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Cover: 9783030771386 | Sharpening Mathematical Analysis Skills | Ovidiu Furdui (u. a.) | Buch
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Sharpening Mathematical Analysis Skills
Buch von Ovidiu Furdui (u. a.)
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.
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.
Über den Autor
Alina Sînt¿m¿rian is a Professor of Mathematics at Technical University of Cluj-Napoca, Romania. She holds a PhD in Mathematics from Babe¿-Bolyai University, Cluj-Napoca, Romania. Her research interests focus on non-linear operators, fixed point theory, multivalued operators, mathematical analysis, constants evaluation, asymptotic expansions.
Ovidiu Furdui is an Associate Professor of Mathematics at Technical University of Cluj-Napoca, Romania. He has published more than 500 problems in journals, with a problem column, from all over the world and he is the author of Limits, Series, and Fractional Part Integrals and has co-authored Square Matrices of Order 2, both published by Springer.
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: 2021
Fachbereich: Analysis
Genre: Mathematik, Medizin, Naturwissenschaften, Technik
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
Einband: Gebunden
Autor: Furdui, Ovidiu
Sînt¿m¿rian, Alina
Auflage: 1st edition 2021
Hersteller: Springer International Publishing
Verantwortliche Person für die EU: Springer Verlag GmbH, Tiergartenstr. 17, D-69121 Heidelberg, juergen.hartmann@springer.com
Maße: 241 x 160 x 34 mm
Von/Mit: Ovidiu Furdui (u. a.)
Erscheinungsdatum: 26.10.2021
Gewicht: 1,093 kg
Artikel-ID: 119926821
Über den Autor
Alina Sînt¿m¿rian is a Professor of Mathematics at Technical University of Cluj-Napoca, Romania. She holds a PhD in Mathematics from Babe¿-Bolyai University, Cluj-Napoca, Romania. Her research interests focus on non-linear operators, fixed point theory, multivalued operators, mathematical analysis, constants evaluation, asymptotic expansions.
Ovidiu Furdui is an Associate Professor of Mathematics at Technical University of Cluj-Napoca, Romania. He has published more than 500 problems in journals, with a problem column, from all over the world and he is the author of Limits, Series, and Fractional Part Integrals and has co-authored Square Matrices of Order 2, both published by Springer.
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: 2021
Fachbereich: Analysis
Genre: Mathematik, Medizin, Naturwissenschaften, Technik
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
Einband: Gebunden
Autor: Furdui, Ovidiu
Sînt¿m¿rian, Alina
Auflage: 1st edition 2021
Hersteller: Springer International Publishing
Verantwortliche Person für die EU: Springer Verlag GmbH, Tiergartenstr. 17, D-69121 Heidelberg, juergen.hartmann@springer.com
Maße: 241 x 160 x 34 mm
Von/Mit: Ovidiu Furdui (u. a.)
Erscheinungsdatum: 26.10.2021
Gewicht: 1,093 kg
Artikel-ID: 119926821
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