Irresistible integrals
The problem of evaluating integrals is well known to every student who has had a year of calculus. It was an especially important subject in 19th century analysis and it has now been revived with the appearance of symbolic languages. In this book, the authors use the problem of exact evaluation of definite integrals as a starting point for exploring many areas of mathematics. The questions discussed in this book, first published in 2004, are as old as calculus itself. In presenting the combination of methods required for the evaluation of most integrals, the authors take the most interesting, rather than the shortest, path to the results. Along the way, they illuminate connections with many subjects, including analysis, number theory, algebra and combinatorics. This will be a guided tour of exciting discovery for undergraduates and their teachers in mathematics, computer science, physics, and engineering.
Stats for nerds
2recommend
2mentions
2people
2023years
100% recommend
What Hacker News says
- 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.
- 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...
Related
Inside Interesting Integrals
4 recommend · 6
The Princeton Companion to Mathematics
62 recommend · 101
Mathematical Methods in the Physical Sciences
11 recommend · 12
Gödel's proof
30 recommend · 45
2024–2026
Mathematica
12 recommend · 20
The Princeton Companion to Applied Mathematics
6 recommend · 19
