Searching for a more rigorous math book for Physics.

[1stepatatime]

I've decided to major in Physics and just finished E&M as well as Calculus 3. I understand how to do most of the problems in my Calc book (the same text was used for all three courses) mechanically.

Our classes used James Stewart's text and I had Ron Larson's as another reference. My concern is that I've read on these forums that there are other Calculus books that go more in-depth into the subject. Personally, I feel that not studying from these books can lead to me being at a disadvantage when I start taking 3rd year and beyond Physics courses.

Is this the case where certain "proof heavy" books such as Apostol's, Spivak's and Courant's would benefit a Physics major more than Stewart's and Larson's? I'm aware that there are those that were fine with just reading Stewart's and/or Larson's, but how about the ones who have studied from the other Calc books mentioned? Any insight would be much appreciated.

 

[Feldoh]

A lot of the stuff you learn in a math class is not all too applicable to physics. I mean you can teach yourself the mathematical concepts along the way as you learn physics.

I'm not saying don't read those math books, but I'd really only read them if it indeed does interest you.

 

[hitmeoff]

If you are referring to Apostol's Mathematical Analysis book, then yes, it is much more "proof heavy." But this is because its an analysis book...for junior and senior math majors. The point of analysis is to redevelop Calculus from axioms and definitions.

Could it help you with physics? Dunno. I am a math and physics major myself, but haven't gone far enough in one or the other to really tell how much of an advantage it is to me to be able to develop the calculus from the definitions of Natural numbers on to sequences and limits.

Remember that math is a tool for physicists. A mechanic needs a wrench to fix a car, he might need to know certain specs about the wrench, but does he really need to know how the wrench was manufactured from "the concept of a tool" all the way through "manufacturing process" to effectively fix a car? Prob not.

Certainly, the maturity in thought that advanced math can develop won't hurt. THere is also something to be said about certain great physicist contributing greatly to math (and vice versa). So if math really turns you on, absolutely go out and get yourself some of these undergrad math books

 

[George Jones]

From anolther post of mine:

Typically, mathematical physics courses emphasize techniques for solving differential equations, e.g., special functions, series solutions, Green's functions, etc. These techniques are still very important, but, over the last several decades, abstract mathematical structures have come to play an increasingly important role in fundamental theoretical physics. Consequentlly, useful courses include real/functional analysis, topology, differential geometry (from a modern perspective), abstract algebra, representation theory, etc., and, usually, should be taken from a math department, not a physics department.

These courses, supply vital background mathematics, and, just as importantly, facilitate a new way of thinking about mathematics that complements (but does not replace) the way one thinks about mathematics in traditional mathematical physics courses.

I don't want to mislead anyone, most areas of physics do not require this background in abstract mathematics.