# Elementary Numerical Analysis

### Course Description

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.

Source: Duke University
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### Video Lectures & Study Materials

Visit the official course website for more study materials: http://nptel.ac.in/syllabus/syllabus.php?subjectId=111101003

# Lecture Play Lecture
I. Polynomials and Piecewise Polynomial Interpolation
1 Introduction (0050:24) Play Video
2 Polynomial Approximation (0048:35) Play Video
3 Interpolating Polynomials (0049:37) Play Video
4 Properties of Divided Difference (0050:01) Play Video
5 Error in the Interpolating Polynomial (0049:45) Play Video
6 Cubic Hermite Interpolation (0050:16) Play Video
7 Piecewise Polynomial Approximation (0047:58) Play Video
8 Cubic Spline Interpolation (0047:47) Play Video
9 Tutorial 1 (0051:55) Play Video
II. Numerical Integration
10 Numerical Integration: Basic Rules (0049:41) Play Video
11 Composite Numerical Integration (0046:42) Play Video
12 Gauss 2-point Rule: Construction (0054:50) Play Video
13 Gauss 2-point Rule: Error (0045:21) Play Video
14 Convergence of Gaussian Integration (0048:49) Play Video
15 Tutorial 2 (0052:53) Play Video
III. Numerical Differentiation
16 Numerical Differentiation (0049:10) Play Video
17 Gaussian Elimination (0046:38) Play Video
IV. Vector and Matrix Norms
18 LU Decomposition (0046:26) Play Video
19 Cholesky Decomposition (0047:18) Play Video
V. Solution of System of Linear Equations
20 Gauss Elimination with Partial Pivoting (0045:00) Play Video
21 Vector and Matrix Norms (0048:51) Play Video
22 Perturbed Linear Systems (0048:29) Play Video
23 ILL-conditioned Linear System (0048:35) Play Video
24 Tutorial 3 (0045:21) Play Video
25 Effect of Small Pivots (0047:48) Play Video
VI. Solution of Nonlinear System of Equations
26 Solution of Non-linear Equations (0048:38) Play Video
27 Quadratic Convergence of Newton's Method (0047:24) Play Video
28 Jacobi Method (0051:43) Play Video
29 Gauss-Seidel Method (0048:52) Play Video
30 Tutorial 4 (0046:27) Play Video
VII. Initial Value Problems
31 Initial Value Problem (0051:04) Play Video
32 Multi-step Methods (0050:40) Play Video
33 Predictor-Corrector Formulae (0047:45) Play Video
VIII. Boundary Value Problem
34 Boundary Value Problems (0050:35) Play Video
35 Eigenvalues and Eigenvectors (0048:20) Play Video
36 Spectral Theorem (0048:13) Play Video
37 Power Method (0049:48) Play Video
38 Inverse Power Method (0049:59) Play Video
39 QR Decomposition (0049:53) Play Video
40 QR Method (0048:43) Play Video

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