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 32 - Newton-Raphson Method (cont.)
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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