This course is designed to prepare students who are interested to follow a program and/or a career in computational science and mathematical modeling. It covers the required background needed in those fields, such as linear algebra, solving ordinary and partial differential equation, interpolation and curve fitting, solving non-linear equations, optimization, matrices and eigenvalues, and Laplace and Fourier transform. It also prepares the students to implement these algorithms efficiently using computer or high-performance computing (HPC).
- W.Y. Yang, W. Cao, TS. Chung, J. Morris, “Applied Numerical Methods Using MATLAB®”, John Wiley & Sons, 2005.
- R.E. White, “Elements of Matrix Modeling and Computing with MATLAB®”, Chapman & Hall/CRC, 2007.
- V.G. Ganzha, E.V. Vorozhtsov, “Numerical Solutions for Partial Differential Equations – Problem Solving Using Mathematica®”, CRC Press, 1996.
- H.P. Langtangen, “Python Scripting for Computational Science (Texts in Computational Science and Engineering)”, Springer, 2010.
- W.H. Press, S.A. Teukolsky, W.T. Vetterling, B.P. Flannery, “Numerical Recipes 3rd Edition: The Art of Scientific Computing”, Cambridge University Press, 2007.
- Week 1: Series and Review. (PDF)
- Week 2: System of Linear Equations (PDF).
- Week 3: Interpolation and Curve Fitting (PDF).
- Week 4: Nonlinear Equations (PDF).
- Week 5 and 6: Numerical Differentiation/Integration.
- Week 7 and 8: Ordinary Differential Equations.
- Week 9 to 12: Partial Differential Equations.
- Week 13: Matrices and Eigenvalues.
- Week 14: Optimization.
- Week 15: Laplace and Fourier Transforms.