Category Archives: Applied Mathematics

Natural Ventilation

The study of how to ventilate a room without recourse to air conditioning has practical application to theatres and libraries where all but the quietest noise has to be avoided.   This project examines how classical fluid dynamics aids this practical application. You could be using complex analysis through mapping and solving partial differential equations in

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Non-linear Waves

This project concerns deriving equations that govern the propagation of waves on water, then solving them. These equations have two well-known solutions, the solitary wave (or soliton) and cnoidal waves. Some of the mathematics is quite involved but the satisfaction comes in being able to describe known observable wave phenomena. There is some opportunity for

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Waves

Wave motion is found everywhere: sound waves, water waves, electromagnetic waves, traffic waves and Mexican waves are just some examples. The mathematical description of wave motion can be fairly straightforward, as with the oscillations of a guitar string for example, but as more physical effects are allowed for the theory becomes more complicated. In this

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Chebychev Polynomials

In this project the aim is to study the mathematical properties of Chebychev polynomials and their role in numerical approximation. The concept of ‘good’ and ‘best’ numerical approximations and the Remes algorithm will be investigated and, if time permits, further applications of Chebychev polynomials could be considered. This project is mainly analytical but would involve

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Numerical methods for PDE’s

Partial differential equations describe how the three/four dimensional world works. Solving such equations is the key to understanding the behaviour of many physical, chemical, biological or financial systems. A large range of numerical methods is available to solve such problems (for example finite difference, finite element, finite volume, boundary element or pseudo-spectral methods to name

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