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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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