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?)

in most all schools i know of, math and physics for science and engineering majors are the top courses you can take. I haven't seen schools with a unique math course for, say, scientists and physicists, and another unique one for mathematicians. Mathematicians essentially count as scientists. they get BS degrees.