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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).