Abstract: When we first learn about applications of differential equations, we typically learn about quantities (distance, current, etc.) changing with respect to time. These are "ordinary differential equations", that is, equations with a single independent variable (time). Further applications will involve quantities that vary with respect to both time and space and are described by "partial differential equations", that is, equations with several independent variables (and involve partial derivatives).

For example, if a dye crystal is dropped into water, the resulting concentration visibly changes in time as it spreads out in space. The physical process is called "diffusion", and the the partial differential equation describing it is called the "diffusion equation".

This talk describes where the diffusion equation comes from, gives a bit of its history, and gives examples of simple solutions. Some third semester calculus will be used.

If you want to learn more about partial differential equations, try taking Math 483/683, which will be offered in Spring 2009 (see Professor Bocea).