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...
Guardado en:
| Autor principal: | |
|---|---|
| Formato: | Livre numérique |
| Lenguaje: | Anglais |
| Publicado: |
New York, NY :
Springer New York
[20..].
Cham : Springer Nature |
| Edición: | 2nd edition. |
| Colección: | Universitext
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| Materias: | |
| Acceso en línea: | Accès sur la plateforme de l'éditeur Accès sur la plateforme Istex Accès Université d'Orléans Accès INSA CVL |
| Nota: |
Archives Springer e-books (Licence nationale) Archives Springer e-books (Licence nationale) |
| Autres localisations: | Voir dans le Sudoc |
| Edition sous un autre format: | • An introduction to manifolds, Loring W. Tu, 2nd edition [revue et augmentée], 2011, New York, Springer, 1 vol. (XVIII-410 p.), Universitext, 978-1-4419-7399-3 • An Introduction to Manifolds, Texte imprimé, 9781441974013 |
Tabla de Contenidos:
- 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.
- 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