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Mathematics - Analysis | Limits, Series, and Fractional Part Integrals - Problems in Mathematical Analysis

Limits, Series, and Fractional Part Integrals

Problems in Mathematical Analysis

Furdui, Ovidiu

2013, XVIII, 274 p.

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  • 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​

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.

 

Content Level » Graduate

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

Related subjects » Analysis

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