Ask HN: Can you suggest advanced books on integral calculation?

#1

Post by jackcooper » Wed, Oct 18, 2023, 1:28 PM UTC

I enjoy calculating hard integrals and would like to master it. I just started with my master in physics, so I would love to see some "next-level" techniques.

Re: Ask HN: Can you suggest advanced books on integral calculation?

#2

Post by Jugurtha » Wed, Oct 18, 2023, 1:31 PM UTC

"A Course of Higher Mathematics" - Smirnov

"Differential and Integral Calculus" - Piskunov

"Problems in Mathematical Analysis" - Demidovich (exercises/problems)

Re: Ask HN: Can you suggest advanced books on integral calculation?

#3

Post by siegelzero » Wed, Oct 18, 2023, 3:15 PM UTC

"Irresistible Integrals: Symbolics, Analysis and Experiments in the Evaluation of Integrals" - Boros and Moll

"Inside Interesting Integrals" - Nahin

Re: Ask HN: Can you suggest advanced books on integral calculation?

#4

Post by misiti3780 » Wed, Oct 18, 2023, 3:16 PM UTC

Since you are already doing this, can you suggest some good books you have be using for beginners. ?

Re: Ask HN: Can you suggest advanced books on integral calculation?

#5

Post by NotYourLawyer » Wed, Oct 18, 2023, 3:21 PM UTC

Advanced Calculus by Woods.

https://zackyzz.github.io/feynman.html

Re: Ask HN: Can you suggest advanced books on integral calculation?

#6

Post by ydnaclementine » Wed, Oct 18, 2023, 3:34 PM UTC

misiti3780 wrote: post #4

Since you are already doing this, can you suggest some good books you have be using for beginners. ?

I've been looking at Foundation Maths by Croft and Davison as a refresher for everything math, which includes calc

Re: Ask HN: Can you suggest advanced books on integral calculation?

#7

Post by adharmad » Wed, Oct 18, 2023, 3:52 PM UTC

The MIT integration bee has some good problems. So do the Putnam tests.

Re: Ask HN: Can you suggest advanced books on integral calculation?

#8

Post by jjgreen » Wed, Oct 18, 2023, 4:03 PM UTC

Get Gradshteyn and Ryzhik and follow the references ...

https://en.wikipedia.org/wiki/Gradshteyn_and_Ryzhik

Re: Ask HN: Can you suggest advanced books on integral calculation?

#9

Post by ykonstant » Wed, Oct 18, 2023, 4:03 PM UTC

Besides the suggestions below, it is instructive to go to the math stackexchange and look at the highest voted Q&As tagged 'integrals' or 'definite-integrals'. Legends like Cleo lurk there demonstrating mind-boggling feats of integration. The corresponding mathoverflow tags are also interesting, but likely to involve more advanced concepts.

Re: Ask HN: Can you suggest advanced books on integral calculation?

#10

Post by mixedmath » Wed, Oct 18, 2023, 4:15 PM UTC

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 references are often old and lacking (like Erdelyi's prior table of integrals).

You might also like Solved Problems for the Gamma and Beta Functions, Legendre Polynomials, and Bessel functions by Farrel and Ross. This is a bit closer to real analysis and veers towards more practical integral magic.

Finally, I'll note that all of these largely omit complex residue calculus (using complex analysis to solve real integrals). I don't know of a good book specifically aimed at this, unfortunately.