| 词条 | 微分流形导论 |
| 释义 | 图书信息出版社: 世界图书出版公司; 第1版 (2010年9月1日) 外文书名: Introduction to Differentiable Manifolds Second Edition 平装: 250页 正文语种: 英语 开本: 24 ISBN: 9787510027468, 7510027462 条形码: 9787510027468 尺寸: 22.2 x 14.6 x 1.2 cm 重量: 340 g 作者简介作者：（美国）朗（Serge Lang） 内容简介《微分流形导论(第2版)(英文版)》内容简介：This book is an outgrowth of my Introduction to Differentiable Manifolds (1962) and Differential Manifolds (1972). Both I and my publishers felt it worth while to keep available a brief introduction to differential manifolds. 目录Foreword Acknowledgments CHAPTER I Differential Calculus 1. Categories 2. Finite Dimensional Vector Spaces 3. Derivatives and Composition of Maps 4. Integration and Tayior's Formula 5. The Inverse Mapping Theorem CHAPTER II Manifolds 1. Atlases, Charts, Morphisms 2. Submanifolds, Immersions, Submersions 3. Partitions of Unity 4. Manifolds with Boundary CHAPTER III Vector Bundles l. Definition, Pull Backs 2. The Tangent Bundle 3. Exact Sequences of Bundles 4. Operations on Vector Bundles 5. Splitting of Vector Bundles CHAPTER IV Vector Fields and Differential Equations 1. Existence Theorem for Differential Equations 2. Vector Fields, Curves, and Flows 3. Sprays 4. The Flow of a Spray and the Exponential Map 5. Existence of Tubular Neighborhoods 6. Uniqueness of Tubular Neighborhoods CHAPTER V Oiretions on Vector Fields end Differential Forms 1. Vector Fields, Differential Operators, Brackets 2. Lie Derivative 3. Exterior Derivative 4. The Poincare Lemma 5. Contractions and Lie Derivative 6. Vector Fields and l-Forms Under Self Duality 7. The Canonical 2-Form 8. Darboux's Theorem CHAPTER VI The Theorem of Frobenius 1. Statement of the Theorem 2. Differential Equations Depending on a Parameter 3. Proof of the Theorem 4. The Global Formulation 5. Lie Groups and Subgroups CHAPTER VII Metrics 1. Definition and Functoriality 2. The Metric Group 3. Reduction to the Metric Group 4. Metric Tubular Neighborhoods 5. The Morse Lemma 6. The Riemannian Distance 7. The Canonical Spray CHAPTER VIII Integretion of Differential Forms 1. Sets of Measure 0 2. Change of Variables Formula 3. Orientation 4. The Measure Associated with a Differential Form CHAPTER IX Stokes' Theorem 1. Stokes' Theorem for a Rectangular Simplex 2. Stokes' Theorem on a Manifold 3. Stokes' Theorem with Singularities CHAPTER X Applications of Stokes' Theorem 1. The Maximal de Rham Cohomology 2. Volume forms and the Divergence 3. The Divergence Theorem 4. Cauchy's Theorem 5. The Residue Theorem Bibliography Index |
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