The Resource Understanding analysis, Stephen Abbott

Understanding analysis, Stephen Abbott

Label
Understanding analysis
Title
Understanding analysis
Statement of responsibility
Stephen Abbott
Creator
Author
Subject
Genre
Language
eng
Summary
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
Member of
Cataloging source
GW5XE
http://library.link/vocab/creatorDate
1964-
http://library.link/vocab/creatorName
Abbott, Stephen
Dewey number
515
Illustrations
illustrations
Index
index present
LC call number
QA300
Literary form
non fiction
Nature of contents
  • dictionaries
  • bibliography
Series statement
Undergraduate texts in mathematics
http://library.link/vocab/subjectName
  • Mathematical analysis
  • Analyse mathématique
  • Engineering & Applied Sciences
  • Applied Mathematics
  • Mathematics
  • Analysis
Label
Understanding analysis, Stephen Abbott
Link
https://ezproxy.lib.ou.edu/login?url=http://link.springer.com/10.1007/978-1-4939-2712-8
Instantiates
Publication
Antecedent source
unknown
Bibliography note
Includes bibliographical references and index
Carrier category
online resource
Carrier category code
  • cr
Carrier MARC source
rdacarrier
Color
multicolored
Content category
text
Content type code
  • txt
Content type MARC source
rdacontent
Contents
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
Dimensions
unknown
Edition
Second edition.
Extent
1 online resource (xii, 312 pages)
File format
unknown
Form of item
online
Isbn
9781493927111
Level of compression
unknown
Media category
computer
Media MARC source
rdamedia
Media type code
  • c
Note
SpringerLink
Other control number
10.1007/978-1-4939-2712-8
Other physical details
illustrations
Quality assurance targets
not applicable
Reformatting quality
unknown
Sound
unknown sound
Specific material designation
remote
System control number
  • (OCoLC)910160716
  • (OCoLC)ocn910160716
Label
Understanding analysis, Stephen Abbott
Link
https://ezproxy.lib.ou.edu/login?url=http://link.springer.com/10.1007/978-1-4939-2712-8
Publication
Antecedent source
unknown
Bibliography note
Includes bibliographical references and index
Carrier category
online resource
Carrier category code
  • cr
Carrier MARC source
rdacarrier
Color
multicolored
Content category
text
Content type code
  • txt
Content type MARC source
rdacontent
Contents
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
Dimensions
unknown
Edition
Second edition.
Extent
1 online resource (xii, 312 pages)
File format
unknown
Form of item
online
Isbn
9781493927111
Level of compression
unknown
Media category
computer
Media MARC source
rdamedia
Media type code
  • c
Note
SpringerLink
Other control number
10.1007/978-1-4939-2712-8
Other physical details
illustrations
Quality assurance targets
not applicable
Reformatting quality
unknown
Sound
unknown sound
Specific material designation
remote
System control number
  • (OCoLC)910160716
  • (OCoLC)ocn910160716

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