[18 Jan 2007]
Here’s an interesting article on the use of Mathematica to model the wave action of a tsunami.
Such a model involves a system of coupled partial differential equations. The computing power required for such calculations is awesome.
You may like to see an introduction to differential equations. That chapter does not get up to partial DEs, nor does it talk about systems of DEs, both of which are fascinating topics. But it does give you an idea of what differential equations are about and what they are used for.