Introduction to Real Analysis, 4th Edition

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Wiley Global Education, Jan 14, 2011 - Mathematics - 402 pages
2 Reviews
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.
 

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User Review  - dwarfplanet9 - LibraryThing

This book was used in my Real Analysis course. The subject would be hard to learn from this book alone, but lucky for me I had a great teacher at San Jose State University. For those trying to use the ... Read full review

LibraryThing Review

User Review  - ssd7 - LibraryThing

Introduction to Real Analysis is easily one of my favorite mathematics textbooks. The explanation is excellent and the in-text examples are interesting. Unlike most mathematics text books I've read ... Read full review

Contents

CHAPTER 1 PRELIMINARIES
1
CHAPTER 2 THE REAL NUMBERS
23
CHAPTER 3 SEQUENCES AND SERIES
54
CHAPTER 4 LIMITS
102
CHAPTER 5 CONTINUOUS FUNCTIONS
124
CHAPTER 6 DIFFERENTIATION
161
CHAPTER 7 THE RIEMANN INTEGRAL
198
CHAPTER 8 SEQUENCES OF FUNCTIONS
241
LOGIC AND PROOFS
348
FINITE AND COUNTABLE SETS
357
THE RIEMANN AND LEBESGUE CRITERIA
360
APPROXIMATE INTEGRATION
364
TWO EXAMPLES
367
REFERENCES
370
PHOTO CREDITS
371
HINTS FOR SELECTED EXERCISES
372

CHAPTER 9 INFINITE SERIES
267
CHAPTER 10 THE GENERALIZED RIEMANN INTEGRAL
288
CHAPTER 11 A GLIMPSE INTO TOPOLOGY
326
INDEX
395
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