# Introduction to Real Analysis, 4th Edition

Wiley Global Education, Jan 14, 2011 - Mathematics - 402 pages
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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#### LibraryThing Review

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