MATHEMATICAL METHODS FOR PHYSICSTS (5TH ED)
Arfken (Miami U., Oxford, Ohio) and Weber (U. of Virginia) offer a textbook with more than enough material for a two-semester undergraduate or graduate course. They include proofs as well as examples of almost all the mathematical relations, though in some cases mathematicians would scoff at the level of rigor. Some of the theorems they incorporate are usually not cited under the most general assumptions, but are tailored to the more restricted applications required by physics. Earlier editions appeared between 1966 and 1995; the fifth is revised to account for changes not so much in the field as in the content of standard courses.