Introduction - Computational Techniques

Preview 17:38

Meet the TAs - Intro 1

Preview 01:00

Meet the TAs - Intro 2

Preview 01:02

Overview of Learning Modules

Preview 08:56

Course Plan

Preview 05:23

Tutorial: Excel

Preview 16:41

Errors and Approximations

Preview 09:05

Truncation and Round-Off Errors

Preview 09:19

Binary Numbers: Introduction

Preview 05:15

Floating Point: Real numbers in decimal system

Preview 19:19

Floating Point in Binary system

Preview 08:20

Iterative Method

Preview 17:56

Direct Method

Preview 10:25

Sequential Method

Preview 15:56

Linear Algebra: Basics

Preview 10:20

Introduction to Linear Equations

Preview 15:26

Rank Condition for Solving Linear Equations

Preview 08:22

Motivating Gauss Elimination

Preview 17:07

Gauss Elimination

Preview 28:20

Tutorial Recap: Gauss Elimination

Preview 07:21

Back Substitution to find solution

Preview 08:03

Gauss Jordan and LU Decomposition

Preview 42:53

Partial Pivoting in Gauss Elimination

Preview 21:22

Analysis of Gauss Elimination

Preview 28:00

Tri-Diagonal Systems: Practical Relevance

Preview 16:32

Thomas Algorithm for Tri-Diagonal Systems

Preview 12:43

Gauss Siedel Method

Preview 13:10

Analysis of Gauss Siedel Method

Preview 11:59

Gauss Siedel vs. Jacobi Methods

Preview 11:02

Bonus: Example using MS Excel

Preview 16:14

Summary: Linear Equations

Preview 05:29

Introduction to Nonlinear Equations

Preview 14:29

Bisection Method

Preview 15:07

Analysis of Bisection Method

Preview 13:57

Bonus: Excel Solution for Bisection Method

Preview 11:55

Regula-Falsi Method

Preview 10:04

Bonus: Excel Solution for Regula-Falsi Method

Preview 10:30

Regula-Falsi vs. Secant Method

Preview 12:41

Bonus: Excel Solution for Secant Method

Preview 07:50

Some special cases

Preview 08:12

Fixed-Point Iteration

Preview 17:06

Newton-Raphson Method

Preview 15:09

Analysis of Fixed-Point Iteration

Preview 11:24

Analysis of Newton-Raphson

Preview 14:32

Problems with Newton-Raphson

Preview 08:27

Multi-Variable Fixed-Point Iteration

Preview 18:44

Multi-Variable Newton-Raphson

Preview 12:15

Out of Syllabus: Improvements to NR Methods

Preview 18:17

Out of Syllabus: Roots of a polynomial

Preview 33:27

Summary

Preview 16:26

Introduction: Regression and Interpolation

Preview 18:38

Linear Regression in One Variable

Preview 26:03

Recap: Formula for Linear Regression

Preview 03:09

Bonus: Linear Regression using MS-Excel

Preview 13:53

Linear Regression in Multiple Variables

Preview 16:13

Matrix Method for Multi-Linear Regression

Preview 10:37

Polynomial Regression

Preview 14:51

Functional Regression

Preview 10:14

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

Preview 20:44

Interpolation: Introduction & A Naïve Extension

Preview 07:39

Bonus: MS-Excel for Naïve Interpolation

Preview 25:59

Lagrange Interpolating Polynomials

Preview 13:23

Newton's Forward Difference Polynomial

Preview 15:53

Newton's Divided Differences: Derivation

Preview 15:45

Interpolation Examples

Preview 22:21

Bonus: MS-Excel for Newton's Polynomial

Preview 20:41

Summary: Regression and Interpolation

Preview 04:41

Numerical Differentiation: Introduction

Preview 09:24

Numerical Differentiation Formula and Analysis

Preview 18:11

Derivation using "Method of undetermined coefficients"

Preview 12:15

Three-point differentiation formulae

Preview 09:14

Bonus: Differentiation using MS-Excel

Preview 19:15

Truncation vs. Round-Off Errors

Preview 15:58

Numerical Differentiation Examples

Preview 12:28

Summary of Numerical Differentiation

Preview 06:23

Numerical Integration: Introduction

Preview 10:44

Trapezoidal rule and Derivation

Preview 20:14

Simpson's Rules for Integration

Preview 21:48

Bonus: MS-Excel for Numerical Integration

Preview 12:01

Error Analysis for Simpson's Rules

Preview 20:50

Numerical Integration Examples

Preview 20:10

Bonus: Integration using MS-Excel

Preview 26:30

Summary of "Newton Cotes" Formulae

Preview 07:29

Richardson's Extrapolation

Preview 25:38

Gauss Quadrature

Preview 14:38

Summary of Numerical Integration

Preview 08:52

Introduction to ODE-IVP

Preview 16:03

Motivation using an Example (Bonus)

Preview 14:21

Euler's Methods and Second-Order Methods

Preview 17:36

Second-Order Runge-Kutta Methods

Preview 44:24

Summary of RK-2

Preview 12:16

Higher order RK Methods

Preview 12:29

Bonus: ODE-IVP using MS-Excel

Preview 22:50

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

Preview 36:57

Summary and Recap

Preview 17:30

Introduction to Predictor-Corrector Methods

Preview 21:15

Stability of Implicit Methods: Overview

Preview 15:26

Stability Analysis of Euler's Methods

Preview 25:23

Extension to multiple variables

Preview 10:49

Local vs. Global Truncation Errors

Preview 14:49

Richardson's Extrapolation

Preview 11:57

Stiff System of ODEs: Introduction

Preview 11:43

Adaptive Step-sizing

Preview 12:03

Adaptive step-sizing and Embedded Methods

Preview 19:04

Bonus: Errors and Extrapolation using MS-Excel

Preview 23:14

Summary and Recap (Weeks 10 and 11)

Preview 13:18

Introduction to ODE-BVP

Preview 14:14

Shooting Method: An Overview

Preview 22:48

Finite Difference Method: An Overview

Preview 12:28

Solution using Shooting Method

Preview 30:47

Algorithm for Shooting Method

Preview 09:34

Problems with Shooting Method

Preview 20:07

Solving ODE-BVP using Finite Difference Method

Preview 10:53

Microsoft Excel based Solution

Preview 14:54

Recap of Week-12 (ODE-BVP)

Preview 02:43

Live Session 03-10-2019

Preview 41:58

Live Session 29-08-2019

Preview 38:20