I am not really familiar with the US system, so this might be too advanced.

Maybe it would be interesting to discuss partial differential equations that can be reduced to ordinary differential equations, if one uses symmetries. Take the hydrogen atom for example: You get a decomposition in a radial and spherical part, the second can be solved by separation of variables. So you get three ordinary differential equations and their solution will give you a description of the hydrogen atom in non relativistic quantum mechanics.

There are of course a lot of other examples from physics, where similiar reasoning is applied.