Limits, Series, and Fractional Part Integrals

Ovidiu Furdui

ISBN 10: 148999243X / ISBN 13: 9781489992437

Editore: Springer New York, Springer US Jun 2015, 2015

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Neuware -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 chapterfocuses onthe 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 whichare 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 whoworks 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.Springer Verlag GmbH, Tiergartenstr. 17, 69121 Heidelberg 292 pp. Englisch.

Codice articolo 9781489992437

Dati bibliografici

• Titolo: Limits, Series, and Fractional Part Integrals
• Editore: Springer New York, Springer US Jun 2015
• Data di pubblicazione: 2015
• Lingua: Inglese
• ISBN 10: 148999243X
• ISBN 13: 9781489992437
• Rilegatura: Taschenbuch
• Condizione: Neu

Descrizione articolo

Riassunto

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.

Informazioni sull?autore

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.