I took the Math GRE Subject Test last October and tried to relearn vector calculus via the current edition of Stewart's text.
I thought, to put it lightly, that the exposition was atrocious and unmotivated, with too much of a focus on memorizing the equations needed to solve problems. I did do well on the calculus questions on the Subject Test [I think], but if I need to teach myself vector calculus again, I can't use Stewart to do it.
What do you all recommend for a good rigorous, motivational text on vector calculus? I need the book to cover Green's Theorem [which I've noticed, for example, Kline's text does not cover].
[This is one of those times that I wished Spivak covered vector calculus.]
Best Answer
I quite liked the way that Leithold covered line integrals. It might be worth taking a look at the rest. In my opinion, better than books, is the course given in MIT, by prof. Denis Auroux, which is available online. I taught myself multivariable calculus using these videos before, and it was most probably the easiest subject I had in university because of that. I really recommend seeing other subjects there too.