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Introduction to Real Analysis - Hardcover, by Bartle Robert G.; Sherbert - Good
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- Buy It NowIntroduction to Real Analysis - Hardcover, by Bartle Robert G.; Sherbert - Good
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Item specifics
- Condition
- Book Title
- Introduction to Real Analysis
- ISBN
- 9780471433316
- Subject Area
- Mathematics
- Publication Name
- Introduction to Real Analysis
- Item Length
- 10.1 in
- Publisher
- Wiley & Sons, Incorporated, John
- Subject
- Functional Analysis, Mathematical Analysis
- Publication Year
- 2011
- Type
- Textbook
- Format
- Hardcover
- Language
- English
- Item Height
- 1.1 in
- Item Width
- 7.1 in
- Item Weight
- 28 Oz
- Number of Pages
- 416 Pages
About this product
Product Information
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, analyze 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 additional 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.
Product Identifiers
Publisher
Wiley & Sons, Incorporated, John
ISBN-10
0471433314
ISBN-13
9780471433316
eBay Product ID (ePID)
92268344
Product Key Features
Publication Name
Introduction to Real Analysis
Format
Hardcover
Language
English
Subject
Functional Analysis, Mathematical Analysis
Publication Year
2011
Type
Textbook
Subject Area
Mathematics
Number of Pages
416 Pages
Dimensions
Item Length
10.1 in
Item Height
1.1 in
Item Width
7.1 in
Item Weight
28 Oz
Additional Product Features
Edition Number
4
LCCN
2010-045251
Intended Audience
College Audience
Lc Classification Number
Qa300.B294 2011
Table of Content
CHAPTER 1 PRELIMINARIES. 1.1 Sets and Functions. 1.2 Mathematical Induction. 1.3 Finite and Infinite Sets. CHAPTER 2 THE REAL NUMBERS. 2.1 The Algebraic and Order Properties of R. 2.2 Absolute Value and the Real Line. 2.3 The Completeness Property of R. 2.4 Applications of the Supremum Property. 2.5 Intervals. CHAPTER 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. CHAPTER 4 LIMITS. 4.1 Limits of Functions. 4.2 Limit Theorems. 4.3 Some Extensions of the Limit Concept. CHAPTER 5 CONTINUOUS FUNCTIONS. 5.1 Continuous Functions. 5.2 Combinations of Continuous Functions. 5.3 Continuous Functions on Intervals. 5.4 Uniform Continuity. 5.5 Continuity and Gauges. 5.6 Monotone and Inverse Functions. CHAPTER 6 DIFFERENTIATION. 6.1 The Derivative. 6.2 The Mean Value Theorem. 6.3 L'Hospital's Rules. 6.4 Taylor's Theorem. CHAPTER 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. CHAPTER 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. CHAPTER 9 INFINITE SERIES. 9.1 Absolute Convergence. 9.2 Tests for Absolute Convergence. 9.3 Tests for Nonabsolute Convergence. 9.4 Series of Functions. CHAPTER 10 THE GENERALIZED RIEMANN INTEGRAL. 10.1 Definition and Main Properties. 10.2 Improper and Lebesgue Integrals. 10.3 Infinite Intervals. 10.4 Convergence Theorems. CHAPTER 11 A GLIMPSE INTO TOPOLOGY. 11.1 Open and Closed Sets in R. 11.2 Compact Sets. 11.3 Continuous Functions. 11.4 Metric 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. REFERENCES. PHOTO CREDITS. HINTS FOR SELECTED EXERCISES. INDEX.
Copyright Date
2011
Dewey Decimal
515
Dewey Edition
22
Illustrated
Yes
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- 27 Jun, 2019
Introduction to real analysis
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