Lecture 1 - Introduction
Lecture 2 - Mathematical Preliminaries: Taylor Approximation
Lecture 3 - Mathematical Preliminaries: Order of Convergence
Lecture 4 - Arithmetic Error: Floating-point Approximation
Lecture 5 - Arithmetic Error: Significant Digits
Lecture 6 - Arithmetic Error: Condition Number and Stable Computation
Lecture 7 - Tutorial Session-1: Problem Solving
Lecture 8 - Python Coding: Introduction
Lecture 9 - Linear Systems: Gaussian Elimination Method
Lecture 10 - Linear Systems: LU-Factorization (Doolittle and Crout)
Lecture 11 - Linear Systems: LU-Factorization (Cholesky)
Lecture 12 - Linear Systems: Operation Count for Direct Methods
Lecture 13 - Tutorial Session-2: Python Coding for Naive Gaussian Elimination Method
Lecture 14 - Tutorial Session-3: Python Coding for Thomas Algorithm
Lecture 15 - Matrix Norms: Subordinate Matrix Norms
Lecture 16 - Matrix Norms: Condition Number of a Matrix
Lecture 17 - Iterative Methods: Jacobi Method
Lecture 18 - Iterative Methods: Convergence of Jacobi Method
Lecture 19 - Iterative Methods: Gauss-Seidel Method
Lecture 20 - Iterative Methods: Convergence Analysis of Iterative Methods
Lecture 21 - Iterative Methods: Successive Over Relaxation Method
Lecture 22 - Tutorial Session-4: Python implementation of Jacobi Method
Lecture 23 - Eigenvalues and Eigenvectors: Power Method (Construction)
Lecture 24 - Eigenvalues and Eigenvectors: Power Method (Convergence Theorem)
Lecture 25 - Eigenvalues and Eigenvectors: Gerschgorin's Theorem and Applications
Lecture 26 - Eigenvalues and Eigenvectors: Power Method (Inverse and Shifted Methods)
Lecture 27 - Nonlinear Equations: Overview
Lecture 28 - Nonlinear Equations: Bisection Method
Lecture 29 - Tutorial Session-5: Implementation of Bisection Method
Lecture 30 - Nonlinear Equations: Regula-falsi and Secant Methods
Lecture 31 - Nonlinear Equations: Convergence Theorem of Secant Method
Lecture 32 - Nonlinear Equations: Newton-Raphson's method
Lecture 33 - Nonlinear Equations: Newton-Raphson's method (Convergence Theorem)
Lecture 34 - Nonlinear Equations: Fixed-point Iteration Methods
Lecture 35 - Nonlinear Equations: Fixed-point Iteration Methods (Convergence) and Modified Newton's Method
Lecture 36 - Nonlinear Equations: System of Nonlinear Equations
Lecture 37 - Nonlinear Equations: Implementation of Newton-Raphson's Method as Python Code
Lecture 38 - Polynomial Interpolation: Existence and Uniqueness
Lecture 39 - Polynomial Interpolation: Lagrange and Newton Forms
Lecture 40 - Polynomial Interpolation: Newton’s Divided Difference Formula
Lecture 41 - Polynomial Interpolation: Mathematical Error in Interpolating Polynomial
Lecture 42 - Polynomial Interpolation: Arithmetic Error in Interpolating Polynomials
Lecture 43 - Polynomial Interpolation: Implementation of Lagrange Form as Python Code
Lecture 44 - Polynomial Interpolation: Runge Phenomenon and Piecewise Polynomial Interpolation
Lecture 45 - Polynomial Interpolation: Hermite Interpolation
Lecture 46 - Polynomial Interpolation: Cubic Spline Interpolation
Lecture 47 - Polynomial Interpolation: Tutorial Session
Lecture 48 - Numerical Integration: Rectangle Rule
Lecture 49 - Numerical Integration: Trapezoidal Rule
Lecture 50 - Numerical Integration: Simpson's Rule
Lecture 51 - Numerical Integration: Gaussian Quadrature Rule
Lecture 52 - Numerical Integration: Tutorial Session
Lecture 53 - Numerical Differentiation: Primitive Finite Difference Formulae
Lecture 54 - Numerical Differentiation: Method of Undetermined Coefficients and Arithmetic Error
Lecture 55 - Numerical ODEs: Euler Methods
Lecture 56 - Numerical ODEs: Euler Methods (Error Analysis)
Lecture 57 - Numerical ODEs: Runge-Kutta Methods
Lecture 58 - Numerical ODEs: Modified Euler's Methods
Lecture 59 - Numerical ODEs: Multistep Methods
Lecture 60 - Numerical ODEs: Stability Analysis
Lecture 61 - Numerical ODEs: Two-point Boundary Value Problems
