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Does anyone else have a good reference or book on the topic?
Since you are already doing this, can you suggest some good books you have be using for beginners. ?
Along a similar line, the only book that I've found that has goes through a careful derivation of the divergence theorem using Lebesgue integration is, "A Concise Introduction to the Theory of Integration," Second Edition by Daniel W. Stroock. I prefer this one to his later book, "Essentials of Integration Theory for Analysis." Does anyone else have a good reference or book on the topic?
Along a similar line, the only book that I've found that has goes through a careful derivation of the divergence theorem using Lebesgue integration is, "A Concise Introduction to the Theory of Integration," Second Edition by Daniel W. Stroock. I prefer this one to his later book, "Essentials of Integration Theory for Analysis." Does anyone else have a good reference or book on the topic?
I could suggest the following Inside Interesting Integrals, by Nahin. This contains integrals with often arithmetic inspiration. Imagine things like, lots of special values of the zeta function or partial sums of harmonic numbers and that sort of thing. Irresistible Integrals, by Boros and Moll. This is inspired by their work to prove all of the integrals in the enormous book of Gradshteyn and Ryzhik, whose reference…
(Almost) Impossible Integrals, Sums, and Series - Cornel Ioan Vălean
There's also those CRC manuals filled with solutions to integrals that show the steps.
I remember study guides for the first actuarial exam give tricks to calculate repeated integrals fast. There's also those CRC manuals filled with solutions to integrals that show the steps.