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

Using integration techniques is an area of undergraduate mathematics that has been shunted along the neglected road of late. With the advent of other areas of mathematics and the increased use of symbolic mathematics packages, it is possible to teach concepts that could not be offered a few years ago. However, a great deal can be learned from the underlying principles of integration, and this book can be used to teach them. The authors state that their target level is the advanced undergraduate student and they achieve that goal. Most of the concepts can be understood by anyone who has successfully completed the three-course sequence in basic calculus. Some of the topics are integrals involving binomial coefficients, partial fractions, trigonometric functions, quartic integrals, Euler's constant, the gamma and beta functions and the Riemann zeta function. The authors use Mathematica commands to perform many of the operations and those commands are easy to understand. Furthermore, the use of Mathematica is as a supplement, it would not be necessary to understand a single Mathematica command in order to be able to follow all of the demonstrations. I rarely teach math classes any more, and those that I do teach are at the lower levels. However, if I was given the opportunity to teach a special topics class in mathematics, I would seriously consider offering one in the fundamental techniques of integration and use this as the text.