# GL(s,R)

## January 17, 2011

### A multivariable calculus list

In addition to my calculus course this semester, I also get to teach a multivariable calculus course with only six students. I’ll start with the standard list for those interested in that sort of thing.

Spring 2011 Multivariable Calculus Standards List

Let me admit something, here, in between two documents—less likely to read in here—about teaching this course, now for the third time: I’m a fraud. That’s right, I’m a fake, a charlatan, an impostor. I’ve created a counterfeit course and hustle the students with a dash of hocus-pocus and a sprinkle of hoodwinking. It is only through mathematical guile that my misrepresentations, chicanery and flim-flam go unnoticed. In short, and in the passing Christmas spirit, I am a humbug. This is a physics course. It should be taught be someone proficient in physics, someone with honed intuition about the geometry of abstract mathematical notions like div, grad, curl and all that, someone who sees everything as an application of Stokes’ theorem and has strong feelings about whether it should be written Stokes’ theorem or Stokes’s theorem. About the only thing I bring to the table is that I can teach students to remember that:

$\mathrm{curl}(\mathbf{F}) = \nabla \times \mathbf{F}$

and

$\mathrm{div}(\mathbf{F}) = \nabla \cdot \mathbf{F}$