Overview
- Provides original problems on special topics in classical analysis such as the computation of limits, series, and exotic integrals
- The first book to concern the calculation of fractional part integrals and series of various types
- Illustrates fundamental results of real analysis and reveals new, simple methods of proofs for classical facts
- Includes full solutions and new techniques for solving problems in integration theory and the computation of limits of special sequences?
- Includes supplementary material: sn.pub/extras
Part of the book series: Problem Books in Mathematics (PBM)
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Table of contents (3 chapters)
Keywords
About this book
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.
Reviews
From the reviews:
“This book contains a collection of unusual problems and solutions in mathematical analysis in the area of limits, series and fractional part integrals. … This book is indispensable for graduate students of mathematics, physics, engineering and other researchers interested in exploring the powerful techniques of mathematical analysis in their research work.” (James Adedayo Oguntuase, zbMATH, Vol. 1279, 2014)
Authors and Affiliations
About the author
Bibliographic Information
Book Title: Limits, Series, and Fractional Part Integrals
Book Subtitle: Problems in Mathematical Analysis
Authors: Ovidiu Furdui
Series Title: Problem Books in Mathematics
DOI: https://doi.org/10.1007/978-1-4614-6762-5
Publisher: Springer New York, NY
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer Science+Business Media New York 2013
Hardcover ISBN: 978-1-4614-6761-8Published: 30 May 2013
Softcover ISBN: 978-1-4899-9243-7Published: 23 June 2015
eBook ISBN: 978-1-4614-6762-5Published: 30 May 2013
Series ISSN: 0941-3502
Series E-ISSN: 2197-8506
Edition Number: 1
Number of Pages: XVIII, 274
Topics: Analysis, Sequences, Series, Summability, Special Functions