| 书目名称 | Real Mathematical Analysis |
| 编辑 | Charles Chapman Pugh |
| 视频video | |
| 概述 | The exposition is informal and relaxed, with many helpful asides, and examples.Contains an excellent selection of more than 500 exercises.Ideal for self-study |
| 丛书名称 | Undergraduate Texts in Mathematics |
| 图书封面 |  |
| 描述 | Was plane geometry your favorite math course in high school? Did you like proving theorems? Are you sick of memorizing integrals? If so, real analysis could be your cup of tea. In contrast to calculus and elementary algebra, it involves neither formula manipulation nor applications to other fields of science. None. It is pure mathematics, and I hope it appeals to you, the budding pure mathematician. Berkeley, California, USA CHARLES CHAPMAN PUGH Contents 1 Real Numbers 1 1 Preliminaries 1 2 Cuts . . . . . 10 3 Euclidean Space . 21 4 Cardinality . . . 28 5* Comparing Cardinalities 34 6* The Skeleton of Calculus 36 Exercises . . . . . . . . 40 2 A Taste of Topology 51 1 Metric Space Concepts 51 2 Compactness 76 3 Connectedness 82 4 Coverings . . . 88 5 Cantor Sets . . 95 6* Cantor Set Lore 99 7* Completion 108 Exercises . . . 115 x Contents 3 Functions of a Real Variable 139 1 Differentiation. . . . 139 2 Riemann Integration 154 Series . . 179 3 Exercises 186 4 Function Spaces 201 1 Uniform Convergence and CO[a, b] 201 2 Power Series . . . . . . . . . . . . 211 3 Compactness and Equicontinuity in CO . 213 4 Uniform Approximation in CO 217 Contractions and ODE‘s . . . . . . . . 228 5 |
| 出版日期 | Textbook 20021st edition |
| 关键词 | Real Mathematical Analysis; calculus; integral; mathematical analysis; real analysis; real number |
| 版次 | 1 |
| doi | https://doi.org/10.1007/978-0-387-21684-3 |
| isbn_softcover | 978-1-4419-2941-9 |
| isbn_ebook | 978-0-387-21684-3Series ISSN 0172-6056 Series E-ISSN 2197-5604 |
| issn_series | 0172-6056 |
| copyright | Springer Science+Business Media New York 2002 |
发表于 2025-3-21 19:39:30
