This fall I'm teaching the "second half" of the standard entry-level undergraduate multivariable calculus course: the focus is on double and triple integrals, path integrals, Green's theorem, Stokes' theorem, and the divergence theorem. This is apparently not usually enough to fill the entire semester, and I'm told that other instructors often use the last two weeks or so to briefly introduce another topic, often a brief discussion of functions of a complex variable.

I seem to have free reign to do what I want with those last two weeks (within reason), so I thought I would solicit suggestions from MO. I would like to pick a topic that is at least somewhat related to the rest of the course; aside from the complex analysis idea I am also considering a brief introduction to Maxwell's equations. It should of course be suitable for undergraduate math, physics, engineering, and economics majors (mostly in their second year I think). Any ideas would be appreciated!

The question doesn't really have one correct answer, so I made it a community wiki. I realize that this is not really a research question, but I believe that it is likely to be relevant to many MO users and that the MO community is uniquely suited to answering it. I hope my record shows that I do not post questions on here lightly.

free rein$\endgroup$ – Yemon Choi Sep 2 '12 at 23:371more comment