Numerical Analysis

From Errors and Approximations to PDEs and Fourier Transforms

A comprehensive course covering the theory, implementation (with code), and practical applications of Numerical Analysis.

Author Aditya Kumar

Published October 1, 2026

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Numerical Analysis

Theory, Implementation, and Practice Problems

This course covers everything from basic error approximations to solving Partial Differential Equations and performing Fast Fourier Transforms. Each chapter includes rigorous mathematical theory, practical code examples, and practice problems to solidify your understanding.

Course Syllabus

Module 01

Methods of Approximation and Errors

Truncation and round-off errors, accuracy, and precision.

Module 02

Computer Programming

Programming fundamentals required for implementing numerical methods.

Module 03

Roots of Equations

Bracketing methods (Bisection, False Position), Newton-Raphson, and Linear Algebraic Equations.

Module 04

System of Nonlinear Equations

Bisection, Newton’s method, and Fixed-point iteration for non-linear systems.

Module 05

Curve Fitting

Least squares regression, linear regression, and nonlinear regression.

Module 06

Interpolation Methods

Interpolating polynomials and Newton’s divided difference.

Module 07

Numerical Differentiation

Finite difference approximation (Taylor series) and differentiation using curve fitting.

Module 08

Numerical Integration

Rectangle, midpoint, Trapezoidal, Simpson’s methods, and Gauss quadrature.

Module 09

Ordinary Differential Equations

Euler’s method, Runge-Kutta methods, boundary value, and eigenvalue problems.

Module 10

Partial Differential Equations

Laplace’s equation solutions and practical applications.

Module 11

Fourier Approximation

Introduction, Discrete Fourier Transform (DFT), and Fast Fourier Transform (FFT).