This course contains the use of artificial intelligence

Welcome to Numerical Methods from Theory to Python Implementation, a comprehensive course designed to bridge the gap between mathematical theory and computational problem-solving. Numerical methods play a vital role in modern science, engineering, data analysis, and scientific computing, enabling us to solve complex mathematical problems that cannot be solved easily using analytical techniques.

In this course, you will learn the fundamental concepts and practical applications of numerical methods through a combination of theory, worked examples, and Python programming. We begin by exploring the solution of nonlinear and transcendental equations using techniques such as the Bisection Method, Regula-Falsi Method, Newton-Raphson Method, and Secant Method. You will understand the underlying principles of these algorithms and learn how to implement them in Python.

The course then introduces numerical integration techniques, including the Trapezoidal Rule and Simpson's Rules, which are widely used to approximate definite integrals in scientific and engineering applications. You will also learn how to analyze and compare the accuracy of different numerical integration methods.

A major component of the course focuses on the numerical solution of ordinary differential equations. Topics include Euler's Method, Modified Euler's Method, and the Runge-Kutta Fourth-Order Method. Through real-world examples and coding exercises, you will learn how to model and solve dynamic systems computationally.

Designed for students of Mathematics, Engineering, Physics, Computer Science, and related disciplines, this course emphasizes conceptual understanding, algorithm development, and practical implementation. By the end of the course, you will be able to confidently apply numerical techniques, write Python programs for mathematical computations, and solve a wide range of scientific and engineering problems using numerical methods.