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