Lately I've been working (again) on understanding multi-variable calculus. I always wished I had time to cover this material in college, but I took lots of courses in biochemistry and molecular biology instead. I wanted to put up the best resources I've found for this so far.
First, and no surprise, the ocw videos at MIT by Denis Auroux (here). I am currently at #25, about to jump off into integrals in 3D space. (It's my second time to get this far). This time I think I really have everything under control. The proof of Green's theorem was perfect, a kind of mathematical satori.
I also work through everything in Gilbert Strang's book as well. I need to read carefully there, because he's so concise, but his insight is just incredible. Check out the proof of the flux version of Green's theorem.
Two more are recently discovered resources that are especially helpful because they develop everything slowly but completely:
Paul's lecture notes
A beautiful set of pages from someone at U Minnesota
All highly recommended.
