Scientific Computing using Matlab

Overview

Syllabus 12

1. MATLAB
   • Introduction to Matlab
   • Plotting of Functions in Matlab
   • Symbolic Computation in Matlab
   • Functions definition in Matlab
   • In continuation of basics of Matlab
2. Module 2
   • In continuation of basics of Matlab (contd...)
   • Floating point representation of a number
   • Errors arithmetic
   • Iterative method for solving nonlinear equations
   • Bisection method for solving nonlinear equations
3. Module 3
   • Order of Convergence of an Iterative Method
   • Regula-Falsi and Secant Method for Solving Nonlinear Equations
   • Raphson method for solving nonlinear equations
   • Newton-Raphson Method for Solving Nonlinear System of Equations
   • Matlab Code for Fixed Point Iteration Method
4. Module 4
   • Matlab Code for Newton-Raphson and Regula-Falsi Method
   • Matlab Code for Newton Method for Solving System of Equations
   • Linear System of Equations
   • Linear System of Equations (contd.)
   • Gauss Elimination Method for solving Linear System of Equation
   • Matlab Code for Gauss Elimination Method
5. Module 5
   • LU Decomposition Method for Solving Linear System of Equations
   • LU Decomposition Method for Solving Linear System of Equations (contd.)
   • Iterative Method for Solving Linear System of Equations
   • Iterative Method for Solving Linear System of Equations (contd.)
   • Matlab Code for Gauss Jacobi Method
   • Matlab Code for Gauss Seidel Method
6. Module 6
   • Matlab Code for Gauss Seidel Method
   • Power Method for Solving Eigenvalues of a Matrix
   • Power Method for Solving Eigenvalues of a Matrix (Contd.)
   • Gershgorin Circle Theorem for Estimating Eigenvalues of a Matrix
   • Gershgorin Circle Theorem for Estimating Eigenvalues of a Matrix
   • Matlab Code for Power Method/ Shifted Inverse Power Method
7. Module 7
   • Interpolation
   • Interpolation (Contd.)
   • Interpolation (Contd.)
   • Interpolating Polynomial Using Newton's Forward Difference Formula
   • Error Estimates in Polynomial Approximation
   • Interpolating Polynomial Using Newton's Backward Difference Formula
8. Module 8
   • Stirling's Formula and Lagrange's Interpolating Polynomial
   • In Continuation of Lagrange's Interpolating Formula
   • Interpolating Polynomial Using Newton's Divided Difference Formula
   • Examples Based on Lagrange's and Newton's Divided Difference Interpolation
   • Spline Interpolation
   • Cubic Spline
9. Module 9
   • Cubic Spline (contd.)
   • Curve Fitting
   • Quadratic Polynomial Fitting and Code for Lagrange's Interpolating Polynomial using Octave
   • Matlab Code for Newton's Divided Difference and Least Square Approximation
   • Matlab Code for Cubic Spline
   • Numerical Differentiation
10. Module 10
    • Various Numerical Differentiation Formulas
    • Higher Order Accurate Numerical Differentiation Formula For First Order Derivative
    • Higher Order Accurate Numerical Differentiation Formula For Second Order Derivative
    • Numerical Integration
    • Trapezoidal Rule for Numerical Integration
    • Simpson's 1/3 rule for Numerical Integration
11. Module 11
    • Simpson's 3/8 Rule for Numerical Integration
    • Method of Undetermined Coefficients
    • Octave Code for Trapezoidal and Simpson's Rule
    • Taylor Series Method for Ordinary Differential Equations
    • Linear Multistep Method (LMM) for Ordinary Differential Equations
12. Module 12
    • Convergence and Zero Stability for LMM
    • Matlab/Octave Code for Initial Value Problems
    • Advantage of Implicit and Explicit Methods Over Each other via Matlab/Octave Codes for Initial value Problem

Advantages and disadvantages

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Taught by

• Prof. Mani Mehra, Prof. Vivek Kumar AggarwalIIT Delhi Delhi Technological University