Irresistible Integrals

Symbolics, Analysis and Experiments in the Evaluation of Integrals

George Boros, Victor H. Moll

304 pages, parution le 02/09/2004

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Résumé

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 here 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.

Sommaire

Introduction
Factorials and binomial coefficients
the method of partial fractions
A simple rational function
A review of power series
The exponential and logarithm functions
The trigonometric functions and pi
A quartic integral
The normal integral
Euler’s constant
Eulerian integrals: the Gamma and Beta functions
The Riemann zeta function
Logarithmic integrals
A master formula
Appendix: the revolutionary WZ method

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Caractéristiques techniques

	PAPIER
Éditeur(s)	Cambridge University Press
Auteur(s)	George Boros, Victor H. Moll
Parution	02/09/2004
Nb. de pages	304
Format	15 x 23
Couverture	Broché
Poids	430g
Intérieur	Noir et Blanc
EAN13	9780521796361
ISBN13	978-0-521-79636-1