Numerical Analysis YK4M0KCQ4A

URI	`m2://res/YK4M0KCQ4A`
Kind	course
Creators	S. Baskar (instructor)
Date	2023-01-14
Scope	in
Ids	course 02qyf5152:111101165

Expressions

e1: edition

Language	en
Date	2023-01-14

m1: page, IIT Bombay (record). nptel 111101165
m2: page, 2023-01-14 (record). nptel 111101165

Contents

part 1: week-01
session 1: Week 1 : Lecture 1 : Introduction
session 2: Week 1 : Lecture 2 : Mathematical Preliminaries: Taylor Approximation
session 3: Week 1 : Lecture 3 : Mathematical Preliminaries: Order of Convergence
session 4: Week 1 : Lecture 4 : Arithmetic Error: Floating-point Approximation
session 5: Week 1 : Lecture 5 : Arithmetic Error: Significant Digits
session 6: Week 1 : Lecture 6 : Arithmetic Error: Condition Number and Stable Computation
part 2: week-02
session 7: Week 2 : Lecture 7 : Tutorial Session - 1: Problem Solving
session 8: Week 2 : Lecture 8 : Python Coding: Introduction
session 9: Week 2 : Lecture 9 : Linear Systems: Gaussian Elimination Method
session 10: Week 2 : Lecture 10 : Linear Systems: LU-Factorization (Doolittle and Crout)
session 11: Week 2 : Lecture 11 : Linear Systems: LU-Factorization (Cholesky)
part 3: week-03
session 12: Week 3 : Lecture 12 : Linear Systems: Operation Count for Direct Methods
session 13: Week 3 : Lecture 13 : Tutorial Session - 2: Python Coding for Naive Gaussian Elimination Method
session 14: Week 3 : Lecture 14 : Tutorial Session - 3: Python Coding for Thomas Algorithm
session 15: Week 3 : Lecture 15 : Matrix Norms: Subordinate Matrix Norms
session 16: Week 3 : Lecture 16 : Matrix Norms: Condition Number of a Matrix
part 4: week-04
session 17: Week 4 : Lecture 17 : Iterative Methods: Jacobi Method
session 18: Week 4 : Lecture 18 : Iterative Methods: Convergence of Jacobi Method
session 19: Week 4 : Lecture 19 : Iterative Methods: Gauss-Seidel Method
session 20: Week 4 : Lecture 20 : Iterative Methods: Convergence Analysis of Iterative Methods
session 21: Week 4 : Lecture 21 : Iterative Methods: Successive Over Relaxation Method
part 5: week-05
session 22: Week 5 : Lecture 22 : Tutorial Session - 4: Python implementation of Jacobi Method
session 23: Week 5 : Lecture 23 : Eigenvalues and Eigenvectors: Power Method (Construction)
session 24: Week 5 : Lecture 24 : Eigenvalues and Eigenvectors: Power Method (Convergence Theorem)
session 25: Week 5 : Lecture 25 : Eigenvalues and Eigenvectors: Gerschgorin's Theorem and Applications
session 26: Week 5 : Lecture 26 : Eigenvalues and Eigenvectors: Power Method (Inverse and Shifted Methods)
part 6: week-06
session 27: Week 6 : Lecture 27 : Nonlinear Equations: Overview
session 28: Week 6 : Lecture 28 : Nonlinear Equations: Bisection Method
session 29: Week 6 : Lecture 29 : Tutorial Session - 5: Implementation of Bisection Method
session 30: Week 6 : Lecture 30 : Nonlinear Equations: Regula-falsi and Secant Methods
session 31: Week 6 : Lecture 31 : Nonlinear Equations: Convergence Theorem of Secant Method
part 7: week-07
session 32: Week 7 : Lecture 32 : Nonlinear Equations: Newton-Raphson's method
session 33: Week 7 : Lecture 33 : Nonlinear Equations: Newton-Raphson's method (Convergence Theorem)
session 34: Week 7 : Lecture 34 : Nonlinear Equations: Fixed-point Iteration Methods
session 35: Lecture 35:Nonlinear Equations: Fixed-point Iteration Methods (Convergence)&Modified Newton's Method
session 36: Week 7 : Lecture 36 : Nonlinear Equations: System of Nonlinear Equations
part 8: week-08
session 37: Week 8 : Lecture 37 : Nonlinear Equations: Implementation of Newton-Raphson's Method as Python Code
session 38: Week 8 : Lecture 38 : Polynomial Interpolation: Existence and Uniqueness
session 39: Week 8 : Lecture 39 : Polynomial Interpolation: Lagrange and Newton Forms
session 40: Week 8 : Lecture 40 : Polynomial Interpolation: Newton’s Divided Difference Formula
session 41: Week 8 : Lecture 41 : Polynomial Interpolation: Mathematical Error in Interpolating Polynomial
part 9: week-09
session 42: Week 9 : Lecture 42 : Polynomial Interpolation: Arithmetic Error in Interpolating Polynomials
session 43: Week 9 : Lecture 43 : Polynomial Interpolation: Implementation of Lagrange Form as Python Code
session 44: Week 9 : Lecture 44: Polynomial Interpolation: Runge Phenomenon & Piecewise Polynomial Interpolation
session 45: Week 9 : Lecture 45 : Polynomial Interpolation: Hermite Interpolation
session 46: Week 9 : Lecture 46 : Polynomial Interpolation: Cubic Spline Interpolation
part 10: week-10
session 47: Week 10 : Lecture 47 : Polynomial Interpolation: Tutorial Session
session 48: Week 10 : Lecture 48 : Numerical Integration: Rectangle Rule
session 49: Week 10 : Lecture 49 : Numerical Integration: Trapezoidal Rule
session 50: Lecture 50 : Numerical Integration: Simpson's Rule
session 51: Week 10 : Lecture 51 : Numerical Integration: Gaussian Quadrature Rule
part 11: week-11
session 52: Week 11 : Lecture 52 : Numerical Integration: Tutorial Session
session 53: Week 11 : Lecture 53 : Numerical Differentiation: Primitive Finite Difference Formulae
session 54: Lecture 54 : Numerical Differentiation: Method of Undetermined Coefficients and Arithmetic Error
session 55: Week 11 : Lecture 55 : Numerical ODEs: Euler Methods
session 56: Week 11 : Lecture 56 : Numerical ODEs: Euler Methods (Error Analysis)
part 12: week-12
session 57: Week 12 : Lecture 57 : Numerical ODEs: Runge-Kutta Methods
session 58: Week 12 : Lecture 58 : Numerical ODEs: Modified Euler's Methods
session 59: Week 12 : Lecture 59 : Numerical ODEs: Multistep Methods
session 60: Week 12 : Lecture 60 : Numerical ODEs: Stability Analysis
session 61: Week 12 : Lecture 61 : Numerical ODEs: Two-point Boundary Value Problems
part 13: Live Session
session 62: Live Session 21-02-2024
session 63: Live Session 06-03-2025

Catalogue records

nptel: 111101165 (manifestation)
nptel_video: 111101165 (manifestation)