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

This book is better viewed as a collection of essays than as a traditional text book. As a result it can assume a good bit on behalf of the reader (read: doesn't start at first principles) and thus many details and topics are given that would have no room in text books. This makes the reading more captivating; the trade off is it isn't leisurely and readers will need to toil somewhat. That being said, if a reader would like to do research in the area of evaluation of integrals, applying themselves to some of the chapters here will get them there.

satisfactory

This is a very engaging introduction to the wonderful worldof integrals from many perspectives. It is very elegantlywritten. It has a chuckfull of ideas for projects forundergraduates, with or without computer algebra.I strongly recommend it to everyone from smartsophmores to full professors, in all areas of mathematics.

A good math book for UG students.

Two of my students and I have been using this book this year for an independent study project. We have found the material quite fascinating and we have learned a lot. The material is well-organized and, as we approach the last chapter, it becomes clear what the authors' overarching theme was.The exercises range from trivial to challenging. We skipped most of the projects, but it seems like they are quite challenging as well.However, the book is full of typographical errors, many of them significant. This has been an unending source of frustration for us. Nothing is more aggravating than to spend an hour trying to prove some statement that turns out to be false as written, only to find out that there is a missing factor or minus sign. Chapter 11 alone has at least 9 such errors among its 18 pages.So I recommend this book if you are interested in learning more about integrals, but be prepared to check every statement and do not assume the book is correct.

Everyone who has touched calculus and analysis during the very first university years knows how much time must be `lost' in the justification of quite clear facts (almost obvious to our intuition). At the same time, one becomes familiar with several tricky counterexamples to those clear facts if a condition (looking rather inessential!) is missed. Arriving then at the subject of definite and indefinite integration, one usually starts to think of calculus as a boring but unavoidable part of mathematics, and it is only on a higher level of university study when one may taste the real beauty of analysis by seeing so many wonderful applications of those boring statements.It is astonishing to see in the book "Irresistible integrals" that even the first steps in calculus may be full of an irresistible grace and that many contemporary beautiful results may become available so early. It is the task of the authors to introduce the reader to the subject of analysis by means of methods of definite integration and their applications to mathematical functions. The methods involved are not only classical (purely analytic) but also modern, like symbolic evaluation in computer algebra systems. An important novelty of the book is demonstrating the role of experiment in mathematics. This is really something that may help the beginner to understand the basic ideas of proofs and evaluations before doing the proofs rigorously and the evaluations formally. The book contains a lot of exercises, examples and computer algebra programs. Complex analysis is completely avoided to make the book as elementary as possible. Among the applications, the reader will find many results on special mathematical functions and mathematical constants.Do not think that the book can be used only by those who are starting the study of higher mathematics or who have missed a reasonable introduction to calculus. "Irresistible Integrals" is also nice reading for experts in analysis, number theory, combinatorics and algorithmic theory. The authors have themselves participated in developing new evaluation and transformation techniques for definite integrals, which the reader may now get at first hand. I have no doubts in forecasting that this book will not be buried in the reader's bookshelf.

The text provide a lot of investigationIt is good for students or graduate studiesI hope there should be a answer mannual too :)

This book is a gem. It is full of beautiful integral and series formulas for classical mathematical constants, with lucid explanations of how to derive them. There are many examples of using the symbolic language Mathematica to generate conjectures. Connections with number theory are emphasized and the reader will find a glimpse into the magic world of Ramanujan. The main goal of the book is to evaluate integrals, including those of Euler and Laplace. Surprisingly, other topics covered are: Fibonacci and Bernoulli numbers, generating and hypergeometric functions, solutions of 3rd and 4th degree equations, irrationality, the constants of Apery, Catalan and Euler, recursions, the Prime Number Theorem and the Riemann zeta function. The last chapter is an introduction to the revolutionary WZ method of summation. The book is written at the level of a college junior and would make an excellent textbook for a course. Lovers of mathematics will read it for pleasure. (Full disclosure: the book mentions results of the reviewer.)

Got this as a gift that was chosen by my future son in law who is studying a PhD no complaints from him