Applied Numerical Methods (MTH308)

Prof. B. V. R. Kumar, IIT Kanpur
Jan ’25 – Apr ’25

A collection of Python and MATLAB modules implementing classical and iterative numerical algorithms for root‑finding, linear systems, interpolation and integration.

---

📚 Course & Project Overview

This repository contains self‑contained scripts and functions for solving common numerical problems taught in MTH308:

• Nonlinear Root Finding
  • Bisection
  • Regula‑Falsi (False‑Position)
  • Newton‑Raphson
  • Secant
  • Fixed Point
• Linear Algebraic Systems
  • Gaussian Elimination
  • LU Decomposition (Doolittle & Cholesky)
  • Power Method (dominant eigenvalue/vector)
• Interpolation & Numerical Integration
  • Lagrange Polynomials
  • Newton–Cotes (Trapezoidal, Simpson’s Rules)
  • Gauss Quadrature

Each module is implemented in both Python (with NumPy/SciPy) and MATLAB, allowing easy comparison and benchmarking.

---

##📂 Repository Structure

mth308-numerical-methods/
│
├── Python/
│   ├── root_finding/              # Bisection, Regula‑Falsi, Newton, Secant, Fixed‑Point
│   ├── linear_systems/            # Gaussian elimination, LU (Doolittle & Cholesky), Power Method
│   └── interpolation_integration/  # Lagrange, Simpson’s, Newton‑Cotes, Gauss quadrature
│
├── MATLAB/
│   ├── root_finding.m
│   ├── linear_systems.m
│   └── interp_integration.m
│
├── examples/                      # Sample driver scripts and Jupyter notebooks
│   ├── solve_roots.ipynb
│   └── demo_matrix_solvers.ipynb
│
└── README.md