Summer Undergraduate Research Experience  >  Research Topics/Projects Available

Some important and interesting problems in mathematical physics today include using computers to simulate such things as air or fluid flow (for example, in the aerodynamics of a new aircraft), heat diffusion (for example applicable to how heat spreads over the tiles of a space shuttle on reentry) or sound made by a musical instrument. What these all have in common is that the physical situtations can be modelled mathematically using something called partial differential equations, or PDEs. Computers now make it possible to work with many PDE models without extensive prior mathematical background. In this project, we will select together one or more physical situtations of interest together with the appropriate PDEs and explore the tradeoffs in some of the different mathematical algorithms for solving them.

Needs calculus as far as partial derivatives (e.g., towards the beginning of Calc III) and needs to be comfortable working regularly with computers. The program MATLAB may prove ideal for calculations, but no specific prior knowledge is assumed, and other computer software could be used instead for someone with familiar with other software. No prior knowledge of differential equations is necessary.