AMAT 22292: Scientific Computing using appropriate software II

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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
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