Sharpening Mathematical Analysis Skills

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Sprache: Englisch

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Beschreibung

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.

Zusammenfassung

Brings carefully selected, challenging problems in mathematical analysis

Explores the standard topics of mathematical analysis in ways not seen in regular textbooks

Offers original problems of mathematical analysis called gems, scattered throughout the text, that stimulate the reader who enjoy creativity and discovery in mathematics

Useful for students seeking to strengthen their skills in analysis, to prepare for math contests, instructors and connoisseurs of ingenious computations

Inhaltsverzeichnis

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.

Details

Erscheinungsjahr:	2022
Fachbereich:	Analysis
Genre:	Mathematik , Medizin , Naturwissenschaften , Technik
Rubrik:	Naturwissenschaften & Technik
Medium:	Taschenbuch
Inhalt:	xx 536 S. 1 s/w Illustr. 10 farbige Illustr. 536 p. 11 illus. 10 illus. in color.
ISBN-13:	9783030771416
ISBN-10:	3030771415
Sprache:	Englisch
Einband:	Kartoniert / Broschiert
Autor:	Furdui, Ovidiu Sînt¿m¿rian, Alina
Auflage:	1st edition 2021
Hersteller:	Springer Nature Switzerland Springer International Publishing
Verantwortliche Person für die EU:	Springer Verlag GmbH, Tiergartenstr. 17, D-69121 Heidelberg, juergen.hartmann@springer.com
Maße:	235 x 155 x 30 mm
Von/Mit:	Ovidiu Furdui (u. a.)
Erscheinungsdatum:	27.10.2022
Gewicht:	0,832 kg

Artikel-ID: 125330985