मुफ्त ऑनलाइन कोर्सComputer-Oriented Numerical Methods - Numerical Method

कोर्स का विवरण

Computer-Oriented Numerical Methods is a free online course in basic studies that builds a practical foundation in numerical methods with a clear computer-focused approach. It helps you understand how numbers are represented in machines, why floating point arithmetic behaves the way it does, and how these details influence accuracy in real computations.

You will explore the core sources of numerical error, including data error, truncation error, round off error, and computational error, then learn how to reason about reliability when solving mathematical problems on a computer. The course introduces key equation types and solution strategies, with emphasis on iterative techniques commonly used in scientific and engineering calculations.

Root-finding methods are covered in depth, including bisection and its variants, regula falsi, secant, and Newton Raphson, giving you multiple tools to handle algebraic and transcendental equations. You then move into interpolation, studying Lagrange interpolation and a range of Newton-based formulas, along with central difference approaches such as Gauss forward and backward as well as Stirling interpolation.

The course also develops techniques for linear systems, including Gauss elimination, Gauss Jordan, and iterative solvers like Jacobi and Gauss Seidel. For numerical integration, you will learn Newton Cotes methods such as the trapezoidal rule, Simpson 1/3, Simpson 3/8, and Weddle rule. Finally, it covers numerical solutions of ordinary differential equations using Euler, Picard, Taylor series, and fourth-order Runge-Kutta methods. Ideal for learners who want a structured, computation-ready path through essential numerical methods.