AMAT 22292: Scientific Computing Using Appropriate Software II

Course Code : AMAT 22292

Title               : Scientific Computing using appropriate software II

Pre-requisites   : AMAT 21262

Co-requisites   : AMAT 22282

Learning Outcomes:

On completion of this unit, the student should be able to

• develop computer programs for curve fitting applications

• use software environment for numerical integration and optimization

• define function files for solving linear systems of equations

• solve initial value problems numerically.

Course Contents:

Curve Fitting: 

• Linear Least-Squares Regression, Linearization of nonlinear relationships: exponential, power and Saturation Growth Rate models, interpolation, extrapolation, interpolation hazards: multiple curve fitting.

Numerical Integration: 

• Trapezoidal, Simpson’s methods, Gauss quadrature.

Optimization: 

• One-Dimensional optimization and multidimensional optimization.

Solving Linear Systems: 

• Solving linear algebraic equations using the software, Direct methods: naive Gauss elimination, pivoting, Gauss Elimination as LU Factorization, Iterative methods: Jacobi method, Gauss-Seidel method, Richardson method, and SOR methods.

Initial-Value Problems: 

• Euler’s method, Heun’s method, Midpoint method, Runge Kutta Methods, adaptive methods for solving initial value problems, comparison of described methods. Appropriate built-in functions in the software environment for selected numerical methods.

Method of Teaching and Learning : A combination of lectures and computer laboratory sessions.

Assessment : Based on tutorials, tests and end of course examination.

Recommended Reading                

1. C. Chapra, Applied Numerical Methods with MATLAB for Engineers and Scientists, McGraw-Hill, (2017).

2. Jaan Kiusalaas, Numerical Methods in Engineering with MATLAB (3e), Cambridge University Press, 2015

3. R. Otto and J.P. Denier, An Introduction to Programming and Numerical Methods in MATLAB, Springer-Verlag London Limited 2005