An Introduction to Manifolds
Manifolds, the higher-dimensional analogues of smooth curves and surfaces, are fundamental objects in modern mathematics. Combining aspects of algebra, topology, and analysis, manifolds have also been applied to classical mechanics, general relativity, and quantum field theory. In this streamlined i...
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| Format: | eBook |
| Language: | English |
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New York, NY
Springer New York
2011, 2011
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| Edition: | 2nd ed. 2011 |
| Series: | Universitext
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| Subjects: | |
| Online Access: | |
| Collection: | Springer eBooks 2005- - Collection details see MPG.ReNa |
Table of Contents:
- Preface to the Second Edition
- Preface to the First Edition
- Chapter 1. Euclidean Spaces
- Chapter 2. Manifolds
- Chapter 3. The Tangent Space
- Chapter 4. Lie Groups and Lie Algebras.-Chapter 5. Differential Forms
- Chapter 6. Integration.-Chapter 7. De Rham Theory
- Appendices
- A. Point-Set Topology
- B. The Inverse Function Theorem on R(N) and Related Results
- C. Existence of a Partition of Unity in General
- D. Linear Algebra
- E. Quaternions and the Symplectic Group
- Solutions to Selected Exercises
- Hints and Solutions to Selected End-of-Section Problems
- List of Symbols
- References
- Index