A Garden Of Integrals

Download or read book A Garden of Integrals written by Frank Burk and published by MAA. This book was released on 2007-08-30 with total page 312 pages. Available in PDF, EPUB and Kindle. Book excerpt: The derivative and the integral are the fundamental notions of calculus. Though there is essentially only one derivative, there is a variety of integrals, developed over the years for a variety of purposes, and this book describes them. No other single source treats all of the integrals of Cauchy, Riemann, Riemann-Stieltjes, Lebesgue, Lebesgue-Steiltjes, Henstock-Kurzweil, Weiner, and Feynman. The basic properties of each are proved, their similarities and differences are pointed out, and the reasons for their existence and their uses are given, with plentiful historical information. The audience for the book is advanced undergraduate mathematics students, graduate students, and faculty members, of which even the most experienced are unlikely to be aware of all of the integrals in the Garden of Integrals. Professor Burk's clear and well-motivated exposition makes this book a joy to read. There is no other book like it.

Download or read book Approximate Calculation of Integrals written by V. I. Krylov and published by Courier Corporation. This book was released on 2012-01-27 with total page 372 pages. Available in PDF, EPUB and Kindle. Book excerpt: An introduction to the principal ideas and results of the contemporary theory of approximate integration, this volume approaches its subject from the viewpoint of functional analysis. The 3-part treatment begins with concepts and theorems encountered in the theory of quadrature and then explores the problem of calculation of definite integrals and methods for the calculation of indefinite integral. 1962 edition.

Download or read book Asymptotic Expansions of Integrals written by Norman Bleistein and published by Courier Corporation. This book was released on 1986-01-01 with total page 453 pages. Available in PDF, EPUB and Kindle. Book excerpt: Excellent introductory text, written by two experts, presents a coherent and systematic view of principles and methods. Topics include integration by parts, Watson's lemma, LaPlace's method, stationary phase, and steepest descents. Additional subjects include the Mellin transform method and less elementary aspects of the method of steepest descents. 1975 edition.

Download or read book Integrals of Bessel Functions written by Yudell L. Luke and published by Courier Corporation. This book was released on 2014-10-20 with total page 436 pages. Available in PDF, EPUB and Kindle. Book excerpt: A massive compendium of useful information, this volume represents a valuable tool for applied mathematicians in many areas of academia and industry. A dozen useful tables supplement the text. 1962 edition.

Download or read book (Almost) Impossible Integrals, Sums, and Series written by Cornel Ioan Vălean and published by Springer. This book was released on 2019-05-10 with total page 572 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book contains a multitude of challenging problems and solutions that are not commonly found in classical textbooks. One goal of the book is to present these fascinating mathematical problems in a new and engaging way and illustrate the connections between integrals, sums, and series, many of which involve zeta functions, harmonic series, polylogarithms, and various other special functions and constants. Throughout the book, the reader will find both classical and new problems, with numerous original problems and solutions coming from the personal research of the author. Where classical problems are concerned, such as those given in Olympiads or proposed by famous mathematicians like Ramanujan, the author has come up with new, surprising or unconventional ways of obtaining the desired results. The book begins with a lively foreword by renowned author Paul Nahin and is accessible to those with a good knowledge of calculus from undergraduate students to researchers, and will appeal to all mathematical puzzlers who love a good integral or series.

Download or read book Limits, Series, and Fractional Part Integrals written by Ovidiu Furdui and published by Springer Science & Business Media. This book was released on 2013-05-30 with total page 289 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book features challenging problems of classical analysis that invite the reader to explore a host of strategies and tools used for solving problems of modern topics in real analysis. This volume offers an unusual collection of problems — many of them original — specializing in three topics of mathematical analysis: limits, series, and fractional part integrals. The work is divided into three parts, each containing a chapter dealing with a particular problem type as well as a very short section of hints to select problems. The first chapter collects problems on limits of special sequences and Riemann integrals; the second chapter focuses on the calculation of fractional part integrals with a special section called ‘Quickies’ which contains problems that have had unexpected succinct solutions. The final chapter offers the reader an assortment of problems with a flavor towards the computational aspects of infinite series and special products, many of which are new to the literature. Each chapter contains a section of difficult problems which are motivated by other problems in the book. These ‘Open Problems’ may be considered research projects for students who are studying advanced calculus, and which are intended to stimulate creativity and the discovery of new and original methods for proving known results and establishing new ones. This stimulating collection of problems is intended for undergraduate students with a strong background in analysis; graduate students in mathematics, physics, and engineering; researchers; and anyone who works on topics at the crossroad between pure and applied mathematics. Moreover, the level of problems is appropriate for students involved in the Putnam competition and other high level mathematical contests.

Download or read book Complex Integration and Cauchy's Theorem written by G. N. Watson and published by . This book was released on 1914 with total page 100 pages. Available in PDF, EPUB and Kindle. Book excerpt: Originally published in 1914, this book provides a concise proof of Cauchy's Theorem, with applications of the theorem to the evaluation of definite integrals.