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Book Title
Introduction to Real Analysis
ISBN
9780471433316
Publication Year
2011
Type
Textbook
Format
Hardcover
Language
English
Publication Name
Introduction to Real Analysis
Item Height
0.8in
Author
Robert G. Bartle, Donald R. Sherbert
Item Length
10.2in
Publisher
Wiley & Sons, Incorporated, John
Item Width
7.2in
Item Weight
27.9 Oz
Number of Pages
416 Pages

關於產品

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

Author
Robert G. Bartle, Donald R. Sherbert
Publication Name
Introduction to Real Analysis
Format
Hardcover
Language
English
Publication Year
2011
Type
Textbook
Number of Pages
416 Pages

Dimensions

Item Length
10.2in
Item Height
0.8in
Item Width
7.2in
Item Weight
27.9 Oz

Additional Product Features

Lc Classification Number
Qa300.B294 2011
Edition Number
4
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
Topic
Functional Analysis, Mathematical Analysis
Lccn
2010-045251
Dewey Decimal
515
Intended Audience
College Audience
Dewey Edition
22
Illustrated
Yes
Genre
Mathematics

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