Integrals and Sums Fiesta: An Integral Part of a Math Enthusiast's Life

This book contains a collection of integral and series identities derived in an intuitive and playful manner. In each chapter, we start with some integral and series identities, and then we derive other identities from them by using certain methods to manipulate the integrals and series. This book features many integration and summation topics such as Harmonic numbers, Maclaurin series, Fourier series, Cauchy-Schlömilch transformation, and Mellin transform.

Reviews

"This is a neat new book, the result of 'playing with mathematics'. And what could be better than that??" - Dr. Gilbert Strang, Professor of Mathematics, MIT, USA

"This book is an engaging introduction to some of the most elementary and intriguing sums and integrals in Mathematics. It can best be described as 'calculations starting from Calculus can be fun'. These notes illustrate that the coupled interplay of sums and integrals is a highly useful technique in obtaining formulas that underlie important mathematical concepts." - Dr. William Beckner, Professor of Mathematics, University of Texas at Austin, USA

"El título del libro... es muy elocuente, por cuanto lo define totalmente. El autor, haciendo juegos malabares, consigue resolver un número importante de integrales... y de sumas de series cuya acometida inicial podría parecer una empresa irrealizable. Es notable el bagaje mínimo que usa en la resolución. Más allá de los resultados concretos, la obra abre caminos que pueden ser comunes para otras muchas empresas." - Dr. Juan Carlos Cabello Piñar, Head of Department of Mathematical Analysis and Associate Professor of Mathematics, University of Granada, Spain (English translation available in the book)

"In this book, the author proves many interesting identities related with definite integrals and infinite sums.... It is remarkable that the author did it in the framework of calculus only. For this reason, it may be the case that the calculations given in this book are not very rigorous although the results are correct. Usually, such identities are rigorously proved by applying the techniques of complex analysis or real analysis. Nevertheless, I am sure that this book will give strong motivations to the readers for studying the subjects such as introduction to mathematical analysis, complex analysis, and real analysis." - Dr. Young-One Kim, Professor of Mathematics, Seoul National University, South Korea

"It is an amazing book with kaleidoscope of formulas and relations, of which the author shares with enthusiasm and interest." - Dr. Man Chun Leung, Associate Professor of Mathematics, National University of Singapore, Singapore

"Books like Integrals and Sums Fiesta have become harder to come by. With the growth of computing packages and people's tendency to defer algebraic manipulations to other sources, fewer and fewer craftsmen practice the art of explicitly computing integrals and sums.... The work is elegantly presented, and some of the final formulae obtained are, after taking a step back, no short of stunning. I’m sure that many readers will enjoy this book. I certainly had fun trying to guess which tricks would come into play and how." - Dr. Martin Louis Marie Lesourd, Lecturer in Mathematics, Harvard University, USA

"This book is a remarkable collection of 130 equations involving integrals and sums, all derived in the spirit of 'play,' as the author describes his method....The only problem with the book is that... [it's] not clear why some of these identities should be of interest to us. On the other hand, mathematicians have spent a century working out identities in Ramanujan’s notebooks.... Unlike Ramanujan, this author clearly spells out his method.... The author has made an amazing contribution with this work." - Dr. Raymond Greenwell, Professor Emeritus of Mathematics, Hofstra University, USA

Full reviews and more reviews available in the book.