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Sharpening mathematical analysis skills

Furdui, Ovidiu.

Sharpening mathematical analysis skills

Record Type:	Electronic resources : Monograph/item
Title/Author:	Sharpening mathematical analysis skillsby Alina Sintamarian, Ovidiu Furdui.
Author:	Sintamarian, Alina.
other author:	Furdui, Ovidiu.
Published:	Cham :Springer International Publishing :2021.
Description:	xx, 536 p. :ill. (chiefly col.), digital ;24 cm.
Contained By:	Springer Nature eBook
Subject:	Mathematical analysis.
Online resource:	https://doi.org/10.1007/978-3-030-77139-3
ISBN:	9783030771393$q(electronic bk.)

Sharpening mathematical analysis skills
Sintamarian, Alina.

Sharpening mathematical analysis skills[electronic resource] /by Alina Sintamarian, Ovidiu Furdui. - Cham :Springer International Publishing :2021. - xx, 536 p. :ill. (chiefly col.), digital ;24 cm. - Problem books in mathematics,2197-8506. - Problem books in mathematics..

Preface -- Notations -- Sequences of Real Numbers -- Series of Real Numbers -- Power Series -- Derivatives and Applications -- Partial Derivatives and Applications -- Implicit Functions -- Challenges, Gems, and Mathematical Beauties -- An Artistry of Quadratic Series. Two New Proofs of Sandham-Yeung Series -- Solutions -- References -- Index.

This book gathers together a novel collection of problems in mathematical analysis that are challenging and worth studying. They cover most of the classical topics of a course in mathematical analysis, and include challenges presented with an increasing level of difficulty. Problems are designed to encourage creativity, and some of them were especially crafted to lead to open problems which might be of interest for students seeking motivation to get a start in research. The sets of problems are comprised in Part I. The exercises are arranged on topics, many of them being preceded by supporting theory. Content starts with limits, series of real numbers and power series, extending to derivatives and their applications, partial derivatives and implicit functions. Difficult problems have been structured in parts, helping the reader to find a solution. Challenges and open problems are scattered throughout the text, being an invitation to discover new original methods for proving known results and establishing new ones. The final two chapters offer ambitious readers splendid problems and two new proofs of a famous quadratic series involving harmonic numbers. In Part II, the reader will find solutions to the proposed exercises. Undergraduate students in mathematics, physics and engineering, seeking to strengthen their skills in analysis, will most benefit from this work, along with instructors involved in math contests, individuals who want to enrich and test their knowledge in analysis, and anyone willing to explore the standard topics of mathematical analysis in ways that aren't commonly seen in regular textbooks.

ISBN: 9783030771393$q(electronic bk.)

Standard No.: 10.1007/978-3-030-77139-3doiSubjects--Topical Terms:

186133
Mathematical analysis.

LC Class. No.: QA300 / .S56 2021

Dewey Class. No.: 515

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505 0 $a Preface -- Notations -- Sequences of Real Numbers -- Series of Real Numbers -- Power Series -- Derivatives and Applications -- Partial Derivatives and Applications -- Implicit Functions -- Challenges, Gems, and Mathematical Beauties -- An Artistry of Quadratic Series. Two New Proofs of Sandham-Yeung Series -- Solutions -- References -- Index.
520 $a This book gathers together a novel collection of problems in mathematical analysis that are challenging and worth studying. They cover most of the classical topics of a course in mathematical analysis, and include challenges presented with an increasing level of difficulty. Problems are designed to encourage creativity, and some of them were especially crafted to lead to open problems which might be of interest for students seeking motivation to get a start in research. The sets of problems are comprised in Part I. The exercises are arranged on topics, many of them being preceded by supporting theory. Content starts with limits, series of real numbers and power series, extending to derivatives and their applications, partial derivatives and implicit functions. Difficult problems have been structured in parts, helping the reader to find a solution. Challenges and open problems are scattered throughout the text, being an invitation to discover new original methods for proving known results and establishing new ones. The final two chapters offer ambitious readers splendid problems and two new proofs of a famous quadratic series involving harmonic numbers. In Part II, the reader will find solutions to the proposed exercises. Undergraduate students in mathematics, physics and engineering, seeking to strengthen their skills in analysis, will most benefit from this work, along with instructors involved in math contests, individuals who want to enrich and test their knowledge in analysis, and anyone willing to explore the standard topics of mathematical analysis in ways that aren't commonly seen in regular textbooks.
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