Can anyone recommand a simple but complete mathematical methods book written especially for undergrad physics students?
Boas is pretty good for undergrad physics. But then, it depends on what you mean by 'complete'. You can check the contents of the book(3rd Ed.) at amazon.
I knew that. But undergrads in different schools around the world may be exposed to a little more or a little less of the "average curriculum". By now you may know that Boas does not cover group theory, for example. Another book that I have heard about, but never read, is by Morse and Feshbach.
So a complete one would include group theory. I like to be on the safe side. However the depth of the maths shouldn't be too deep. So wide scope but not deep.
Take a look at Riley, Hobson, Bence - Mathematical Methods I'd say this has pretty much everything you'll cover in a 4 year degree. Boas would also suit, but i'd say it's a bit more cookbookish than the likes of R, H, B.... Arfken is smashin' but better used in conjunction with a more elaborate book.. well i find that at the early years of my undergrad degree
I've had a look at Boas and was impressed. Its nice layout and font complements it even more. However for higher stuff like hilbert spaces, one will need Arfken. Does R,H,B have stuff on hilbert spaces? I think not. Maybe a combintation of Boas and Arfken would form a complete mathematical book I am after. Although it does have Representation theory and group theory.
Chapter 17, "Eigenfunction methods for differential equations," covers the aspects of Hilbert spaces that are relevant to undergrad physics. I personally haven't used Riley, Hobson & Bence all that much, but I think that is because American universities tend to favor textbooks written by American authors.