Inside Interesting Integrals
by Paul J. Nahin · first published 2014
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5HN commenters
2016–2023first – last mentioned
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What’s the point of calculating definite integrals since you can’t possibly do them all? What makes doing the specific integrals in this book of value aren’t the specific answers we’ll obtain, but rather the methods we’ll use in obtaining those answers; methods you can use for evaluating the integrals you will encounter in the future. This book is written in a light-hearted manner for students who have completed the first year of college or high school AP calculus, and have just a bit of exposure to the concept of a differential equation. Every result is fully derived. If you are fascinated by
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…category theory, geared towards teaching you Lawvere's clarification and generalization of the incompleteness theorems. Cormen - Algorithms Unlocked. Pop Science version of some of the textbook. Nahin - Inside interesting Integrals. Lots of fun integrations! Nahin - He also wrote some books about euler and imaginary numbers which ive partially read, they seemed good. Pierce - An introduction to information theory; symbols signals…
on “Classic Mathematics Books for Lifelong Learners” ↗For those interested in math and particularly in learning how to attack challenging (definite) integrals, I can recommend this book by Paul Nahin: Inside Interesting Integrals [1]. It's well reviewed on Amazon and I enjoyed the writing. [1] https://www.amazon.com/gp/product/1493912763/ref=oh_aui_sear...
on “An integral with a couple lessons” ↗"Irresistible Integrals: Symbolics, Analysis and Experiments in the Evaluation of Integrals" - Boros and Moll "Inside Interesting Integrals" - Nahin
on “Ask HN: Can you suggest advanced books on integral calculation techniques?” ↗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…
on “Ask HN: Can you suggest advanced books on integral calculation techniques?” ↗…in different materials. These, relatively, plain looking definite integrals stumped some of the world's most famous mathematicians. See [1] and/or [2] for their interesting history. [1] Paul J. Nahin, Inside Interesting Integrals, Springer, 2015. Section 6.5, The Watson/van Peype Triple Integrals. [2] I.J. Zucker, 70+ Years of the Watson Integrals, http://www.inp.nsk.su/~silagadz/Watson_Integral.pdf
on “Symbolic mathematics finally yields to neural networks” ↗Entire books have been written about curious integrals. Irresistible Integrals: Symbolics, Analysis and Experiments in the Evaluation of Integrals, by George Boros https://www.amazon.com/dp/0521796369/ Inside Interesting Integrals, by Paul J. Nahin https://www.amazon.com/Inside-Interesting-Integrals-Substitu...
on “A Curious Integral” ↗