What book gives a rigorous but elementary exposition of "div, grad, curl, and all that"? Conventional second-year calculus books are as far from rigorous as anything ever gets.
Rigorous but elementary exposition of "div, grad, curl, and all that"
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multivariable-calculus
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1@t.b.: I do not complain, I rather recall that the only area in my Analysis course where I felt the lack of rigor was multidimensional integration, especially Fubini's theorem and Green and Stokes formulas. I had a guess what are the reasons - I only wonder how much pages in appendix will take the necessary theory. – 2011-10-23
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Have you taken a look at Fleming's Functions of Several Variables? Relative to most of books that I've looked at, it provides the least amount of machinery necessary to prove (rigorously) the basic theorems of integral vector calculus. I find it to be very readable and easy to understand.
This question that I posed awhile back which, inexplicably, was closed as being off-topic, might also be relevant.
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0The only local library that has that book has two copies and both are currently checked out. But I'll look at it soon, I think. Thank you. – 2011-10-21