Understanding Analysis - Stephen Abbott

Understanding Analysis

(Autor)

Buch | Softcover
312 Seiten
2016 | Softcover reprint of the original 2nd ed. 2015
Springer-Verlag New York Inc.
978-1-4939-5026-3 (ISBN)
42,79 inkl. MwSt
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.
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 ζ(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.

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.          

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.          

Erscheinungsdatum
Reihe/Serie Undergraduate Texts in Mathematics
Zusatzinfo 36 Illustrations, color; XII, 312 p. 36 illus. in color.
Verlagsort New York
Sprache englisch
Maße 155 x 235 mm
Themenwelt Mathematik / Informatik Mathematik Analysis
Schlagworte Abbott analysis • Baire category theorem • Calculus • Derivatives • fundamental theorem of calculus • gamma function • generalized Riemann integral • general topology • Henstock integral • intermediate value theorem • mean value theorem • power series • Real analysis • Real Numbers • Riemann integral • Taylor series • Weierstrass approximation theorem
ISBN-10 1-4939-5026-6 / 1493950266
ISBN-13 978-1-4939-5026-3 / 9781493950263
Zustand Neuware
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