NPTEL : Elementary Numerical Analysis (Mathematics)

Co-ordinators : Prof. Rekha P. Kulkarni


Lecture 1 - Introduction

Lecture 2 - Polynomial Approximation

Lecture 3 - Interpolating Polynomials

Lecture 4 - Properties of Divided Difference

Lecture 5 - Error in the Interpolating polynomial

Lecture 6 - Cubic Hermite Interpolation

Lecture 7 - Piecewise Polynomial Approximation

Lecture 8 - Cubic Spline Interpolation

Lecture 9 - 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 - L U decomposition

Lecture 19 - Cholesky decomposition

Lecture 20 - Gauss Elimination with partial pivoting

Lecture 21 - Vector and Matrix Norms

Lecture 22 - Perturbed Linear Systems

Lecture 23 - Ill-conditioned Linear System

Lecture 24 - Tutorial 3

Lecture 25 - Effect of Small Pivots

Lecture 26 - Solution of Non-linear 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 Formulae

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 - Q R Decomposition

Lecture 40 - Q R Method