hey guys & gals ... i need your advice in selecting the best possible Vector Calculus book for a physics major planning on pursuing his Master's and perhaps more in the future ... i have been away from math and physics for some time (~ 4 years) and do not have a solid Vec-Calc background. I've read mixed reviews about different books on amazon.com and can't quite decide on which book to go with. I have a general Calc book from the late 90s but it's not enough for advanced physics (well, as advanced as a master's degree would require). Your advice is appreciated, phyz76 8 )
RE: book by Schey Davers, thanks for your reply. But isn't your recommended book an informal text on vector calculus? it does have great reviews, but i need something more fundamental with rigorous proofs, examples, and problems ... Griffiths which is the typical E&M undergrad also has vector calculus but there isn't much proof and examples. if you have other recommendations like which to choose between "Tromba, Hubbard, Colley, or Stewart" (or another author) as a more formal text on V-Calc, please let me know.
Schaum's omits a lot of rigour and/or leaves it as exercise without answers. The book my school uses is "Advanced Calculus by Folland, and it may be what your looking for. Very rigorous, but at the same time difficult. Its what physicists here are expected to know. Reviews aren't looking too great though. Check it out: http://www.amazon.com/Advanced-Calculus-Gerald-B-Folland/dp/0130652652 Another one my school used to use is Vector Calculus by Marsden & Tromba. It too is very rigorous and somewhat theoretical. Check it out: http://www.amazon.com/Vector-Calculus-Jerrold-E-Marsden/dp/0716724324 These are very difficult texts from what I know, that really go in depth into vector calc. I haven't actually used them yet, because I start my course in a week. However, if your doing independent study, it might be difficult to grasp advanced concepts alone. So I'd reccommend you take an easier book to supplement it, something like Stewart's Multivariable calculus which is rich on illustrations and gives you a strong intutitive feel. Once that is down, you can get down to the proofs and rigour in the books I mentioned above. Hope this helps.
Here's two that have served me well: Mathematical Methods in the Physical Sciences by Mary L Boas, Wiley $ Sons (This one is not at a high level, but thorough) and Mathematical Methods for Physicists by Arfken and Weber, Elsevier Academic Press. (This one seems to come in several versions... The two I have are both useful.)
i liked tromba and marsden when i taught out of it to hionors high school students about 25 years ago. the classic for years was williamson, crowell, and trotter. of course apostol.