Description:
| Aims: To continue to develop algorithm design and programming techniques in MATLAB.
To acquire a large variety of numerical and mathematical techniques to be used for those engineering problems modelled in terms of PDEs.
To provide a strong mathematical and computational foundation for solving equations arising in the modelling of engineering systems.
Learning Outcomes: On successful completion of this unit the student will have:
* Demonstrated a knowledge and understanding of how the various standard partial differential equations (PDEs) arise in engineering.
* Demonstrated a knowledge and understanding of the use of numerical and analytical techniques in the solution of such PDEs.
* Demonstrated a knowledge and understanding of the application of Fourier series and transforms.
Skills: Problem solving; numeracy; working independently.
Content: Fourier's equation of heat conduction, Laplace's equation and Poisson's equation: derivation, numerical solution and analytical solutions. The wave equation: derivation, D'Alembert's solution, separation of variables solution, numerical solution using Method of Characteristics. Fourier series: application in ODEs and PDEs governing various engineering systems. Fourier Transforms: definition, general results, application in solving ODEs and PDEs. Discrete Fourier transforms.
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