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.