Stephen Abbott: Understanding Analysis

Cover: 9781493950263 | Understanding Analysis | Stephen Abbott | Taschenbuch | xii | Englisch

Rückseite: 9781493950263 | Understanding Analysis | Stephen Abbott | Taschenbuch | xii | Englisch

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Beschreibung

This lively introductory text exposes the student to the rewards of a rigorous study of functions of a real variable. In each chapter, informal discussions of questions that give analysis its inherent fascination are followed by precise, but not overly formal, developments of the techniques needed to make sense of them. By focusing on the unifying themes of approximation and the resolution of paradoxes that arise in the transition from the finite to the infinite, the text turns what could be a daunting cascade of definitions and theorems into a coherent and engaging progression of ideas. Acutely aware of the need for rigor, the student is much better prepared to understand what constitutes a proper mathematical proof and how to write one.

Fifteen years of classroom experience with the first edition of Understanding Analysis have solidified and refined the central narrative of the second edition. Roughly 150 new exercises join a selection of the best exercises fromthe first edition, and three more project-style sections have been added. Investigations of Euler's computation of zeta(2), the Weierstrass Approximation Theorem, and the gamma function are now among the book's cohort of seminal results serving as motivation and payoff for the beginning student to master the methods of analysis.

Zusammenfassung

Stephen D. Abbott is Professor of Mathematics at Middlebury College. He is a two-time winner of Middlebury's Perkins Award for Excellence in Teaching (1998, 2010). His published work includes articles in the areas of operator theory and functional analysis, the algorithmic foundations of robotics, and the intersection of science, mathematics and the humanities.

Inhaltsverzeichnis

Preface.- 1 The Real Numbers.- 2 Sequences and Series.- 3 Basic Topology of R.- 4 Functional Limits and Continuity.- 5 The Derivative.- 6 Sequences and Series of Functions.- 7 The Riemann Integral.- 8 Additional Topics.- Bibliography.- Index.

Details

Erscheinungsjahr:	2016
Fachbereich:	Analysis
Genre:	Importe , Mathematik
Rubrik:	Naturwissenschaften & Technik
Medium:	Taschenbuch
Inhalt:	xii 312 S. 36 farbige Illustr. 312 p. 36 illus. in color.
ISBN-13:	9781493950263
ISBN-10:	1493950266
Sprache:	Englisch
Einband:	Kartoniert / Broschiert
Autor:	Abbott, Stephen
Auflage:	Softcover reprint of the original 2nd edition 2015
Hersteller:	Springer Springer US, New York, N.Y.
Verantwortliche Person für die EU:	Springer Verlag GmbH, Tiergartenstr. 17, D-69121 Heidelberg, juergen.hartmann@springer.com
Maße:	235 x 155 x 18 mm
Von/Mit:	Stephen Abbott
Erscheinungsdatum:	29.10.2016
Gewicht:	0,493 kg