Irresistible Integrals: Symbolics, Analysis and Experiments in the Evaluation of Integrals

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George Boros (Xavier University of Louisiana) Victor Moll (Tulane University, Louisiana)

Irresistible Integrals

Symbolics, Analysis and Experiments in the Evaluation of Integrals

George Boros (Xavier University of Louisiana), Victor Moll (Tulane University, Louisiana)

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English

Cambridge University Press
22 December 2004

Mathematics & Sciences; Calculus & mathematical analysis

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.

By: George Boros (Xavier University of Louisiana), Victor Moll (Tulane University, Louisiana)
Imprint: Cambridge University Press
Country of Publication: United Kingdom
Dimensions: Height: 228mm, Width: 154mm, Spine: 19mm
Weight: 430g
ISBN: 9780521796361
ISBN 10: 0521796369
Pages: 320
Publication Date: 22 December 2004
Audience: College/higher education , Professional and scholarly , Primary , Undergraduate
Format: Paperback
Publisher's Status: Active

1. Introduction; 2. Factorials and binomial coefficients; 3. The method of partial fractions; 4. A simple rational function; 5. A review of power series; 6. The exponential and logarithm functions; 7. The trigonometric functions and pi; 8. A quartic integral; 9. The normal integral; 10. Euler's constant; 11. Eulerian integrals: the Gamma and Beta functions; 12. The Riemann zeta function; 13. Logarithmic integrals; 14. A master formula; 15. Appendix: the revolutionary WZ method.

Reviews for Irresistible Integrals: Symbolics, Analysis and Experiments in the Evaluation of Integrals

'I recommend this book highly as a source of rewarding projects for undergraduates (and others) to home their analytic skills and gain an appreciation for this area of mathematics. The authors clearly had great love for the material and their enthusiasm comes through in an infectious manner.' SIAM Review 'The authors have managed to write a very readable account about integrals, accessible even to advanced undergraduates. Some of the topics of the book could be used for undergraduate reading and research projects. This way the book could serve as a 'springboard to many unexpected investigations and discoveries in mathematics.' Zentralblatt MATH