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Last updated:

September 23, 2023

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Description

Numerical Analysis. Instructor: Prof. R. Usha, Department of Mathematics, IIT Madras. This course on NUMERICAL ANALYSIS introduces the theory and application of numerical methods or techniques to approximate mathematical procedures (such as reconstruction of a function, evaluation of an integral) or solutions of problems that arise in science and engineering.

Such approximations are needed because the analytical methods are either intractable or the problem under consideration can not be solved analytically. Explanations for why and how these approximation techniques work are provided with emphasis on accuracy and efficiency of the developed methods. The course also provides a firm foundation for further study on Numerical Analysis. (from nptel.ac.in)

Course Curriculum

  • Lecture 01 – Introduction Unlimited
    • Lecture 02 – Mathematical Preliminaries, Polynomial Interpolation (Part 1) Unlimited
    • Lecture 03 – Polynomial Interpolation (cont.) (Part 1) Unlimited
    • Lecture 04 – Polynomial Interpolation (cont.) Unlimited
    • Lecture 05 – Lagrange Interpolation Polynomial, Error in Interpolation (Part 1) Unlimited
    • Lecture 06 – Error in Interpolation (Part 1) Unlimited
    • Lecture 07 – Divided Difference Interpolation Polynomial Unlimited
    • Lecture 08 – Properties of Divided Differences Unlimited
    • Lecture 09 – Inverse Interpolation, Remarks on Polynomial Interpolation Unlimited
    • Lecture 10 – Taylor Series Method Unlimited
    • Lecture 11 – Polynomial Interpolation Method Unlimited
    • Lecture 12 – Operator Method, Numerical Integration Unlimited
    • Lecture 13 – Numerical Integration: Error in Trapezoidal Rule, Simpson’s Rule Unlimited
    • Lecture 14 – Error in Simpson’s Rule, Composite Trapezoidal Rule Error Unlimited
    • Lecture 15 – Composite Simpson’s Rule, Error Method of Undetermined Coefficient Unlimited
    • Lecture 16 – Gaussian Quadrature (Two Point Method) Unlimited
    • Lecture 17 – Gaussian Quadrature (Three Point Method), Adaptive Quadrature Unlimited
    • Lecture 18 – Numerical Solution of Ordinary Differential Equations Unlimited
    • Lecture 19 – Stability, Single Step Methods, Taylor Series Method Unlimited
    • Lecture 20 – Examples for Taylor Series Method, Euler’s Method Unlimited
    • Lecture 21 – Runge-Kutta Methods Unlimited
    • Lecture 22 – Example for RK-method of Order 2, Modified Euler’s Method Unlimited
    • Lecture 23 – Predictor-Corrector Methods (Adam-Moulton) Unlimited
    • Lecture 24 – Predictor-Corrector Methods (Milne) Unlimited
    • Lecture 25 – Linear Boundary Value Problems Unlimited
    • Lecture 26 – Boundary Value Problems: Finite-Difference Methods Unlimited
    • Lecture 27 – Boundary Value Problems: Shooting Methods Unlimited
    • Lecture 28 – Boundary Value Problems: Shooting Methods (cont.) Unlimited
    • Lecture 29 – Root Finding Methods: The Bisection Method Unlimited
    • Lecture 30 – The Bisection Method (cont.) Unlimited
    • Lecture 31 – Newton-Raphson Method Unlimited
    • Lecture 32 – Newton-Raphson Method (cont.) Unlimited
    • Lecture 33 – Secant Method, Method of False Position Unlimited
    • Lecture 34 – Fixed Point Methods Unlimited
    • Lecture 35 – Fixed Point Methods (cont.) Unlimited
    • Lecture 36 – Fixed Point Iteration Methods Unlimited
    • Lecture 37 – Practice Problems Unlimited
    • Lecture 38 – Solution of Linear Systems of Equations: Decomposition Methods Unlimited
    • Lecture 39 – Decomposition Methods (cont.) Unlimited
    • Lecture 40 – Gauss Elimination Method Unlimited
    • Lecture 41 – Gauss Elimination Method with Partial Pivoting Unlimited
    • Lecture 42 – Gauss-Jordan Method Unlimited
    • Lecture 43 – Solution of Linear Systems of Equations: Error Analysis Unlimited
    • Lecture 44 – Error Analysis (cont.) Unlimited
    • Lecture 45 – Iterative Improvement Method, Iterative Methods Unlimited
    • Lecture 46 – Iterative Methods, Matrix Eigenvalue Problems, Power Method Unlimited
    • Lecture 47 – Power Method, Gerschgorin’s Theorem, Brauer’s Theorem Unlimited
    • Lecture 48 – Practical Problems Unlimited

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