Problem Books in Mathematics

Limits, Series, and Fractional Part Integrals

Problems in Mathematical Analysis

Authors: Furdui, Ovidiu

  • 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​
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  • ISBN 978-1-4614-6762-5
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  • ISBN 978-1-4899-9243-7
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About this Textbook

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.

About the authors

Ovidiu Furdui is an Assistant Professor of Mathematics at the Technical University of Cluj-Napoca, Romania. He has published more than 100 original problems in publications such as The American Mathematical Monthly and The Fibonacci Quarterly. He is the author of Selected Problems on Limits of Special Sequences.

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)


Table of contents (3 chapters)

  • Special Limits

    Furdui, Ovidiu

    Pages 1-97

  • Fractional Part Integrals

    Furdui, Ovidiu

    Pages 99-137

  • A Bouquet of Series

    Furdui, Ovidiu

    Pages 139-251

Buy this book

eBook n/a
  • ISBN 978-1-4614-6762-5
  • Digitally watermarked, DRM-free
  • Included format: EPUB, PDF
  • ebooks can be used on all reading devices
Hardcover n/a
  • ISBN 978-1-4614-6761-8
  • Free shipping for individuals worldwide
Softcover n/a
  • ISBN 978-1-4899-9243-7
  • Free shipping for individuals worldwide
Rent the eBook  
  • Rental duration: 1 or 6 month
  • low-cost access
  • online reader with highlighting and note-making option
  • can be used across all devices
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Bibliographic Information

Bibliographic Information
Book Title
Limits, Series, and Fractional Part Integrals
Book Subtitle
Problems in Mathematical Analysis
Authors
Series Title
Problem Books in Mathematics
Copyright
2013
Publisher
Springer-Verlag New York
Copyright Holder
Springer Science+Business Media New York
eBook ISBN
978-1-4614-6762-5
DOI
10.1007/978-1-4614-6762-5
Hardcover ISBN
978-1-4614-6761-8
Softcover ISBN
978-1-4899-9243-7
Series ISSN
0941-3502
Edition Number
1
Number of Pages
XVIII, 274
Topics