[.ca] Modern Mathematical Methods for Physicists and Engineers (ISBN 0521598273)

Highly recommended:
Of all the "mathematical methods" or "applied mathematics" books on my shelf, this is the one I find myself turning to most often. There are many other books where you can look up, say, the orthogonality properties of some "special function," but for an authoritative explanation of fundamental mathematics as used in physics today -- especially computational physics -- Cantrell is excellent. I often have to check with Cantrell to get an answer to questions like "Is this result in this other text true in general, or only in the special case that its author describes?". I never have to double check to see to what extent the results in Cantrell apply -- he makes things like that quite clear. Cantrell has included a healthy dose of linear algebra and functional analysis in his text, at the expense of some of the chapters in more traditional mathematical physics texts, such as those on contour integration or special functions. However, examples of the use of special functions are sprinkled liberally thoughout the text. And although the chapter on that subject is mostly about Bessel functions, Cantrell's discussion of Bessel functions is, typically, different from and more insightful than conventional treatments. My quibbles with the book have to do not with its content, but with "first edition" glitches -- a figure here or a typo there. And some sort of bug in the index preparation process left many of the page numbers referred to in the index "off" by a page or two. On the other hand, the hardcover edition that I have lays open nicely on my desk, and after heavy use the binding has not broken, and no pages have fallen out. It would be nice if there were an appendix of "Answers to Exercises," or maybe a "Student's Guide." However, many of the exercises are of the "Show that ..." variety, so the lack of such an appendix is not nearly the drawback that it might be. Overall: Excellent book, highly recommended.