+    this.setData({ answer: e.detail.value });
+  },
+  getHint() {
+    const { selectedEx, hintLevel } = this.data;
+    if (!selectedEx || hintLevel >= selectedEx.hints.length) return;
+    wx.vibrateShort({ type: 'light' });
+    this.setData({ hintLevel: hintLevel + 1 });
+  },
+  toggleRubric() {
+    this.setData({ showRubric: !this.data.showRubric });
+  },
+  submitForGrading() {
+    const { selectedEx, answer, chapterId, kpId } = this.data;
+    if (!selectedEx) return;
+    if (!answer.trim()) {
+      wx.showToast({ title: '请先写下解答', icon: 'none', duration: 1500 });
+      return;
+    }
+    this.setData({ gradingStatus: 'submitting', gradingError: '', gradeResult: null });
+
+    gradeRequest(selectedEx, answer, {
+      onSuccess: (result) => {
+        saveExerciseAttempt(chapterId, kpId, selectedEx.id, result);
+        // Refresh exercise list scores
+        const exercisesWithScore = this.data.kp.exercises.map(ex => ({
+          ...ex,
+          bestScore: getBestScore(ex.id),
+          diffLabel: ex.difficulty === 'basic' ? '基础' : ex.difficulty === 'medium' ? '中档' : '提升',
+        }));
+        // Re-apply current filter
+        const { exFilter } = this.data;
+        const filteredExercises = exFilter === 'all' ? exercisesWithScore
+          : exFilter === 'todo' ? exercisesWithScore.filter(ex => ex.bestScore == null)
+          : exercisesWithScore.filter(ex => ex.difficulty === exFilter);
+        const VERDICT_TITLES = {
+          excellent: '非常棒！',
+          good: '做得不错',
+          partial: '部分正确',
+          incorrect: '还需改进',
+        };
+        const enriched = { ...result, verdictTitle: VERDICT_TITLES[result.verdict] || '批改完成' };
+        wx.vibrateShort({ type: 'medium' });
+        this.setData({
+          gradeResult: enriched,
+          gradingStatus: 'success',
+          exercisesWithScore,
+          filteredExercises,
+        });
+        wx.pageScrollTo({ selector: '#grade-result', duration: 300 });
+      },
+      onError: (msg) => {
+        this.setData({ gradingStatus: 'error', gradingError: 'AI 批改暂时不可用：' + msg });
+      },
+    });
+  },
+
+  // ── Chat ─────────────────────────────────────────────────────
+  goToChat() {
+    const { chapter, kp } = this.data;
+    if (!chapter || !kp) return;
+    wx.navigateTo({ url: '/pages/chat/chat?chapterId=' + chapter.id + '&kpId=' + kp.id });
+  },
+});
diff --git a/wx-miniprogram/pages/study/study.json b/wx-miniprogram/pages/study/study.json
new file mode 100644
index 0000000..9af6900
--- /dev/null
+++ b/wx-miniprogram/pages/study/study.json
@@ -0,0 +1,7 @@
+{
+  "navigationBarTitleText": "知识点",
+  "usingComponents": {
+    "diagram-card": "/components/diagram-card/diagram-card",
+    "math-text": "/components/math-text/math-text"
+  }
+}
diff --git a/wx-miniprogram/pages/study/study.wxml b/wx-miniprogram/pages/study/study.wxml
new file mode 100644
index 0000000..fac956c
--- /dev/null
+++ b/wx-miniprogram/pages/study/study.wxml
@@ -0,0 +1,279 @@
+<view class="page" wx:if="{{kp}}">
+
+  <!-- KP navigation bar -->
+  <view class="kp-nav-bar">
+    <view
+      class="kp-nav-btn {{kpIndex <= 0 ? 'is-disabled' : ''}}"
+      bindtap="goPrevKp"
+    >‹ 上一节</view>
+    <view class="kp-nav-center">
+      <text class="kp-nav-pos">第 {{kpIndex + 1}} / {{totalKps}} 节</text>
+      <view class="kp-nav-badges">
+        <text wx:if="{{kp.diagrams.length}}" class="kp-badge kp-badge-diagram">{{kp.diagrams.length}} 图</text>
+        <text wx:if="{{kp.exercises.length}}" class="kp-badge kp-badge-ex">{{kp.exercises.length}} 题</text>
+        <text wx:if="{{kpProgress.bestExScore != null}}" class="kp-badge kp-badge-score {{kpProgress.bestExScore >= 80 ? 'good' : 'ok'}}">
+          {{kpProgress.bestExScore}} 分
+        </text>
+      </view>
+    </view>
+    <view
+      class="kp-nav-btn {{kpIndex >= totalKps - 1 ? 'is-disabled' : ''}}"
+      bindtap="goNextKp"
+    >下一节 ›</view>
+  </view>
+
+  <!-- Tab bar -->
+  <view class="tab-bar">
+    <view class="tab-item {{activeTab === 'learn' ? 'is-active' : ''}}" bindtap="switchTab" data-tab="learn">
+      讲义
+    </view>
+    <view class="tab-item {{activeTab === 'exercise' ? 'is-active' : ''}}" bindtap="switchTab" data-tab="exercise">
+      练习（{{kp.exercises.length}}）
+    </view>
+  </view>
+
+  <!-- ===== LEARN TAB ===== -->
+  <view wx:if="{{activeTab === 'learn'}}" class="tab-content">
+
+    <!-- Breadcrumb -->
+    <view class="breadcrumb">
+      <text class="breadcrumb-ch">第 {{chapter.number}} 章 {{chapter.title}}</text>
+      <text class="breadcrumb-sep">›</text>
+      <text class="breadcrumb-kp">{{kp.title}}</text>
+    </view>
+
+    <!-- Learning goals -->
+    <view class="goals-card" wx:if="{{kp.learningGoals.length}}">
+      <text class="goals-label">本节你将掌握</text>
+      <view wx:for="{{kp.learningGoals}}" wx:key="*this" class="goal-item">
+        <text class="goal-dot">·</text>
+        <math-text text="{{item}}" size="small" />
+      </view>
+    </view>
+
+    <!-- Core explanation -->
+    <view class="explanation-block">
+      <math-text text="{{kp.coreExplanation}}" size="normal" />
+    </view>
+
+    <!-- Teaching diagrams -->
+    <view class="diagram-section" wx:if="{{kp.diagrams.length}}">
+      <view class="section-header-row">
+        <text class="section-title">教学图示</text>
+        <text class="section-hint">{{kp.diagrams.length}} 张</text>
+      </view>
+      <diagram-card
+        wx:for="{{kp.diagrams}}"
+        wx:key="id"
+        diagram="{{item}}"
+      />
+    </view>
+
+    <!-- Socratic questions -->
+    <view class="collapsible" wx:if="{{kp.socraticQuestions.length}}">
+      <view class="collapsible-header" bindtap="toggleSocratic">
+        <text class="collapsible-title">思考题 · 检验理解</text>
+        <text class="collapsible-icon">{{showSocratic ? '▲' : '▼'}}</text>
+      </view>
+      <view class="collapsible-body" wx:if="{{showSocratic}}">
+        <view wx:for="{{kp.socraticQuestions}}" wx:key="*this" class="q-item">
+          <text class="q-num">{{index + 1}}.</text>
+          <math-text text="{{item}}" size="small" />
+        </view>
+      </view>
+    </view>
+
+    <!-- Common mistakes -->
+    <view class="collapsible" wx:if="{{kp.commonMistakes.length}}">
+      <view class="collapsible-header" bindtap="toggleMistakes">
+        <text class="collapsible-title">易错提醒</text>
+        <text class="collapsible-icon">{{showMistakes ? '▲' : '▼'}}</text>
+      </view>
+      <view class="collapsible-body" wx:if="{{showMistakes}}">
+        <view wx:for="{{kp.commonMistakes}}" wx:key="*this" class="mistake-item">
+          <text class="mistake-icon">✕</text>
+          <math-text text="{{item}}" size="small" />
+        </view>
+      </view>
+    </view>
+
+    <!-- Divider -->
+    <view class="section-divider" />
+
+    <!-- AI chat CTA -->
+    <view class="chat-cta" bindtap="goToChat">
+      <text class="chat-cta-icon">💬</text>
+      <view class="chat-cta-body">
+        <text class="chat-cta-title">和 AI 老师讨论这个知识点</text>
+        <text class="chat-cta-sub">苏格拉底式追问，真正弄懂</text>
+      </view>
+      <text class="chat-cta-arrow">›</text>
+    </view>
+
+    <!-- Jump to exercises -->
+    <view wx:if="{{kp.exercises.length}}" class="jump-exercises" bindtap="switchTab" data-tab="exercise">
+      <text>去做 {{kp.exercises.length}} 道练习题 →</text>
+    </view>
+
+    <!-- Next KP button -->
+    <view class="next-kp-row">
+      <view
+        class="next-kp-btn {{kpIndex >= totalKps - 1 ? 'is-last' : ''}}"
+        bindtap="goNextKp"
+      >
+        <text wx:if="{{kpIndex < totalKps - 1}}">下一节：{{chapter.knowledgePoints[kpIndex + 1].title}} ›</text>
+        <text wx:else>✓ 本章已学完</text>
+      </view>
+    </view>
+
+  </view>
+
+  <!-- ===== EXERCISE TAB ===== -->
+  <view wx:elif="{{activeTab === 'exercise'}}" class="tab-content">
+
+    <!-- Empty state -->
+    <view wx:if="{{!kp.exercises.length}}" class="empty-state">
+      <text>本知识点暂无练习题</text>
+    </view>
+
+    <!-- Exercise list -->
+    <view wx:elif="{{selectedExIndex < 0}}" class="ex-list">
+
+      <!-- Filter chips (only shown when 5+ exercises) -->
+      <view wx:if="{{kp.exercises.length >= 5}}" class="ex-filter-row">
+        <view class="ex-filter-chip {{exFilter === 'all' ? 'active' : ''}}" bindtap="setExFilter" data-filter="all">全部</view>
+        <view class="ex-filter-chip {{exFilter === 'basic' ? 'active' : ''}}" bindtap="setExFilter" data-filter="basic">基础</view>
+        <view class="ex-filter-chip {{exFilter === 'medium' ? 'active' : ''}}" bindtap="setExFilter" data-filter="medium">中档</view>
+        <view class="ex-filter-chip {{exFilter === 'advanced' ? 'active' : ''}}" bindtap="setExFilter" data-filter="advanced">提升</view>
+        <view class="ex-filter-chip {{exFilter === 'todo' ? 'active' : ''}}" bindtap="setExFilter" data-filter="todo">待做</view>
+      </view>
+
+      <view wx:if="{{filteredExercises.length === 0}}" class="filter-empty">
+        <text>没有符合筛选条件的练习</text>
+      </view>
+
+      <view
+        wx:for="{{filteredExercises}}"
+        wx:key="id"
+        class="ex-card"
+        bindtap="selectExercise"
+        data-index="{{index}}"
+        data-id="{{item.id}}"
+      >
+        <view class="ex-card-left">
+          <text class="ex-card-num">{{index + 1}}</text>
+        </view>
+        <view class="ex-card-body">
+          <text class="ex-card-title">{{item.title || ('第 ' + (index + 1) + ' 题')}}</text>
+          <view class="ex-card-tags">
+            <text class="difficulty-pill {{item.difficulty}}">{{item.diffLabel}}</text>
+            <text wx:if="{{item.bestScore != null}}" class="score-badge {{item.bestScore >= 80 ? 'good' : item.bestScore >= 60 ? 'ok' : 'low'}}">
+              最高 {{item.bestScore}} 分
+            </text>
+          </view>
+        </view>
+        <text class="ex-card-arrow">›</text>
+      </view>
+    </view>
+
+    <!-- Exercise workspace -->
+    <view wx:else class="ex-workspace">
+      <view class="back-row" bindtap="backToList">
+        <text class="back-arrow">‹</text>
+        <text class="back-label">返回题目列表</text>
+      </view>
+
+      <text class="ex-num-label">第 {{selectedExIndex + 1}} 题 · 共 {{kp.exercises.length}} 题</text>
+
+      <!-- Problem -->
+      <view class="problem-card">
+        <text wx:if="{{selectedEx.title}}" class="problem-title">{{selectedEx.title}}</text>
+        <math-text text="{{selectedEx.prompt}}" size="normal" />
+      </view>
+
+      <!-- Answer -->
+      <text class="answer-label">解答</text>
+      <textarea
+        class="answer-input"
+        placeholder="在这里写思路、计算或证明步骤…"
+        value="{{answer}}"
+        bindinput="onAnswerInput"
+        auto-height
+        maxlength="3000"
+        adjust-position
+      />
+
+      <!-- Actions row 1 -->
+      <view class="action-row">
+        <button
+          class="btn btn-ghost hint-btn"
+          bindtap="getHint"
+          disabled="{{hintLevel >= selectedEx.hints.length}}"
+        >
+          <text wx:if="{{hintLevel === 0}}">获取提示</text>
+          <text wx:elif="{{hintLevel < selectedEx.hints.length}}">再来一个提示（{{hintLevel}}/{{selectedEx.hints.length}}）</text>
+          <text wx:else>已显示全部提示</text>
+        </button>
+        <button
+          class="btn btn-primary grade-btn"
+          bindtap="submitForGrading"
+          disabled="{{gradingStatus === 'submitting'}}"
+        >{{gradingStatus === 'submitting' ? '批改中…' : '提交 AI 批改'}}</button>
+      </view>
+
+      <!-- Actions row 2 -->
+      <view class="action-row">
+        <button class="btn btn-ghost" bindtap="toggleRubric">{{showRubric ? '收起评分要点' : '对照评分要点'}}</button>
+        <button class="btn btn-ghost" bindtap="goToChat">问 AI 老师</button>
+      </view>
+
+      <!-- Error -->
+      <view wx:if="{{gradingError}}" class="grade-error"><text>{{gradingError}}</text></view>
+
+      <!-- Grade result -->
+      <view wx:if="{{gradeResult}}" id="grade-result" class="grade-result {{gradeResult.verdict}}">
+        <view class="grade-result-head">
+          <view>
+            <text class="grade-result-label">AI 批改结果</text>
+            <text class="grade-verdict-title">{{gradeResult.verdictTitle}}</text>
+          </view>
+          <view class="grade-score-wrap">
+            <text class="grade-score">{{gradeResult.score}}</text>
+            <text class="grade-score-unit">分</text>
+          </view>
+        </view>
+        <math-text text="{{gradeResult.feedback}}" size="normal" />
+        <view wx:if="{{gradeResult.missingPoints && gradeResult.missingPoints.length}}" class="missing-points">
+          <text class="missing-label">还缺这些要点：</text>
+          <view wx:for="{{gradeResult.missingPoints}}" wx:key="*this" class="missing-item">
+            <text class="missing-bullet">·</text>
+            <math-text text="{{item}}" size="small" />
+          </view>
+        </view>
+      </view>
+
+      <!-- Hints -->
+      <view wx:if="{{hintLevel > 0}}" class="hint-list">
+        <text class="hint-list-label">提示</text>
+        <view wx:for="{{selectedEx.hints}}" wx:key="*this">
+          <view wx:if="{{index < hintLevel}}" class="hint-item">
+            <text class="hint-num">提示 {{index + 1}}：</text>
+            <math-text text="{{item}}" size="small" />
+          </view>
+        </view>
+      </view>
+
+      <!-- Rubric -->
+      <view wx:if="{{showRubric}}" class="rubric-block">
+        <text class="rubric-label">评分要点</text>
+        <view wx:for="{{selectedEx.gradingRubric}}" wx:key="*this" class="rubric-item">
+          <text class="rubric-bullet">✓</text>
+          <math-text text="{{item}}" size="small" />
+        </view>
+      </view>
+    </view>
+
+  </view>
+</view>
+
+<view wx:else class="loading-wrap"><text>加载中…</text></view>
diff --git a/wx-miniprogram/pages/study/study.wxss b/wx-miniprogram/pages/study/study.wxss
new file mode 100644
index 0000000..3f3fa22
--- /dev/null
+++ b/wx-miniprogram/pages/study/study.wxss
@@ -0,0 +1,425 @@
+.page { background: var(--paper); min-height: 100vh; padding-bottom: 80rpx; }
+
+/* KP navigation bar */
+.kp-nav-bar {
+  display: flex;
+  align-items: center;
+  justify-content: space-between;
+  padding: 12rpx 32rpx;
+  min-height: 80rpx;
+  background: var(--paper-page);
+  border-bottom: 1rpx solid var(--rule);
+}
+.kp-nav-badges { display: flex; align-items: center; justify-content: center; gap: 8rpx; margin-top: 4rpx; }
+.kp-badge {
+  font-size: 18rpx;
+  font-weight: 600;
+  padding: 2rpx 10rpx;
+  border-radius: 16rpx;
+}
+.kp-badge-ex { background: var(--accent-pale); color: var(--accent); }
+.kp-badge-diagram { background: #f6edd4; color: var(--gold); }
+.kp-badge-score { background: #e8f5e9; color: #2e7d32; }
+.kp-badge-score.ok { background: #fff9c4; color: #c17900; }
+
+.kp-nav-btn {
+  font-size: 26rpx;
+  color: var(--accent);
+  font-weight: 600;
+  padding: 16rpx 8rpx;
+}
+.kp-nav-btn.is-disabled { color: var(--rule); }
+.kp-nav-center { flex: 1; text-align: center; display: flex; flex-direction: column; align-items: center; }
+.kp-nav-pos { font-size: 22rpx; color: var(--ink-faint); letter-spacing: 0.08em; }
+
+/* Tab bar */
+.tab-bar {
+  display: flex;
+  background: var(--paper-page);
+  border-bottom: 2rpx solid var(--rule);
+  position: sticky;
+  top: 0;
+  z-index: 10;
+}
+.tab-item {
+  flex: 1;
+  text-align: center;
+  padding: 28rpx 0;
+  font-size: 28rpx;
+  color: var(--ink-faint);
+  font-weight: 500;
+  border-bottom: 3rpx solid transparent;
+}
+.tab-item.is-active {
+  color: var(--accent);
+  font-weight: 700;
+  border-bottom-color: var(--accent);
+}
+
+.tab-content { padding: 24rpx 36rpx 0; }
+
+/* Breadcrumb */
+.breadcrumb {
+  display: flex;
+  align-items: center;
+  gap: 8rpx;
+  flex-wrap: wrap;
+  margin-bottom: 20rpx;
+  padding-bottom: 16rpx;
+  border-bottom: 1rpx solid var(--rule);
+}
+.breadcrumb-ch { font-size: 22rpx; color: var(--ink-faint); }
+.breadcrumb-sep { font-size: 20rpx; color: var(--rule); }
+.breadcrumb-kp { font-size: 22rpx; color: var(--ink-soft); font-weight: 600; }
+
+/* Goals card */
+.goals-card {
+  background: var(--accent-pale);
+  border: 1rpx solid #f2d4cd;
+  border-radius: var(--radius);
+  padding: 28rpx 32rpx;
+  margin-bottom: 24rpx;
+}
+.goals-label {
+  display: block;
+  font-size: 22rpx;
+  font-weight: 700;
+  letter-spacing: 0.1em;
+  text-transform: uppercase;
+  color: var(--accent);
+  margin-bottom: 14rpx;
+}
+.goal-item {
+  display: flex;
+  align-items: flex-start;
+  gap: 12rpx;
+  margin-bottom: 8rpx;
+}
+.goal-dot { color: var(--accent); font-size: 28rpx; flex-shrink: 0; margin-top: 2rpx; }
+.goal-text { flex: 1; }
+
+/* Explanation block */
+.explanation-block {
+  margin-bottom: 24rpx;
+  padding: 28rpx 32rpx;
+  background: var(--paper-page);
+  border: 1rpx solid var(--rule);
+  border-radius: var(--radius);
+}
+
+.diagram-section {
+  margin-bottom: 24rpx;
+}
+
+/* Collapsibles */
+.collapsible {
+  margin-bottom: 16rpx;
+  border: 1rpx solid var(--rule);
+  border-radius: var(--radius);
+  overflow: hidden;
+  background: var(--paper-page);
+}
+.collapsible-header {
+  display: flex;
+  align-items: center;
+  justify-content: space-between;
+  padding: 24rpx 28rpx;
+}
+.collapsible-title { font-size: 28rpx; font-weight: 600; color: var(--ink); }
+.collapsible-icon { font-size: 22rpx; color: var(--ink-faint); }
+.collapsible-body { padding: 0 28rpx 24rpx; border-top: 1rpx solid var(--rule); }
+
+.q-item { display: flex; gap: 12rpx; margin-top: 16rpx; align-items: flex-start; }
+.q-num { font-size: 26rpx; color: var(--accent); font-weight: 700; flex-shrink: 0; margin-top: 2rpx; }
+.q-text { flex: 1; }
+
+.mistake-item { display: flex; gap: 12rpx; margin-top: 14rpx; align-items: flex-start; }
+.mistake-icon { font-size: 22rpx; color: var(--accent); font-weight: 700; flex-shrink: 0; margin-top: 4rpx; }
+.mistake-text { flex: 1; }
+
+/* Chat CTA */
+.chat-cta {
+  display: flex;
+  align-items: center;
+  gap: 20rpx;
+  margin-top: 28rpx;
+  padding: 28rpx 32rpx;
+  background: var(--paper-page);
+  border: 1rpx solid var(--rule);
+  border-left: 3rpx solid var(--gold);
+  border-radius: 0 var(--radius) var(--radius) 0;
+}
+.chat-cta-icon { font-size: 44rpx; flex-shrink: 0; }
+.chat-cta-title { display: block; font-size: 30rpx; font-weight: 600; color: var(--ink); }
+.chat-cta-sub { display: block; font-size: 22rpx; color: var(--ink-faint); margin-top: 4rpx; }
+.chat-cta-arrow { font-size: 40rpx; color: var(--ink-faint); margin-left: auto; }
+
+/* Exercise filter */
+.ex-filter-row {
+  display: flex;
+  gap: 12rpx;
+  flex-wrap: wrap;
+  padding: 12rpx 0 20rpx;
+  border-bottom: 1rpx solid var(--rule);
+  margin-bottom: 4rpx;
+}
+.ex-filter-chip {
+  font-size: 22rpx;
+  font-weight: 600;
+  padding: 8rpx 20rpx;
+  border-radius: 30rpx;
+  border: 1.5rpx solid var(--rule);
+  color: var(--ink-faint);
+  background: var(--paper-page);
+}
+.ex-filter-chip.active {
+  border-color: var(--accent);
+  color: var(--accent);
+  background: var(--accent-pale);
+}
+.filter-empty {
+  padding: 40rpx 0;
+  text-align: center;
+  font-size: 26rpx;
+  color: var(--ink-faint);
+}
+
+/* Exercise list */
+.ex-list {}
+.ex-card {
+  display: flex;
+  align-items: center;
+  padding: 28rpx 0;
+  border-bottom: 1rpx solid var(--rule);
+  gap: 20rpx;
+}
+.ex-card-left {
+  width: 56rpx;
+  height: 56rpx;
+  border-radius: 50%;
+  background: var(--accent-pale);
+  display: flex;
+  align-items: center;
+  justify-content: center;
+  flex-shrink: 0;
+}
+.ex-card-num { font-size: 24rpx; font-weight: 700; color: var(--accent); }
+.ex-card-body { flex: 1; min-width: 0; }
+.ex-card-title {
+  display: block;
+  font-size: 28rpx;
+  font-weight: 600;
+  color: var(--ink);
+  margin-bottom: 8rpx;
+  overflow: hidden;
+  text-overflow: ellipsis;
+  white-space: nowrap;
+}
+.ex-card-arrow { font-size: 40rpx; color: var(--ink-faint); flex-shrink: 0; }
+.ex-card-tags { display: flex; align-items: center; gap: 12rpx; margin-top: 8rpx; flex-wrap: wrap; }
+
+/* Difficulty pills */
+.difficulty-pill {
+  display: inline-block;
+  font-size: 20rpx;
+  font-weight: 600;
+  padding: 2rpx 12rpx;
+  border-radius: 20rpx;
+}
+.difficulty-pill.basic   { background: #e8f5e9; color: #2e7d32; }
+.difficulty-pill.medium  { background: #fff9c4; color: #c17900; }
+.difficulty-pill.advanced { background: #fce4ec; color: #880e4f; }
+
+/* Score badge */
+.score-badge {
+  display: inline-block;
+  font-size: 20rpx;
+  font-weight: 700;
+  padding: 2rpx 12rpx;
+  border-radius: 20rpx;
+}
+.score-badge.good { background: #e8f5e9; color: #2e7d32; }
+.score-badge.ok   { background: #fff9c4; color: #f57f17; }
+.score-badge.low  { background: #fce4ec; color: #880e4f; }
+
+/* Section divider */
+.section-divider { height: 1rpx; background: var(--rule); margin: 28rpx 0; }
+
+/* Jump to exercises */
+.jump-exercises {
+  text-align: center;
+  padding: 20rpx;
+  font-size: 26rpx;
+  color: var(--accent);
+  font-weight: 600;
+}
+
+/* Next KP row */
+.next-kp-row {
+  margin-top: 32rpx;
+  padding-bottom: 20rpx;
+}
+.next-kp-btn {
+  display: flex;
+  align-items: center;
+  justify-content: center;
+  padding: 28rpx 32rpx;
+  background: var(--accent);
+  color: #fff;
+  border-radius: var(--radius);
+  font-size: 28rpx;
+  font-weight: 700;
+  text-align: center;
+}
+.next-kp-btn.is-last {
+  background: #2e7d32;
+}
+
+/* Grade score */
+.grade-score-wrap { display: flex; align-items: baseline; gap: 4rpx; }
+.grade-score { font-size: 52rpx; font-weight: 900; color: var(--accent); line-height: 1; }
+.grade-score-unit { font-size: 26rpx; color: var(--ink-faint); }
+
+/* Exercise workspace */
+.ex-workspace { padding-bottom: 60rpx; }
+.back-row {
+  display: flex;
+  align-items: center;
+  gap: 8rpx;
+  padding: 8rpx 0 24rpx;
+  color: var(--accent);
+}
+.back-arrow { font-size: 36rpx; }
+.back-label { font-size: 26rpx; font-weight: 600; }
+.ex-num-label {
+  display: block;
+  font-size: 22rpx;
+  letter-spacing: 0.12em;
+  text-transform: uppercase;
+  color: var(--accent);
+  font-weight: 600;
+  margin-bottom: 16rpx;
+}
+.problem-card {
+  background: var(--paper-page);
+  border: 1rpx solid var(--rule);
+  border-left: 3rpx solid var(--accent);
+  border-radius: 0 var(--radius) var(--radius) 0;
+  padding: 24rpx 28rpx;
+  margin-bottom: 24rpx;
+}
+.problem-title {
+  display: block;
+  font-size: 22rpx;
+  font-weight: 700;
+  letter-spacing: 0.1em;
+  text-transform: uppercase;
+  color: var(--accent);
+  opacity: 0.8;
+  margin-bottom: 10rpx;
+}
+.answer-label {
+  display: block;
+  font-size: 22rpx;
+  font-weight: 600;
+  letter-spacing: 0.12em;
+  text-transform: uppercase;
+  color: var(--ink-faint);
+  margin-bottom: 10rpx;
+}
+.answer-input {
+  width: 100%;
+  min-height: 200rpx;
+  padding: 24rpx;
+  background: var(--paper-page);
+  border: 1.5rpx solid var(--rule);
+  border-radius: var(--radius);
+  font-size: 28rpx;
+  color: var(--ink);
+  line-height: 1.7;
+  box-sizing: border-box;
+  margin-bottom: 20rpx;
+}
+
+/* Action buttons */
+.action-row {
+  display: flex;
+  gap: 16rpx;
+  margin-bottom: 16rpx;
+}
+.action-row .btn { flex: 1; font-size: 26rpx; padding: 18rpx 16rpx; }
+
+/* Grade result */
+.grade-error {
+  padding: 20rpx 24rpx;
+  background: #fff0f0;
+  border: 1rpx solid #ffc9c9;
+  border-radius: var(--radius);
+  font-size: 26rpx;
+  color: #c62828;
+  margin-bottom: 20rpx;
+}
+.grade-result {
+  padding: 28rpx 32rpx;
+  border: 1rpx solid var(--rule);
+  border-radius: var(--radius);
+  margin-bottom: 20rpx;
+}
+.grade-result.excellent { background: #f1f8e9; border-color: #a5d6a7; }
+.grade-result.good { background: #e8f5e9; border-color: #81c784; }
+.grade-result.partial { background: #fff8e1; border-color: #ffe082; }
+.grade-result.incorrect { background: #fce4ec; border-color: #f48fb1; }
+.grade-result-head {
+  display: flex;
+  justify-content: space-between;
+  align-items: center;
+  margin-bottom: 16rpx;
+}
+.grade-result-label { display: block; font-size: 20rpx; font-weight: 600; letter-spacing: 0.1em; text-transform: uppercase; color: var(--ink-faint); margin-bottom: 4rpx; }
+.grade-verdict-title { display: block; font-size: 30rpx; font-weight: 800; color: var(--ink); }
+.grade-score { font-size: 40rpx; font-weight: 800; color: var(--accent); }
+.missing-points { margin-top: 16rpx; }
+.missing-label { display: block; font-size: 24rpx; font-weight: 700; color: var(--ink); margin-bottom: 10rpx; }
+.missing-item { display: flex; gap: 10rpx; margin-bottom: 8rpx; align-items: flex-start; }
+.missing-bullet { color: var(--accent); font-size: 26rpx; }
+
+/* Hints */
+.hint-list {
+  background: var(--paper-page);
+  border: 1rpx solid var(--rule);
+  border-left: 3rpx solid var(--gold);
+  border-radius: 0 var(--radius) var(--radius) 0;
+  padding: 24rpx 28rpx;
+  margin-bottom: 20rpx;
+}
+.hint-list-label {
+  display: block;
+  font-size: 22rpx;
+  font-weight: 700;
+  color: var(--gold);
+  letter-spacing: 0.1em;
+  text-transform: uppercase;
+  margin-bottom: 14rpx;
+}
+.hint-item { margin-bottom: 10rpx; }
+.hint-num { font-size: 22rpx; font-weight: 700; color: var(--ink-faint); }
+
+/* Rubric */
+.rubric-block {
+  background: var(--paper-page);
+  border: 1rpx solid var(--rule);
+  border-radius: var(--radius);
+  padding: 24rpx 28rpx;
+  margin-bottom: 20rpx;
+}
+.rubric-label {
+  display: block;
+  font-size: 22rpx;
+  font-weight: 700;
+  color: var(--ink-faint);
+  letter-spacing: 0.1em;
+  text-transform: uppercase;
+  margin-bottom: 14rpx;
+}
+.rubric-item { display: flex; gap: 10rpx; margin-bottom: 10rpx; align-items: flex-start; }
+.rubric-bullet { color: #2e7d32; font-size: 24rpx; font-weight: 700; }
diff --git a/wx-miniprogram/project.config.json b/wx-miniprogram/project.config.json
new file mode 100644
index 0000000..f0cafce
--- /dev/null
+++ b/wx-miniprogram/project.config.json
@@ -0,0 +1,19 @@
+{
+  "description": "数学分析学习小程序",
+  "projectname": "math-analysis-tutor",
+  "appid": "wx_REPLACE_WITH_YOUR_APPID",
+  "miniprogramRoot": "./",
+  "setting": {
+    "urlCheck": false,
+    "es6": true,
+    "postcss": true,
+    "minified": true,
+    "newFeature": false,
+    "coverView": true,
+    "showShadowRootInWxmlPanel": true,
+    "checkInvalidKey": true,
+    "checkSiteMap": true
+  },
+  "compileType": "miniprogram",
+  "libVersion": "3.3.4"
+}
diff --git a/wx-miniprogram/sitemap.json b/wx-miniprogram/sitemap.json
new file mode 100644
index 0000000..0daa379
--- /dev/null
+++ b/wx-miniprogram/sitemap.json
@@ -0,0 +1,4 @@
+{
+  "desc": "关于本文件的更多信息，请参考文档 https://developers.weixin.qq.com/miniprogram/dev/framework/sitemap.html",
+  "rules": [{ "action": "disallow", "page": "*" }]
+}
diff --git a/wx-miniprogram/utils/api.js b/wx-miniprogram/utils/api.js
new file mode 100644
index 0000000..fcafc7a
--- /dev/null
+++ b/wx-miniprogram/utils/api.js
@@ -0,0 +1,173 @@
+const config = require('../config');
+const { loadApiKeyOverride } = require('./progress');
+
+const CHAT_URL = config.DEEPSEEK_BASE_URL.replace(/\/+$/, '') + '/chat/completions';
+
+function getApiKey() {
+  return loadApiKeyOverride() || config.DEEPSEEK_API_KEY;
+}
+
+function buildSystemPrompt(kp) {
+  const lines = [
+    '你是一位数学分析苏格拉底式助教，辅导大学生学习。',
+    '核心原则：优先提问引导而非直接给答案；一次只问一个问题；语气友好鼓励；数学公式用 LaTeX。',
+    '',
+  ];
+  if (kp && kp.title) lines.push('当前知识点：' + kp.title);
+  if (kp && kp.learningGoals && kp.learningGoals.length) {
+    lines.push('\n学习目标：');
+    kp.learningGoals.forEach((g, i) => lines.push((i + 1) + '. ' + g));
+  }
+  if (kp && kp.coreExplanation) {
+    const snippet = kp.coreExplanation.slice(0, 500);
+    lines.push('\n核心概念（摘要）：\n' + snippet + (kp.coreExplanation.length > 500 ? '…' : ''));
+  }
+  if (kp && kp.socraticQuestions && kp.socraticQuestions.length) {
+    lines.push('\n可用追问示例（选择性使用，不直接照读）：');
+    kp.socraticQuestions.slice(0, 3).forEach(q => lines.push('· ' + q));
+  }
+  if (kp && kp.commonMistakes && kp.commonMistakes.length) {
+    lines.push('\n常见误区（注意引导学生避免）：');
+    kp.commonMistakes.slice(0, 3).forEach(m => lines.push('· ' + m));
+  }
+  return lines.join('\n');
+}
+
+function buildGradePrompt(exercise, studentAnswer) {
+  const rubricText = exercise.gradingRubric && exercise.gradingRubric.length
+    ? exercise.gradingRubric.join('\n')
+    : '整体正确性、逻辑清晰、步骤完整';
+
+  return [
+    '你是一位严格但友好的数学分析助教，请批改以下学生作答。',
+    '',
+    '【题目】',
+    exercise.prompt,
+    '',
+    '【评分标准】',
+    rubricText,
+    '',
+    '【学生答案】',
+    studentAnswer,
+    '',
+    '请严格按如下 JSON 格式返回，不要输出任何其他内容：',
+    '{"verdict":"excellent"|"good"|"partial"|"incorrect","score":整数0到100,"feedback":"对学生答案的评语（指出优点和具体不足，数学符号用LaTeX）","missingPoints":["缺少的要点1","缺少的要点2"]}',
+  ].join('\n');
+}
+
+function httpError(statusCode) {
+  const map = {
+    401: 'API Key 无效，请在设置中更新',
+    403: 'API Key 无权限',
+    429: '请求太频繁，请稍后再试',
+    500: 'DeepSeek 服务器繁忙，请稍后再试',
+    503: 'DeepSeek 服务暂时不可用',
+  };
+  return map[statusCode] || ('服务器返回错误 ' + statusCode);
+}
+
+function networkError(err) {
+  const msg = err && err.errMsg || '';
+  if (msg.includes('timeout')) return '请求超时，请检查网络';
+  if (msg.includes('dns')) return '无法连接到服务器，请检查网络';
+  return '网络错误，请检查网络连接';
+}
+
+function parseGradeJson(raw) {
+  try {
+    // Strip markdown code fences
+    let s = raw.replace(/```json\s*/g, '').replace(/```\s*/g, '').trim();
+    return JSON.parse(s);
+  } catch (_) { /* try extracting JSON object */ }
+  try {
+    const m = raw.match(/\{[\s\S]*\}/);
+    if (m) return JSON.parse(m[0]);
+  } catch (_) { /* ignore */ }
+  return null;
+}
+
+function chatRequest(messages, kp, callbacks) {
+  const systemPrompt = buildSystemPrompt(kp);
+  const apiMessages = [
+    { role: 'system', content: systemPrompt },
+    ...messages.map(m => ({
+      role: m.role === 'assistant' ? 'assistant' : 'user',
+      content: m.content,
+    })),
+  ];
+
+  wx.request({
+    url: CHAT_URL,
+    method: 'POST',
+    header: {
+      'Content-Type': 'application/json',
+      Authorization: 'Bearer ' + getApiKey(),
+    },
+    data: {
+      model: config.DEEPSEEK_MODEL,
+      messages: apiMessages,
+      temperature: 0.5,
+      max_tokens: 1024,
+    },
+    success(res) {
+      if (res.statusCode !== 200) {
+        callbacks.onError(httpError(res.statusCode));
+        return;
+      }
+      const content = res.data && res.data.choices && res.data.choices[0] &&
+        res.data.choices[0].message && res.data.choices[0].message.content;
+      if (!content) {
+        callbacks.onError('AI 返回内容为空');
+        return;
+      }
+      callbacks.onSuccess(content);
+    },
+    fail(err) {
+      callbacks.onError(networkError(err));
+    },
+  });
+}
+
+function gradeRequest(exercise, studentAnswer, callbacks) {
+  const gradePrompt = buildGradePrompt(exercise, studentAnswer);
+
+  wx.request({
+    url: CHAT_URL,
+    method: 'POST',
+    header: {
+      'Content-Type': 'application/json',
+      Authorization: 'Bearer ' + getApiKey(),
+    },
+    data: {
+      model: config.DEEPSEEK_MODEL,
+      messages: [
+        { role: 'user', content: gradePrompt },
+      ],
+      temperature: 0.2,
+      max_tokens: 800,
+    },
+    success(res) {
+      if (res.statusCode !== 200) {
+        callbacks.onError(httpError(res.statusCode));
+        return;
+      }
+      const raw = res.data && res.data.choices && res.data.choices[0] &&
+        res.data.choices[0].message && res.data.choices[0].message.content;
+      if (!raw) {
+        callbacks.onError('AI 返回内容为空');
+        return;
+      }
+      const result = parseGradeJson(raw);
+      if (result) {
+        callbacks.onSuccess(result);
+      } else {
+        callbacks.onError('批改结果格式错误，请重试');
+      }
+    },
+    fail(err) {
+      callbacks.onError(networkError(err));
+    },
+  });
+}
+
+module.exports = { chatRequest, gradeRequest, buildSystemPrompt };
diff --git a/wx-miniprogram/utils/parser.js b/wx-miniprogram/utils/parser.js
new file mode 100644
index 0000000..fc728f7
--- /dev/null
+++ b/wx-miniprogram/utils/parser.js
@@ -0,0 +1,209 @@
+// Text/math parser — converts markdown+LaTeX text into rich-text node arrays
+// rich-text nodes: {name, attrs:{style}, children:[]} | {type:'text', text:''}
+
+const DISPLAY_MATH_STYLE = [
+  'display:block',
+  'background:#f6f0e4',
+  'border-left:4rpx solid #8a2b2b',
+  'padding:12rpx 20rpx',
+  'margin:12rpx 0',
+  'font-family:Courier New,monospace',
+  'font-size:26rpx',
+  'color:#211c16',
+  'word-break:break-all',
+  'white-space:pre-wrap',
+  'line-height:1.7',
+].join(';');
+
+const INLINE_MATH_STYLE = [
+  'font-family:Courier New,monospace',
+  'color:#8a2b2b',
+  'font-size:0.93em',
+  'letter-spacing:-0.01em',
+].join(';');
+
+const PARA_STYLE = 'display:block;margin:0 0 14rpx 0;line-height:1.8;';
+const BULLET_ITEM_STYLE = 'display:block;padding-left:24rpx;margin-bottom:8rpx;line-height:1.8;position:relative;';
+const BULLET_STYLE = 'position:absolute;left:0;color:#8a2b2b;font-weight:700;';
+const ORDERED_ITEM_STYLE = 'display:block;padding-left:36rpx;margin-bottom:8rpx;line-height:1.8;position:relative;';
+const ORDERED_NUM_STYLE = 'position:absolute;left:0;color:#8a2b2b;font-weight:700;font-size:0.9em;';
+
+function normalizeLatex(str) {
+  return str.replace(/\\\\/g, '\\');
+}
+
+// ── Inline parsers ────────────────────────────────────────────
+
+function parseBoldItalic(text) {
+  const nodes = [];
+  const parts = text.split(/(\*\*[^*\n]+\*\*|\*[^*\n]+\*)/g);
+  for (const p of parts) {
+    if (!p) continue;
+    if (p.startsWith('**') && p.endsWith('**') && p.length > 4) {
+      nodes.push({
+        name: 'strong',
+        attrs: { style: 'font-weight:700;' },
+        children: [{ type: 'text', text: p.slice(2, -2) }],
+      });
+    } else if (p.startsWith('*') && p.endsWith('*') && p.length > 2) {
+      nodes.push({
+        name: 'em',
+        attrs: { style: 'font-style:italic;color:#4a3728;' },
+        children: [{ type: 'text', text: p.slice(1, -1) }],
+      });
+    } else {
+      nodes.push({ type: 'text', text: p });
+    }
+  }
+  return nodes;
+}
+
+function parseInline(text) {
+  const nodes = [];
+  const parts = text.split(/(\$[^$\n]+\$)/g);
+  for (const part of parts) {
+    if (!part) continue;
+    if (part.startsWith('$') && part.endsWith('$') && part.length > 2) {
+      nodes.push({
+        name: 'span',
+        attrs: { style: INLINE_MATH_STYLE },
+        children: [{ type: 'text', text: part.slice(1, -1) }],
+      });
+    } else {
+      const lines = part.split('\n');
+      for (let i = 0; i < lines.length; i++) {
+        if (i > 0) nodes.push({ name: 'br', attrs: {}, children: [] });
+        nodes.push(...parseBoldItalic(lines[i]));
+      }
+    }
+  }
+  return nodes;
+}
+
+// ── Block-level line classification ──────────────────────────
+
+function classifyLine(line) {
+  if (/^[-·•]\s/.test(line)) return { type: 'bullet', content: line.replace(/^[-·•]\s/, '') };
+  if (/^\d+[.)]\s/.test(line)) {
+    const m = line.match(/^(\d+)[.)]\s(.*)/);
+    return { type: 'ordered', num: m[1], content: m[2] };
+  }
+  return { type: 'text', content: line };
+}
+
+// ── Block builder ─────────────────────────────────────────────
+
+function buildListItem(content, prefix, prefixStyle, itemStyle) {
+  return {
+    name: 'div',
+    attrs: { style: itemStyle },
+    children: [
+      { name: 'span', attrs: { style: prefixStyle }, children: [{ type: 'text', text: prefix }] },
+      ...parseInline(content),
+    ],
+  };
+}
+
+function buildParagraphNodes(text) {
+  const lines = text.split('\n');
+  const nodes = [];
+  let i = 0;
+
+  while (i < lines.length) {
+    const line = lines[i].trim();
+    if (!line) { i++; continue; }
+
+    const classified = classifyLine(line);
+
+    if (classified.type === 'bullet') {
+      // Collect consecutive bullet items
+      const items = [];
+      while (i < lines.length) {
+        const l = lines[i].trim();
+        if (!l) { i++; break; }
+        const c = classifyLine(l);
+        if (c.type !== 'bullet') break;
+        items.push(c.content);
+        i++;
+      }
+      nodes.push({
+        name: 'div',
+        attrs: { style: 'margin:8rpx 0 14rpx 0;' },
+        children: items.map(item =>
+          buildListItem(item, '·', BULLET_STYLE, BULLET_ITEM_STYLE)
+        ),
+      });
+    } else if (classified.type === 'ordered') {
+      // Collect consecutive ordered items
+      const items = [];
+      while (i < lines.length) {
+        const l = lines[i].trim();
+        if (!l) { i++; break; }
+        const c = classifyLine(l);
+        if (c.type !== 'ordered') break;
+        items.push({ num: c.num, content: c.content });
+        i++;
+      }
+      nodes.push({
+        name: 'div',
+        attrs: { style: 'margin:8rpx 0 14rpx 0;' },
+        children: items.map(item =>
+          buildListItem(item.content, item.num + '.', ORDERED_NUM_STYLE, ORDERED_ITEM_STYLE)
+        ),
+      });
+    } else {
+      // Regular text line — group consecutive text lines into a paragraph
+      const textLines = [];
+      while (i < lines.length) {
+        const l = lines[i].trim();
+        if (!l) { i++; break; }
+        if (classifyLine(l).type !== 'text') break;
+        textLines.push(l);
+        i++;
+      }
+      // Build as a single paragraph with <br> between lines
+      const children = [];
+      for (let j = 0; j < textLines.length; j++) {
+        if (j > 0) children.push({ name: 'br', attrs: {}, children: [] });
+        children.push(...parseInline(textLines[j]));
+      }
+      nodes.push({ name: 'div', attrs: { style: PARA_STYLE }, children });
+    }
+  }
+
+  return nodes;
+}
+
+// ── Main entry ────────────────────────────────────────────────
+
+function parseText(text) {
+  if (!text) return [];
+  const normalized = normalizeLatex(text);
+
+  // Split on display math $$...$$ first
+  const chunks = normalized.split(/(\$\$[\s\S]+?\$\$)/g);
+  const topNodes = [];
+
+  for (const chunk of chunks) {
+    if (!chunk) continue;
+    if (chunk.startsWith('$$') && chunk.endsWith('$$')) {
+      topNodes.push({
+        name: 'div',
+        attrs: { style: DISPLAY_MATH_STYLE },
+        children: [{ type: 'text', text: chunk.slice(2, -2).trim() }],
+      });
+    } else {
+      // Split into paragraphs
+      const paragraphs = chunk.split(/\n{2,}/);
+      for (const para of paragraphs) {
+        const trimmed = para.trim();
+        if (!trimmed) continue;
+        topNodes.push(...buildParagraphNodes(trimmed));
+      }
+    }
+  }
+
+  return topNodes;
+}
+
+module.exports = { parseText, normalizeLatex };
diff --git a/wx-miniprogram/utils/progress.js b/wx-miniprogram/utils/progress.js
new file mode 100644
index 0000000..88dde1a
--- /dev/null
+++ b/wx-miniprogram/utils/progress.js
@@ -0,0 +1,177 @@
+// Persistent progress tracking via wx.setStorageSync
+// Key scheme: ma_progress_<chapterId>_<kpId> for KP state
+//             ma_chat_<chapterId>_<kpId> for chat history
+//             ma_ex_<exerciseId> for exercise attempts
+
+const PREFIX = 'ma_';
+
+// ── KP Progress ──────────────────────────────────────────────
+
+function kpKey(chapterId, kpId) {
+  return PREFIX + 'kp_' + chapterId + '_' + kpId;
+}
+
+/**
+ * Returns { studied, exercisesAttempted, lastScore, lastStudied }
+ */
+function loadKpProgress(chapterId, kpId) {
+  try {
+    return wx.getStorageSync(kpKey(chapterId, kpId)) || {};
+  } catch (e) {
+    return {};
+  }
+}
+
+function markKpStudied(chapterId, kpId) {
+  try {
+    const current = loadKpProgress(chapterId, kpId);
+    wx.setStorageSync(kpKey(chapterId, kpId), {
+      ...current,
+      studied: true,
+      lastStudied: Date.now(),
+    });
+  } catch (e) { /* storage might be full */ }
+}
+
+// ── Exercise Attempts ─────────────────────────────────────────
+
+function exKey(exerciseId) {
+  return PREFIX + 'ex_' + exerciseId;
+}
+
+/**
+ * Returns array of { score, verdict, ts } sorted newest-first
+ */
+function loadExerciseAttempts(exerciseId) {
+  try {
+    return wx.getStorageSync(exKey(exerciseId)) || [];
+  } catch (e) {
+    return [];
+  }
+}
+
+function saveExerciseAttempt(chapterId, kpId, exerciseId, result) {
+  try {
+    const attempts = loadExerciseAttempts(exerciseId);
+    attempts.unshift({ score: result.score, verdict: result.verdict, ts: Date.now() });
+    // Keep at most 10 attempts per exercise
+    wx.setStorageSync(exKey(exerciseId), attempts.slice(0, 10));
+
+    // Update KP progress with highest score
+    const best = attempts.reduce((m, a) => Math.max(m, a.score || 0), 0);
+    const current = loadKpProgress(chapterId, kpId);
+    wx.setStorageSync(kpKey(chapterId, kpId), {
+      ...current,
+      studied: true,
+      lastExScore: result.score,
+      bestExScore: best,
+      exercisesAttempted: (current.exercisesAttempted || 0) + 1,
+      lastStudied: Date.now(),
+    });
+  } catch (e) { /* storage might be full */ }
+}
+
+function getBestScore(exerciseId) {
+  const attempts = loadExerciseAttempts(exerciseId);
+  if (!attempts.length) return null;
+  return attempts.reduce((m, a) => Math.max(m, a.score || 0), 0);
+}
+
+// ── Chapter Summary ───────────────────────────────────────────
+
+/**
+ * Returns { studiedCount, totalCount, avgScore } for a chapter
+ */
+function loadChapterProgress(chapter) {
+  const kps = chapter.knowledgePoints || [];
+  let studiedCount = 0;
+  let scoreSum = 0;
+  let scoreCount = 0;
+
+  for (const kp of kps) {
+    const prog = loadKpProgress(chapter.id, kp.id);
+    if (prog.studied) studiedCount++;
+    if (prog.bestExScore != null) {
+      scoreSum += prog.bestExScore;
+      scoreCount++;
+    }
+  }
+
+  return {
+    studiedCount,
+    totalCount: kps.length,
+    avgScore: scoreCount > 0 ? Math.round(scoreSum / scoreCount) : null,
+    pct: kps.length > 0 ? Math.round(studiedCount / kps.length * 100) : 0,
+  };
+}
+
+// ── Chat History ──────────────────────────────────────────────
+
+function chatKey(chapterId, kpId) {
+  return PREFIX + 'chat_' + chapterId + '_' + kpId;
+}
+
+function saveChat(chapterId, kpId, messages) {
+  try {
+    // Keep last 40 messages to stay within storage limits
+    wx.setStorageSync(chatKey(chapterId, kpId), messages.slice(-40));
+  } catch (e) { /* storage might be full */ }
+}
+
+function loadChat(chapterId, kpId) {
+  try {
+    return wx.getStorageSync(chatKey(chapterId, kpId)) || null;
+  } catch (e) {
+    return null;
+  }
+}
+
+// ── API Key Override ──────────────────────────────────────────
+
+const API_KEY_STORAGE = PREFIX + 'apikey';
+
+function saveApiKeyOverride(key) {
+  try {
+    if (key && key.trim()) {
+      wx.setStorageSync(API_KEY_STORAGE, key.trim());
+    } else {
+      wx.removeStorageSync(API_KEY_STORAGE);
+    }
+  } catch (e) { /* ignore */ }
+}
+
+function loadApiKeyOverride() {
+  try {
+    return wx.getStorageSync(API_KEY_STORAGE) || null;
+  } catch (e) {
+    return null;
+  }
+}
+
+// ── Reset all progress ─────────────────────────────────────────
+
+function clearAllProgress() {
+  try {
+    const info = wx.getStorageInfoSync();
+    const keys = (info && info.keys) || [];
+    for (const key of keys) {
+      if (key.startsWith(PREFIX) && key !== API_KEY_STORAGE) {
+        wx.removeStorageSync(key);
+      }
+    }
+  } catch (e) { /* ignore */ }
+}
+
+module.exports = {
+  loadKpProgress,
+  markKpStudied,
+  loadExerciseAttempts,
+  saveExerciseAttempt,
+  getBestScore,
+  loadChapterProgress,
+  saveChat,
+  loadChat,
+  saveApiKeyOverride,
+  loadApiKeyOverride,
+  clearAllProgress,
+};