Asymptotic Expansions: Their Derivation and Interpretation, R.B. Dingle (Academic Press, 1973)

I could write a long review of this wonderful book.  But, instead you should read the review by his noted student Professor Sir Michael Berry.  As an added benefit of reading this review you can download a copy of this long out of print book.  If you are a physicist interested in wave propagation, this book is a book that you must have and use.

Irresistible Integrals - George Boros and Victor Moll, Cambridge 2004

This is a good companion to Interesting Integrals by Paul Nahin that I reviewed earlier this year.  If you are only going to buy one of them, the book by Nahin is the better option.  However, if you like to calculate integrals or just want to improve your skills you are going to want to own both.  Both books are ideal for building the skills you should have, but don't if your calculus class focused on using calculators.

If you like evaluating integrals you are in good company - G.H. Hardy couldn't resist a challenging integral.  If the books discussed in this post are too advanced for you, Hardy's Pure Mathematics is a good, rigorous introduction to calculus - it is much smaller than modern calculus textbooks, but you will learn more from it than you would from most modern calculus books.