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 methodsfor 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.

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.

Erscheinungsjahr:	2021
Fachbereich:	Analysis
Genre:	Mathematik
Rubrik:	Naturwissenschaften & Technik
Medium:	Buch
Inhalt:	xx 536 S. 1 s/w Illustr. 10 farbige Illustr. 536 p. 11 illus. 10 illus. in color.
ISBN-13:	9783030771386
ISBN-10:	3030771385
Sprache:	Englisch
Herstellernummer:	978-3-030-77138-6
Autor:	Sîntamarian, Alina Furdui, Ovidiu
Auflage:	1st ed. 2021
Hersteller:	Springer Springer, Berlin Springer International Publishing
Abbildungen:	XX, 536 p. 11 illus., 10 illus. in color.
Maße:	241 x 160 x 34 mm
Von/Mit:	Alina Sîntamarian (u. a.)
Erscheinungsdatum:	26.10.2021
Gewicht:	1,043 kg

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