An edition of Introduction to real analysis (2011)

Introduction to real analysis

4th ed.

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Cover of: Introduction to real analysis by Robert Gardner Bartle, Robert Gardner Bartle
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An edition of Introduction to real analysis (2011)

Introduction to real analysis

4th ed.

by

  • ★★★★★ 5.0 (1 rating) ·
  • 1 Have read

"This text provides the fundamental concepts and techniques of real analysis for students in all of these areas. It helps one develop the ability to think deductively, analyse mathematical situations and extend ideas to a new context. Like the first three editions, this edition maintains the same spirit and user-friendly approach with addition examples and expansion on Logical Operations and Set Theory. There is also content revision in the following areas: introducing point-set topology before discussing continuity, including a more thorough discussion of limsup and limimf, covering series directly following sequences, adding coverage of Lebesgue Integral and the construction of the reals, and drawing student attention to possible applications wherever possible"--

Publish Date
Publisher
Wiley
Language
English
Pages
402

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Subjects

Functions of real variables, Mathematical analysis
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Cover of: Introduction to real analysis
Introduction to real analysis
2011, Wiley
in English - 4th ed.

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Book Details

Table of Contents

Ch. 1.Preliminaries: 1.1. Sets and functions; 1.2. Mathematical induction; 1.3. Finite and infinite sets
Ch. 2. The Real Numbers: 2.1. The algebraic and order properties of R; 2.2. Absolute value and real line; 2.3. The completeness property of R; 2.4. Applications of the supremum property; 2.5. Intervals
Ch. 3. Sequences and series: 3.1. Sequences and their limits; 3.2. Limit theorems; 3.3. Monotone sequences; 3.4. Subsequences and the Bolzano-Weierstrass theorem; 3.5. The Cauchy criterion; 3.6. Properly divergent sequences; 3.7. Introduction to infinite series
Ch. 4. Limits: 4.1. Limits of functions; 4.2. Limit theorems; 4.3. Some extensions of the limit concept
Ch. 5. Continuous functions: 5.1. Continuous runctions; 5.2 . Combinations of continuous runctions; 5.3. Continuous functions on intervals; 5.4. Uniform continuity; 5.5. Continuity and gauges; 5.6. Monotone and inverse functions
Ch. 6. Differentiation: 6.1. The derivative; 6.2. The mean value theorem; 6.3. L'Hospital's rules; 6.4. Taylor's Theorem
Ch. 7. The Riemann integral: 7.1. Riemann integral; 7.2. Riemann integrable functions; 7.3. The fundamental theorem; 7.4. The Darboux integral; 7.5. Approximate integration
Ch. 8. Sequences of functions: 8.1. Pointwise and uniform convergence; 8.2. Interchange of limits; 8.3. The exponential and logarithmic functions; 8.4. The trigonometric functions
Ch. 9. Infinite series: 9.1. Absolute convergence; 9.2. Tests for absolute convergence; 9.3. Tests for nonabsolute convergence; 9.4. Series of functions
Ch. 10. The generalized Riemann integral: 10.1. Definition and main poperties; 10.2. Improper and Lebesgue integrals; 10.3. Infinite intervals; 10.4. Convergence theorems
Ch. 11. A glimpse into topology: 11.1. Open and closed sets in R; 11.2 Compact sets; 11.3. Continuous functions; 11.4. Metrtic Spaces
Appendix A. Logic and proofs
Appendix B. Finite and countable sets
Appendix C. The Riemann and Lebesgue criteria
Appendix D. Approximate integration
Appendix E. Two examples.

Edition Notes

Includes bibliographical references and index.

Published in
Hoboken, NJ

Classifications

Dewey Decimal Class
515
Library of Congress
QA300 .B294 2011, QA300.B294 2011

The Physical Object

Pagination
xiii, 402 p. :
Number of pages
402

Edition Identifiers

Open Library
OL25120202M
Internet Archive
introductiontore00bart_077
ISBN 10
0471433314
ISBN 13
9780471433316
LCCN
2010045251
OCLC/WorldCat
671573454

Work Identifiers

Work ID
OL16316417W

Source records

Library of Congress MARC record
Internet Archive item record
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