A better resource for vector calculus than Stewart? 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.]
 A: 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.
A: I have some recommendations to make.
First: Vector and Tensor Analysis with Applications, by Borisenko and Tarapov.
This is for good old classical vector analysis, with tensor analysis to boost. It has plenty of solved problems, physical intuition and even proofs for Green, Gauss and Stokes's theorems. It does not contain over 500 hundred problems that you'd find in an usual calculus book, though. They are more carefully selected. It is a Dover title, which is financially a plus.
Second: Mathematical Tools for Physics, by James Nearing.
This one's available for free. It is also a Dover title, which you can buy here. While it does not contain just vector calculus nor is it rigorous, it will build intuition and skill at using these tools in a variety of situations. There are two chapters devoted to Vector Calculus, the second focusing more on the computational part.
However, you can always go back to Apostol's Calculus, volume 2. It should contain everything you need (I haven't personally studied it, but that's the only calculus book I know that could combine rigor and plenty of exercises).
