Limits, Series, and Fractional Part Integrals

1. Front Matter

   Pages i-xviii

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2. Special Limits

   • Ovidiu Furdui

   Pages 1-97

3. Fractional Part Integrals

   • Ovidiu Furdui

   Pages 99-137

4. A Bouquet of Series

   • Ovidiu Furdui

   Pages 139-251

5. Back Matter

   Pages 253-274

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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.

• Riemann-Zeta numbers
• fractional part integrals
• real analysis problems
• special constants
• special limits

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)

• , Department of Mathematics, Technical University of Cluj-Napoca, Cluj-Napoca, Romania

  Ovidiu Furdui

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.

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