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.