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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