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Course11110213765 lectures

Scientific Computing using Matlab

Prof. Mani Mehra Prof. Vivek K. Aggarwal · IIT Delhi Delhi Technological University

Start with lecture 1 At NPTEL

Lectures

MATLAB

  1. Introduction to Matlab Video
  2. Plotting of Functions in Matlab Video
  3. Symbolic Computation in Matlab Video
  4. Functions definition in Matlab Video
  5. In continuation of basics of Matlab Video

Module 2

  1. In continuation of basics of Matlab (contd...) Video
  2. Floating point representation of a number Video
  3. Errors arithmetic Video
  4. Iterative method for solving nonlinear equations Video
  5. Bisection method for solving nonlinear equations Video

Module 3

  1. Order of Convergence of an Iterative Method Video
  2. Regula-Falsi and Secant Method for Solving Nonlinear Equations Video
  3. Raphson method for solving nonlinear equations Video
  4. Newton-Raphson Method for Solving Nonlinear System of Equations Video
  5. Matlab Code for Fixed Point Iteration Method Video

Module 4

  1. Matlab Code for Newton-Raphson and Regula-Falsi Method Video
  2. Matlab Code for Newton Method for Solving System of Equations Video
  3. Linear System of Equations Video
  4. Linear System of Equations (contd.) Video
  5. Gauss Elimination Method for solving Linear System of Equation Video
  6. Matlab Code for Gauss Elimination Method Video

Module 5

  1. LU Decomposition Method for Solving Linear System of Equations Video
  2. LU Decomposition Method for Solving Linear System of Equations (contd.) Video
  3. Iterative Method for Solving Linear System of Equations Video
  4. Iterative Method for Solving Linear System of Equations (contd.) Video
  5. Matlab Code for Gauss Jacobi Method Video
  6. Matlab Code for Gauss Seidel Method Video

Module 6

  1. Matlab Code for Gauss Seidel Method Video
  2. Power Method for Solving Eigenvalues of a Matrix Video
  3. Power Method for Solving Eigenvalues of a Matrix (Contd.) Video
  4. Gershgorin Circle Theorem for Estimating Eigenvalues of a Matrix Video
  5. Gershgorin Circle Theorem for Estimating Eigenvalues of a Matrix Video
  6. Matlab Code for Power Method/ Shifted Inverse Power Method Video

Module 7

  1. Interpolation Video
  2. Interpolation (Contd.) Video
  3. Interpolation (Contd.) Video
  4. Interpolating Polynomial Using Newton's Forward Difference Formula Video
  5. Error Estimates in Polynomial Approximation Video
  6. Interpolating Polynomial Using Newton's Backward Difference Formula Video

Module 8

  1. Stirling's Formula and Lagrange's Interpolating Polynomial Video
  2. In Continuation of Lagrange's Interpolating Formula Video
  3. Interpolating Polynomial Using Newton's Divided Difference Formula Video
  4. Examples Based on Lagrange's and Newton's Divided Difference Interpolation Video
  5. Spline Interpolation Video
  6. Cubic Spline Video

Module 9

  1. Cubic Spline (contd.) Video
  2. Curve Fitting Video
  3. Quadratic Polynomial Fitting and Code for Lagrange's Interpolating Polynomial using Octave Video
  4. Matlab Code for Newton's Divided Difference and Least Square Approximation Video
  5. Matlab Code for Cubic Spline Video
  6. Numerical Differentiation Video

Module 10

  1. Various Numerical Differentiation Formulas Video
  2. Higher Order Accurate Numerical Differentiation Formula For First Order Derivative Video
  3. Higher Order Accurate Numerical Differentiation Formula For Second Order Derivative Video
  4. Numerical Integration Video
  5. Trapezoidal Rule for Numerical Integration Video
  6. Simpson's 1/3 rule for Numerical Integration Video

Module 11

  1. Simpson's 3/8 Rule for Numerical Integration Video
  2. Method of Undetermined Coefficients Video
  3. Octave Code for Trapezoidal and Simpson's Rule Video
  4. Taylor Series Method for Ordinary Differential Equations Video
  5. Linear Multistep Method (LMM) for Ordinary Differential Equations Video

Module 12

  1. Convergence and Zero Stability for LMM Video
  2. Matlab/Octave Code for Initial Value Problems Video
  3. Advantage of Implicit and Explicit Methods Over Each other via Matlab/Octave Codes for Initial value Problem Video

Syllabus and materials

At NPTEL, as the course publishes them.

Credits and licence

Institution
IIT Delhi Delhi Technological University
Department
Mathematics
Teacher
Prof. Mani Mehra Prof. Vivek K. Aggarwal
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. Coordinated by IIT Delhi.
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