The late Donald McQuarrie's Mathematical Methods for Scientists and Engineers is a masterpiece!
I have used the text for my graduate mathematical methods course for engineers for four years at
Howard University and I have also used Arfken and Weber's Mathematical Methods for Physicists as
a graduate student at Ohio State University many, many years ago. I also have read and consulted
the late Mary Boas' excellent Mathematical Methods in the Physical Sciences, which is now in its 3rd edition.
While it is true that Arfken and Weber covers more topics than McQuarrie (e.g. tensor analysis and
group theory), McQuarrie is actually a textbook that is clearly written for students to read and follow
with a myriad of examples to work through. Arfken and Weber is a reference book and it is really not
a textbook, although it is used extensively throughout the physics community. I wish that more folks
would discover McQuarrie, who was famous for writing very clear texts in the chemical community.
One criticism I have heard from folks is the presence of typos in McQuarrie. There is a web site by
D. Sober who is collecting these errata for future use. Unfortunately, I suspect that we may not see a
second edition of McQuarrie because of his passing in 2009. One should remember that there were
many typos in the first editions of Arfken (then only Arfken and nor Arfken and Weber) and Boas.
In summary, I suspect that the choice of a book depends on your audience! McQuarrie is a pleasure
to read and work through as a student, although some may not be happy with its omission of tensor
analysis and group theory which are, of course, important topics for physicists. Arfken is really a
reference book and not a textbook. Boas is a beautiful book which is not as extensive as McQuarrie
but is a much better written expository textbook than Arfken and Weber and it even includes an
elementary discussion of group theory and tensor analysis. Those seeking a more mathematical and
less applied perspective may not be happy with any of these three.
If you find yourself struggling through Arfken and Weber, then I might suggest checking out McQuarrie,
and even Boas. I would agree with a review I once read that McQuarrie is Arfken and Weber done right!
McQuarrie contains more material than an instructor can cover in a one-year course, but it makes
a serious attempt to provide a considerable amount of background material for a clear expository discussion
of linear algebra, ordinary differential equations, complex variables, partial differential equations,
non-linear differential equations, and probability and statistics. The remarkable thing is that it is all done
in a single textbook. McQuarrie also comes in paperback form for those who want to watch their pennies,
along with a solutions manual for instructors.