Math Textbooks

So, last semester I decided to go from being a physics major to a physics + pure math double major after taking a few high level math classes that I really liked (namely algebraic topology and real analysis.) The trouble is that I took less rigorous versions of multivariable calculus, partial differential equations, and complex analysis than I think I should have (they were more aimed at engineers + scientists than for mathematicians.)  So my query is if anyone here knows of texts which give a highly rigorous treatment of those topics aimed at people with previous exposure and also available as an e-book.  Sorry if I'm asking too much.  (Also, are there any other Physics+math guys here who can tell me if differential geometry is as useful for general relativity as I hear it is?)

>>1
It's better than nothing.  I hear mathematicians prefer positive definite metrics, which Lorentzian ones aren't.  That shouldn't matter too much.  A lot of GR is brute forcing Einstein's eq/geodesic equations.

>>5
I thought scheme's popularity died out decades ago?

>>10
He wasn't trolling /prog/...  gb2 /prog/ if you're so butthurt about it

Why is there such obsession over this book?  It/scheme sucked, except for comic value.