عنوان

Understanding analysis /

1493927116

1493927124

9781493927111

9781493927128

9781493927111

b623745

Understanding analysis /

[Book]

Stephen Abbott.

Second edition.

1 online resource (xii, 312 pages) :

illustrations

Undergraduate texts in mathematics

Includes bibliographical references and index.

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.

0

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 from the first edition, and three more project-style sections have been added. Investigations of Eulers computation of ℓœ(2), the Weierstrass Approximation Theorem, and the gamma function are now among the books cohort of seminal results serving as motivation and payoff for the beginning student to master the methods of analysis. Review of the first edition: This is a dangerous book. Understanding Analysis is so well-written and the development of the theory so well-motivated that exposing students to it could well lead them to expect such excellence in all their textbooks. Understanding Analysis is perfectly titled; if your students read it, thats whats going to happen. This terrific book will become the text of choice for the single-variable introductory analysis course Steve Kennedy, MAA Reviews.

Springer

9781493927111

Mathematical analysis.

Analysis.

Applied Mathematics.

Engineering & Applied Sciences.

Mathematics.

Analyse mathématique.

Mathematical analysis.

MAT034000

PBK

QA

Abbott, Stephen,1964-

20201221082848.0

pn

[Book]

270410

Y