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?)

Seriously, though, if you want to read an old, outdated textbook on the soon-to-be obsolete skill of computer software design, then yeah, go ahead and read SICP. ¬_¬

Scheme is still developed. And even though MIT has decided to obsolete it, Gerald Sussman has remarked that the book and the exercises within it are still "right-on" with modern computer science. There are also projects/wikis/ect. out there all over Internet land that are interpreting the exercises in languages other than Scheme.

So, I wouldn't consider it obsolete, but rather, SICP is entering a new era. An era where the people control the future of SICP and not MIT and its authors.