Arfken G.B., Weber H.J. Mathematical Methods for Physicists

5th ed. — Harcourt/Academic Press, 2001. — 994 p.Through five editions now, Mathematical Methods for Physicists has provided all the mathematical methods that aspiring physicists are likely to encounter as students and beginning researchers. More than enough material is included for a two-semester undergraduate or graduate course. The book is advanced in the sense that mathematical relations are almost always proven, in addition to being illustrated in terms of examples. These proofs are not what a mathematician would regard as rigorous, but sketch the ideas and emphasize the relations that are essential to the study of physics and related fields. This approach incorporates theorems that are usually not cited under the most general assumptions, but are tailored to the more restricted applications required by physics.
For example, Stokes's Theorem is usually applied by a physicist to a surface with the tacit understanding that it be simply connected. In this edition such assumptions have been made more explicit, starting in Chapter 1.