Learn · NPTEL

Course11110116563 lectures

Numerical Analysis

Prof. S. Baskar · IIT Bombay

Start with lecture 1 At NPTEL

Lectures

week-01

  1. Week 1 : Lecture 1 : Introduction Video
  2. Week 1 : Lecture 2 : Mathematical Preliminaries: Taylor Approximation Video
  3. Week 1 : Lecture 3 : Mathematical Preliminaries: Order of Convergence Video
  4. Week 1 : Lecture 4 : Arithmetic Error: Floating-point Approximation Video
  5. Week 1 : Lecture 5 : Arithmetic Error: Significant Digits Video
  6. Week 1 : Lecture 6 : Arithmetic Error: Condition Number and Stable Computation Video

week-02

  1. Week 2 : Lecture 7 : Tutorial Session - 1: Problem Solving Video
  2. Week 2 : Lecture 8 : Python Coding: Introduction Video
  3. Week 2 : Lecture 9 : Linear Systems: Gaussian Elimination Method Video
  4. Week 2 : Lecture 10 : Linear Systems: LU-Factorization (Doolittle and Crout) Video
  5. Week 2 : Lecture 11 : Linear Systems: LU-Factorization (Cholesky) Video

week-03

  1. Week 3 : Lecture 12 : Linear Systems: Operation Count for Direct Methods Video
  2. Week 3 : Lecture 13 : Tutorial Session - 2: Python Coding for Naive Gaussian Elimination Method Video
  3. Week 3 : Lecture 14 : Tutorial Session - 3: Python Coding for Thomas Algorithm Video
  4. Week 3 : Lecture 15 : Matrix Norms: Subordinate Matrix Norms Video
  5. Week 3 : Lecture 16 : Matrix Norms: Condition Number of a Matrix Video

week-04

  1. Week 4 : Lecture 17 : Iterative Methods: Jacobi Method Video
  2. Week 4 : Lecture 18 : Iterative Methods: Convergence of Jacobi Method Video
  3. Week 4 : Lecture 19 : Iterative Methods: Gauss-Seidel Method Video
  4. Week 4 : Lecture 20 : Iterative Methods: Convergence Analysis of Iterative Methods Video
  5. Week 4 : Lecture 21 : Iterative Methods: Successive Over Relaxation Method Video

week-05

  1. Week 5 : Lecture 22 : Tutorial Session - 4: Python implementation of Jacobi Method Video
  2. Week 5 : Lecture 23 : Eigenvalues and Eigenvectors: Power Method (Construction) Video
  3. Week 5 : Lecture 24 : Eigenvalues and Eigenvectors: Power Method (Convergence Theorem) Video
  4. Week 5 : Lecture 25 : Eigenvalues and Eigenvectors: Gerschgorin's Theorem and Applications Video
  5. Week 5 : Lecture 26 : Eigenvalues and Eigenvectors: Power Method (Inverse and Shifted Methods) Video

week-06

  1. Week 6 : Lecture 27 : Nonlinear Equations: Overview Video
  2. Week 6 : Lecture 28 : Nonlinear Equations: Bisection Method Video
  3. Week 6 : Lecture 29 : Tutorial Session - 5: Implementation of Bisection Method Video
  4. Week 6 : Lecture 30 : Nonlinear Equations: Regula-falsi and Secant Methods Video
  5. Week 6 : Lecture 31 : Nonlinear Equations: Convergence Theorem of Secant Method Video

week-07

  1. Week 7 : Lecture 32 : Nonlinear Equations: Newton-Raphson's method Video
  2. Week 7 : Lecture 33 : Nonlinear Equations: Newton-Raphson's method (Convergence Theorem) Video
  3. Week 7 : Lecture 34 : Nonlinear Equations: Fixed-point Iteration Methods Video
  4. Lecture 35:Nonlinear Equations: Fixed-point Iteration Methods (Convergence)&Modified Newton's Method Video
  5. Week 7 : Lecture 36 : Nonlinear Equations: System of Nonlinear Equations Video

week-08

  1. Week 8 : Lecture 37 : Nonlinear Equations: Implementation of Newton-Raphson's Method as Python Code Video
  2. Week 8 : Lecture 38 : Polynomial Interpolation: Existence and Uniqueness Video
  3. Week 8 : Lecture 39 : Polynomial Interpolation: Lagrange and Newton Forms Video
  4. Week 8 : Lecture 40 : Polynomial Interpolation: Newton’s Divided Difference Formula Video
  5. Week 8 : Lecture 41 : Polynomial Interpolation: Mathematical Error in Interpolating Polynomial Video

week-09

  1. Week 9 : Lecture 42 : Polynomial Interpolation: Arithmetic Error in Interpolating Polynomials Video
  2. Week 9 : Lecture 43 : Polynomial Interpolation: Implementation of Lagrange Form as Python Code Video
  3. Week 9 : Lecture 44: Polynomial Interpolation: Runge Phenomenon & Piecewise Polynomial Interpolation Video
  4. Week 9 : Lecture 45 : Polynomial Interpolation: Hermite Interpolation Video
  5. Week 9 : Lecture 46 : Polynomial Interpolation: Cubic Spline Interpolation Video

week-10

  1. Week 10 : Lecture 47 : Polynomial Interpolation: Tutorial Session Video
  2. Week 10 : Lecture 48 : Numerical Integration: Rectangle Rule Video
  3. Week 10 : Lecture 49 : Numerical Integration: Trapezoidal Rule Video
  4. Lecture 50 : Numerical Integration: Simpson's Rule Video
  5. Week 10 : Lecture 51 : Numerical Integration: Gaussian Quadrature Rule Video

week-11

  1. Week 11 : Lecture 52 : Numerical Integration: Tutorial Session Video
  2. Week 11 : Lecture 53 : Numerical Differentiation: Primitive Finite Difference Formulae Video
  3. Lecture 54 : Numerical Differentiation: Method of Undetermined Coefficients and Arithmetic Error Video
  4. Week 11 : Lecture 55 : Numerical ODEs: Euler Methods Video
  5. Week 11 : Lecture 56 : Numerical ODEs: Euler Methods (Error Analysis) Video

week-12

  1. Week 12 : Lecture 57 : Numerical ODEs: Runge-Kutta Methods Video
  2. Week 12 : Lecture 58 : Numerical ODEs: Modified Euler's Methods Video
  3. Week 12 : Lecture 59 : Numerical ODEs: Multistep Methods Video
  4. Week 12 : Lecture 60 : Numerical ODEs: Stability Analysis Video
  5. Week 12 : Lecture 61 : Numerical ODEs: Two-point Boundary Value Problems Video

Live Session

  1. Live Session 21-02-2024 Video
  2. Live Session 06-03-2025 Video

Syllabus and materials

At NPTEL, as the course publishes them.

Credits and licence

Institution
IIT Bombay
Department
Mathematics
Teacher
Prof. S. Baskar
Level
Undergraduate
Language
English
Subjects
Mathematics
Source
NPTEL
Licence
CC BY-NC-SA, as NPTEL states it. Non-commercial use only. NPTEL's terms
Attribution
NPTEL states: "Distributed under Creative Commons Attribution-ShareAlike / CC BY - NC - SA", beside a BY-NC-SA badge.
Who can watch
NPTEL gives no rating. Invisible Network shows it to Tweens profiles and older, judged from what the source says about it. How courses are placed