Irresistible integrals. Symbolics, analysis and experiments in the evaluation of integrals. (English)

Cambridge University Press, Cambridge (ISBN 0-521-79636-9). 320 p. (2004).

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 nineteenth-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, and algebra. This is a guided tour of discovery for undergraduates and their teachers in mathematics, computer science, physics, and engineering.