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
- C. Chapra, Applied Numerical Methods with MATLAB for Engineers and Scientists, McGraw-Hill, (2017).
- Jaan Kiusalaas, Numerical Methods in Engineering with MATLAB (3e), Cambridge University Press, 2015
- R. Otto and J.P. Denier, An Introduction to Programming and Numerical Methods in MATLAB, Springer-Verlag London Limited 2005