Understanding Analysis (with Instructor's Solutions Manual)

✍ Scribed by Stephen Abbott

• Publisher: Springer
• Year: 2010
• Tongue: English
• Leaves: 429
• Category: Library

✦ Synopsis

This elementary presentation exposes readers to both the process of rigor and the rewards inherent in taking an axiomatic approach to the study of functions of a real variable. The aim is to challenge and improve mathematical intuition rather than to verify it. The philosophy of this book is to focus attention on questions which give analysis its inherent fascination. Each chapter begins with the discussion of some motivating examples and concludes with a series of questions.

✦ Table of Contents

Front Cover......Page 1
Back Cover......Page 2
Copyright......Page 4
Preface......Page 5
Contents......Page 11
1. The Real Numbers......Page 13
2. Sequences and Series......Page 47
3. Basic Topology of R......Page 87
4. Functional Limits and Continuity......Page 111
5. The Derivative......Page 141
6. Sequences and Series of Functions......Page 163
7. The Riemann Integral......Page 195
8. Additional Topics......Page 225
Bibliography......Page 263
Index......Page 265
Instructor's Solutions Manual......Page 270
Author's note......Page 273
Contents......Page 275
1. The Real Numbers......Page 277
2. Sequences and Series......Page 295
3. Basic Topology of R......Page 321
4. Functional Limits and Continuity......Page 333
5. The Derivative......Page 351
6. Sequences and Series of Functions......Page 365
7. The Riemann Integral......Page 387
8. Additional Topics......Page 405