# InfoCoBuild

## Elementary Numerical Analysis

Elementary Numerical Analysis. Instructor: Prof. Rekha P. Kulkarni, Department of Mathematics, IIT Bombay. This course introduces the implementation and analysis of numerical algorithms for finding an approximate solution to a mathematical problem. The important topics covered in this course are polynomial and piecewise polynomial (spline) interpolation, numerical integration and numerical differentiation, approximate solutions of differential equations, direct and iterative solution of a system of linear equations and eigenvalue problems. The theory behind various methods is rigorously discussed. Emphasis is on comparison of various methods and their implementation using a computer. (from nptel.ac.in)

 Introduction

 Lecture 01 - Introduction Lecture 02 - Polynomial Approximation Lecture 03 - Interpolating Polynomials Lecture 04 - Properties of Divided Difference Lecture 05 - Error in the Interpolating Polynomial Lecture 06 - Cubic Hermite Interpolation Lecture 07 - Piecewise Polynomial Approximation Lecture 08 - Cubic Spline Interpolation Lecture 09 - Tutorial 1 Lecture 10 - Numerical Integration: Basic Rules Lecture 11 - Composite Numerical Integration Lecture 12 - Gauss 2-point Rule: Construction Lecture 13 - Gauss 2-point Rule: Error Lecture 14 - Convergence of Gaussian Integration Lecture 15 - Tutorial 2 Lecture 16 - Numerical Differentiation Lecture 17 - Gauss Elimination Lecture 18 - LU Decomposition Lecture 19 - Cholesky Decomposition Lecture 20 - Gauss Elimination with Partial Pivoting Lecture 21 - Vector and Matrix Norms Lecture 22 - Perturbed Linear System Lecture 23 - Ill-Conditioned Linear System Lecture 24 - Tutorial 3 Lecture 25 - Effect of Small Pivots Lecture 26 - Solution of Nonlinear Equations Lecture 27 - Quadratic Convergence of Newton's Method Lecture 28 - Jacobi Method Lecture 29 - Gauss-Seidel Method Lecture 30 - Tutorial 4 Lecture 31 - Initial Value Problem Lecture 32 - Multi-Step Methods Lecture 33 - Predictor-Corrector Formula Lecture 34 - Boundary Value Problems Lecture 35 - Eigenvalues and Eigenvectors Lecture 36 - Spectral Theorem Lecture 37 - Power Method Lecture 38 - Inverse Power Method Lecture 39 - QR Decomposition Lecture 40 - QR Method

 References Elementary Numerical Analysis Instructor: Prof. Rekha P. Kulkarni, Department of Mathematics, IIT Bombay. This course introduces the implementation and analysis of numerical algorithms for finding an approximate solution to a mathematical problem.