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Limits, Series, and Fractional Part Integrals: Problems in Mathematical Analysis (Problem Books in Mathematics), by Ovidiu Furdui
Ebook Download Limits, Series, and Fractional Part Integrals: Problems in Mathematical Analysis (Problem Books in Mathematics), by Ovidiu Furdui
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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.
- Sales Rank: #2612351 in Books
- Published on: 2013-05-30
- Original language: English
- Number of items: 1
- Dimensions: 9.21" h x .69" w x 6.14" l, 1.30 pounds
- Binding: Hardcover
- 274 pages
Review
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)
From the Back Cover
Limits, Series, and Fractional Part Integrals: Problems in Mathematical Analysis features original problems in classical analysis that invite the reader to explore a host of strategies and mathematical tools used for solving real analysis problems. The book is designed to fascinate the novice, puzzle the expert, and trigger the imaginations of all. The text is geared toward graduate students in mathematics and engineering, researchers, and anyone who works on topics at the frontier of pure and applied mathematics. Moreover, it is the first book in mathematical literature concerning the calculation of fractional part integrals and series of various types.
Most problems are neither easy nor standard and deal with modern topics of classical analysis. Each chapter has a section of open problems that may be considered as research projects for students who are taking advanced calculus classes. The intention of having these problems collected in the book is to stimulate the creativity and the discovery of new and original methods for proving known results and establishing new ones.
The book is divided into three parts, each of them containing a chapter dealing with a particular type of problems. The first chapter contains problems on limits of special sequences and Riemann integrals; the second chapter deals with the calculation of special classes of integrals involving a fractional part term; and the third chapter hosts a collection of problems on the calculation of series (single or multiple) involving either a numerical or a functional term.
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About the Author
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.
Most helpful customer reviews
4 of 4 people found the following review helpful.
A Skyful of Limits
By Henry J. Ricardo
This is an unusual collection of problems and solutions concerning limits, infinite series, and integrals involving fractional parts. I have been following the author's problem posing and problem solving career for several years now and I am delighted that he has provided an exposition of elegant methods of handling challenging problems in analysis at the Advanced Calculus level. I recommend this book highly to anyone interested in classical analysis.
2 of 2 people found the following review helpful.
This book is a treasure trove for math lovers
By Chris Varo
The author has a special gift for creating interesting and challenging problems. His problems appear regularly in popular mathematics journals and the readers love them. All these problems are very educational and inspiring.
Now the reader has a chance to see them together, collected in this wonderful book.
2 of 2 people found the following review helpful.
Truly Marvellous Book
By BJ. Albers
This is a rare masterpiece and a true goldmine for anyone willing to invest time into attempting the exercises in this book. Doing so will elevate your analysis skills to new heights.
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