NPTEL : NOC:Numerical Methods for Engineers (Multi-Disciplinary)

Co-ordinators : Dr. Niket S.Kaisare


Lecture 1 - Introduction

Lecture 2 - Overview of Learning Modules

Lecture 3 - Course Plan

Lecture 4 - Tutorial: Excel

Lecture 5 - Errors and Approximations

Lecture 6 - Truncation and Round-Off Errors

Lecture 7 - Binary Numbers: Introduction

Lecture 8 - Floating Point: Real numbers in decimal system

Lecture 9 - Floating Point in Binary system

Lecture 10 - Iterative Method

Lecture 11 - Direct Method

Lecture 12 - Sequential Method

Lecture 13 - Linear Algebra: Basics

Lecture 14 - Introduction to Linear Equations

Lecture 15 - Rank Condition for Solving Linear Equations

Lecture 16 - Motivating Gauss Elimination

Lecture 17 - Gauss Elimination

Lecture 18 - Tutorial Recap: Gauss Elimination

Lecture 19 - Back Substitution to find solution

Lecture 20 - Gauss Jordan and LU Decomposition

Lecture 21 - Partial Pivoting in Gauss Elimination

Lecture 22 - Analysis of Gauss Elimination

Lecture 23 - Tri-Diagonal Systems: Practical Relevance

Lecture 24 - Thomas Algorithm for Tri-Diagonal Systems

Lecture 25 - Gauss Siedel Method

Lecture 26 - Analysis of Gauss Siedel Method

Lecture 27 - Gauss Siedel vs. Jacobi Methods

Lecture 28 - Bonus: Example using MS Excel

Lecture 29 - Summary: Linear Equations

Lecture 30 - Introduction to Nonlinear Equations

Lecture 31 - Bisection Method

Lecture 32 - Analysis of Bisection Method

Lecture 33 - Bonus: Excel Solution for Bisection Method

Lecture 34 - Regula-Falsi Method

Lecture 35 - Bonus: Excel Solution for Regula-Falsi Method

Lecture 36 - Regula-Falsi vs. Secant Method

Lecture 37 - Bonus: Excel Solution for Secant Method

Lecture 38 - Some special cases

Lecture 39 - Fixed-Point Iteration

Lecture 40 - Newton-Raphson Method

Lecture 41 - Analysis of Fixed-Point Iteration

Lecture 42 - Analysis of Newton-Raphson

Lecture 43 - Problems with Newton-Raphson

Lecture 44 - Multi-Variable Fixed-Point Iteration

Lecture 45 - Multi-Variable Newton-Raphson

Lecture 46 - Out of Syllabus: Improvements to NR Methods

Lecture 47 - Out of Syllabus: Roots of a polynomial

Lecture 48 - Summary

Lecture 49 - Introduction: Regression and Interpolation

Lecture 50 - Linear Regression in One Variable

Lecture 51 - Recap: Formula for Linear Regression

Lecture 52 - Bonus: Linear Regression using MS-Excel

Lecture 53 - Linear Regression in Multiple Variables

Lecture 54 - Matrix Method for Multi-Linear Regression

Lecture 55 - Polynomial Regression

Lecture 56 - Functional Regression

Lecture 57 - Bonus: X-Y versus Y-X data (Using MS Excel)

Lecture 58 - Interpolation: Introduction and A Naïve Extension

Lecture 59 - Bonus: MS-Excel for Naïve Interpolation

Lecture 60 - Lagrange Interpolating Polynomials

Lecture 61 - Newton's Forward Difference Polynomial

Lecture 62 - Newton's Divided Differences: Derivation

Lecture 63 - Interpolation Examples

Lecture 64 - Bonus: MS-Excel for Newton's Polynomial

Lecture 65 - Summary: Regression and Interpolation

Lecture 66 - Numerical Differentiation: Introduction

Lecture 67 - Numerical Differentiation Formula and Analysis

Lecture 68 - Derivation using Method of undetermined coefficients

Lecture 69 - Three-point differentiation formulae

Lecture 70 - Bonus: Differentiation using MS-Excel

Lecture 71 - Truncation vs. Round-Off Errors

Lecture 72 - Numerical Differentiation Examples

Lecture 73 - Summary of Numerical Differentiation

Lecture 74 - Numerical Integration: Introduction

Lecture 75 - Trapezoidal rule and Derivation

Lecture 76 - Simpson's Rules for Integration

Lecture 77 - Bonus: MS-Excel for Numerical Integration

Lecture 78 - Error Analysis for Simpson's Rules

Lecture 79 - Numerical Integration Examples

Lecture 80 - Bonus: Integration using MS-Excel

Lecture 81 - Summary of Newton Cotes Formulae

Lecture 82 - Richardson's Extrapolation

Lecture 83 - Gauss Quadrature

Lecture 84 - Summary of Numerical Integration

Lecture 85 - Introduction to ODE-IVP

Lecture 86 - Motivation using an Example (Bonus)

Lecture 87 - Euler's Methods and Second-Order Methods

Lecture 88 - Second-Order Runge-Kutta Methods

Lecture 89 - Summary of RK-2

Lecture 90 - Higher order RK Methods

Lecture 91 - Bonus: ODE-IVP using MS-Excel

Lecture 92 - Bonus: RK-2 and RK-4 Methods using MS-Excel

Lecture 93 - Summary and Recap

Lecture 94 - Introduction to Predictor-Corrector Methods

Lecture 95 - Stability of Implicit Methods: Overview

Lecture 96 - Stability Analysis of Euler's Methods

Lecture 97 - Extension to multiple variables

Lecture 98 - Local vs. Global Truncation Errors

Lecture 99 - Richardson's Extrapolation

Lecture 100 - Stiff System of ODEs: Introduction

Lecture 101 - Adaptive Step-sizing

Lecture 102 - Adaptive step-sizing and Embedded Methods

Lecture 103 - Bonus: Errors and Extrapolation using MS-Excel

Lecture 104 - Summary and Recap (Weeks 10 and 11)

Lecture 105 - Introduction to ODE-BVP

Lecture 106 - Shooting Method: An Overview

Lecture 107 - Finite Difference Method: An Overview

Lecture 108 - Solution using Shooting Method

Lecture 109 - Algorithm for Shooting Method

Lecture 110 - Problems with Shooting Method

Lecture 111 - Solving ODE-BVP using Finite Difference Method

Lecture 112 - Microsoft Excel based Solution

Lecture 113 - Recap of Week-12 (ODE-BVP)