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Course11110610154 lectures

Numerical Analysis

Prof. R. Usha · IIT Madras

Start with lecture 1 At NPTEL

Lectures

Week 1

  1. Lesson 1 - Introduction , Motivation Video
  2. Lesson 2 - Part 1 - Mathematical Preliminaries , Polynomial Interpolation – 1 Video
  3. Lesson 2 - Part 2 - Mathematical Preliminaries , Polynomial Interpolation – 1 Video
  4. Lesson 3 - Part 1 - Polynomial Interpolation – 2 Video
  5. Lesson 3 - Part 2 - Polynomial Interpolation – 2 Video
  6. Lesson 4 - Polynomial Interpolation – 3 Video

Week 2

  1. Lagrange Interpolation Polynomial , Error In Interpolation - 1 Video
  2. Lagrange Interpolation Polynomial ; Error In Interpolation - 1 Video
  3. Error In Interpolation - 2 Video
  4. Error In Interpolation 2 Video
  5. Divide Difference Interpolation Polynomial Video
  6. Properties Of Divided Difference , Introduction To Inverse Interpolation Video
  7. Properties Of Divided Difference Introduction To Inverse Interpolation Video

Week 3

  1. Inverse Interpolation , Remarks on Polynomial Interpolation Video
  2. Numerical Differentiation - 1 Taylor Series Method Video
  3. Numerical Differentiation - 2 Method Of Undetermined Coefficients Video
  4. Numerical Differentiation - 2 Polynomial Interpolation Method Video
  5. Numerical Differentiation - 3 Operator Method Numerical Integration - 1 Video

Week 4

  1. Numerical Integration - 2 Error in Trapezoidal Rule Simpson's Rule Video
  2. Numerical Integration - 3 Error in Simpson's Rule Composite in Trapezoidal Rule , Error Video
  3. Numerical Integration - 4 Composite Simpsons Rule , Error Method of Undetermined Coefficients Video
  4. Numerical Integration - 5 Gaussian Quadrature (Two-Point Method) Video

Week 5

  1. Numerical Integrature - 5 Gaussian Quadrature (Three-Point Method) Adaptive Quadrature Video
  2. Numerical Solution of Ordinary Differential Equation (ODE) - 1 Video
  3. Numerical Solution Of ODE - 2 Stability , Single-Step Methods - 1 Taylor Series Method Video
  4. Numerical Solution Of ODE - 3 Examples of Taylor Series Method Euler's Method Video

Week 6

  1. Numerical Solution Of ODE-4 Runge-Kutta Methods Video
  2. Numerical Solution Of ODE-5 Example For RK-Method Of Order 2 Modified Euler's Method Video
  3. Numerical Solution Of Ordinary DifferentialEquations- 6 Predictor-Corrector Methods (Adam-Moulton) Video
  4. Numerical Solution Of Ordinary DifferentialEquations- 7 Video

Week 7

  1. Numerical Solution Of Differential Equations - 8 Video
  2. Numerical Solution of Ordinary Differential Equations - 9 Video
  3. Numerical Solution of Ordinary Differential Equations - 10 Video
  4. Numerical Solution of Ordinary Differential Equations - 11 Video

Week 8

  1. Root Finding Methods - 1 The Bisection Method - 1 Video
  2. Root Finding Methods - 2 The Bisection Method - 2 Video
  3. Root Finding Methods - 3 Newton-Raphson Method - 1 Video
  4. Root Finding Methods - 4 Newton-Raphson Method - 2 Video

Week 9

  1. Root Finding Methods - 5 Secant Method, Method Of false Position Video
  2. Root Finding Methods - 6 Fixed Point Methods - 1 Video
  3. Root Finding Methods - 7 Fixed Point Methods - 2 Video
  4. Root Finding Methods - 8 Fixed Point Iteration Methods - 3 Video

Week 10

  1. Root Finding Methods - 9 Practice Problems Video
  2. Solution Of Linear Systems Of Equations - 1 Video
  3. Solution Of Linear Systems Of Equations - 2 Video
  4. Solution Of Linear Systems Of Equations - 3 Video

Week 11

  1. Solution Of Linear Systems Of Equations - 4 Video
  2. Solution Of Linear Systems Of Equations - 5 Video
  3. Solution Of Linear Systems Of Equations - 6 Video
  4. Solution Of Linear Systems Of Equations - 7 Video

Week 12

  1. Solutions Of Linear Systems Of Equations - 8 Iterative Method - 1 Video
  2. Solutions Of Linear Systems Of Equations - 8 Iterative Method - 2 Video
  3. Matrix Eigenvalue Problems - 2 Power Method - 2 Video
  4. Practice Problems Video

Syllabus and materials

At NPTEL, as the course publishes them.

Credits and licence

Institution
IIT Madras
Department
Mathematics
Teacher
Prof. R. Usha
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.
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