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)
