[Math] Mathematical Physics/Methods in Mathematical Physics books

book-recommendationmathematical physicsreference-request

I have a knowledge of calculus, linear algebra, and differential equations. I have read some parts of Boas's and Arfken's mathematical methods book but I found them to be not very satisfying to read, it's as if there's something lacking when I read them. From the information I have gathered, two texts might offer what I'm looking for (rigor but with just the right amount for theoretical physicist).

Methods of Mathematical Physics by Courant and Hilbert

Methods of Theoretical Physics by Morse and Feshbach

1) What are the prerequisite of these books in order for me to be able to penetrate them?

2) Is my background enough?

3) How do they compare to other books in terms of contents? i.e. Boas's book contains tensors (I can learn that somewhere with better books), group theory (again, somewhere), so aside from these can those books replace the books used for standard mathematical methods courses?

4) How does those two books compare with each other? i.e. Pros and Cons; I might use only one book.

If someone knows other alternatives, I would appreciate your suggestions.

Best Answer

I was donated both volumes of Morse & Feshbach by a retiring professor (who had bought copies forgetting he already owned them!), so let me say a few words about them:

  • As noted, the volumes cover a lot of material - inevitably some things are glossed over. Fortunately each chapter ends with an excellent bibliography to chase up those finer details.
  • The material is fairly self-contained; it should certainly be accessible to someone with your background in mathematics.
  • Problems are also given at the end of each chapter, though I am unaware of any (official) solution book in existence.
  • The chapters also end with a summary and/or summarizing table which I have found very useful as a reference. This point (I feel) is quite pertinent: I very much use and feel that M&F is more of a reference book; I have often needed to look elsewhere for the finer mathematical details (which is where the excellent bibliography comes in useful!)
  • The books I own are from the 1950s; hence some terminology and the way the material is presented feels a little dated.

I can't comment too much on Courant & Hilbert other than too say that I have found their treatment of some topics to be more rigorous than that of Morse & Feshbach. These books are both more on analytic methods in mathematical physics; you may also be interested to look at applications of group theory and differential geometry to mathematical and theoretical physics, both of which have entire books devoted to them. Let me finish with a couple of alternatives that I have used:

Best of luck with the studies and hope this helps in some way!

RESPONSE TO COMMENT ON LACK OF PROBLEMS IN H&C:

If you were intent on reading Hilbert & Courant, then the problems in the books already mentioned above can be used to track your progress. There are, however, specific problem books which could be used:

are ones that spring to mind. The first two are Dover books and are therefore inexpensive; the second one is in two volumes: introductory and advanced. And I am sure there are plenty more!

Related Question