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Computational Physics and Engineering

There are three great branches of science: theory, experiment, and computation.
Lloyd N. Trefethen FRS
Professor of Numerical Analysis
Fellow, Balliol College & Oxford Computing Lab
Oxford University, Oxford UK

  Day Topic Ref
1 Sep 01:Tu Introduction to Computational Modeling  
2 Sep 03:Th MATLAB Basics: 1 K1
    desktop environment & data classes  
3 Sep 08:Tu MATLAB Basics: 2 K1
    matrices & vectors  
4 Sep 10:Th MATLAB Basics: 3 K1
    functions & ow control  
5 Sep 15:Tu MATLAB Basics: 4 K1
    plotting  
6 Sep 17:Th Systems of Linear Equations : 1 K2
    existence, uniqueness, & ill conditioning  
7 Sep 22:Tu Systems of Linear Equations : 2 K2
    Gaussian elimination , lu, & banded matrices  
8 Sep 24:Th Systems of Linear Equations : 3 K2
    sparse matrix manipulations & iteration methods  
9 Sep 29:Tu Interpolation & Curve Fitting : 1 K3
    polynomial interpolation  
Test 1: systems of linear equations & basic MATLAB techniques
10 Oct 01:Th Interpolation & Curve Fitting : 2 K3
    least squares methods  
11 Oct 06:Tu Interpolation & Curve Fitting: 3 K3
    Fourier & Chebyshev interpolations  
12 Oct 08:Th Roots of Nonlinear Equations: 1 K4
    incremental search & bisection  
13 Oct 13:Tu Roots of Nonlinear Equations: 2 K4
    Brent's & Newton's methods  
14 Oct 15:Th Roots of Nonlinear Equations: 3 K4
    systems of nonlinear equations & Broyden's method  
  Oct 20:Tu Fall Break  
15 Oct 22:Th Numerical Differentiation : 1  
    finite difference approximation  
Test 2: curve fitting & nonlinear equations
16 Oct 27:Tu Numerical Differentiation: 2 K5
    Richardson extrapolation  
17 Oct 29:Th Quadrature: 1 K6
    Newton- Cotes formulas  
18 Nov 03:Tu Quadrature: 2 K6
    Gauss quadrature  
19 Nov 05 :Th Initial Value Ordinary Differential Equations: 1 K7
    Taylor series & Runge Kutta methods  
20 Nov 10:Tu Initial Value Ordinary Differential Equations : 2 K7
    stability & stiffness  
21 Nov 12:Th Initial Value Ordinary Differential Equations: 3 K7
    adaptive Runge Kutta methods  
22 Nov 17:Tu Initial Value Ordinary Differential Equations: 4 K7
    MATLAB functions - ode45, ode113, & ode15s  
23 Nov 19:Th Boundary Value Ordinary Differential Equations: 1 K8
    shooting method  
24 Nov 24:Tu Boundary Value Ordinary Differential Equations: 2 K8
    finite difference method  
  Nov 26:Th Thanksgiving  
25 Dec 01:Tu Boundary Value Ordinary Differential Equations: 3 K8
    MATLAB functions: bvp4c & bvp5c  
Test 3: quadrature & differential equations
26 Dec 03:Th Eigenvalue Problems: 1 K9
    introduction & Jacobi's method  
27 Dec 08:Tu Eigenvalue Problems: 2 K9
    power methods  
28 Dec 10:Th Eigenvalue Problems: 3 K9
    Householder transform  

K Kiusalaas, J. Numerical Methods in Engineering in ,
2005, (Cambridge University Press : Cambridge, UK).

Grading policy:
Take{home Tests (3 tests 20% each) 60%: Class participation 15%: Homework 25%.
In the absence of an adequate excuse, late homeworks will be penalized at a rate of 10 % per day.

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