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by Michael J. Schramm
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ISBN: 0486469131 Dover Publications Price: $19.95 |
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This text forms a bridge between courses in calculus and real analysis. It focuses on the construction of mathematical proofs as well as their final content. Suitable for upper-level undergraduates and graduate students of real analysis, it also provides a vital reference book for advanced courses in mathematics. 1996 edition.
Reprint of the Prentice Hall, Englewood Cliffs, New Jersey, 1996 edition.
Table of Contents for Introduction to Real Analysis
| Preface | |||||||
| Part One: Preliminaries | |||||||
| Chapter 1. Building Proofs | |||||||
| Chapter 2. Finite, Infinite, and Even Bigger | |||||||
| Chapter 3. Algebra of the Real Numbers | |||||||
| Chapter 4. Ordering, Intervals, and Neighborhoods | |||||||
| Part Two: The Structure of the Real Number System | |||||||
| Chapter 5. Upper Bounds and Suprema | |||||||
| Chapter 6. Nested Intervals | |||||||
| Chapter 7. Cluster Points | |||||||
| Chapter 8. Topology of the Real Numbers | |||||||
| Chapter 9. Sequences | |||||||
| Chapter 10. Sequences and the Big Theorem | |||||||
| Chapter 11. Compact Sets | |||||||
| Chapter 12. Connected Sets | |||||||
| Part Three: Topics from Calculus | |||||||
| Chapter 13. Series | |||||||
| Chapter 14. Uniform Continuity | |||||||
| Chapter 15. Sequences and Series of Functions | |||||||
| Chapter 16. Differentiation | |||||||
| Chapter 17. Integration | |||||||
| Chapter 18. Interchanging Limit Processes | |||||||
| Part Four: Selected Shorts | |||||||
| Chapter 19. Increasing Functions | |||||||
| Chapter 20. Continuous Functions and Differentiability | |||||||
| Chapter 21. Continuous Functions and Integrability | |||||||
| Chapter 22. We Build the Real Numbers | |||||||
| References and further reading | |||||||
| Index |