An introduction to manifolds
Manifolds, the higher-dimensional analogs 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 int...
Shranjeno v:
| Glavni avtor: | |
|---|---|
| Format: | Livre numérique |
| Jezik: | Anglais |
| Izdano: |
New York, NY :
Springer New York
[20..].
Cham : Springer Nature |
| Izdaja: | 1st ed. 2008. |
| Serija: | Universitext
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| Teme: | |
| Online dostop: | Accès sur la plateforme de l'éditeur Accès sur la plateforme Istex Accès Université d'Orléans Accès INSA CVL |
| Sporočilo: |
L'impression du document génère 350 p. 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, 2008, New York, Springer, 1 vol. (XV-360 p.), Universitext, 978-0-387-48098-5 • Agency theory, information, and incentives, Günter Bamberg and Klaus Spremann (eds.), Berlin, Springer-Verlag, 1989, 1 vol. (XVIII-533 p.), 0-387-51675-1 |
Kazalo:
- Euclidean Spaces Smooth Functions on a Euclidean Space Tangent Vectors in Rn as Derivations Alternating k-Linear Functions Differential Forms on Rn Manifolds Manifolds Smooth Maps on a Manifold Quotients Lie Groups and Lie Algebras The Tangent Space Submanifolds Categories and Functors The Rank of a Smooth Map The Tangent Bundle Bump Functions and Partitions of Unity Vector Fields Lie Groups and Lie Algebras Lie Groups Lie Algebras Differential Forms Differential 1-Forms Differential k-Forms The Exterior Derivative Integration Orientations Manifolds with Boundary Integration on a Manifold De Rham Theory De Rham Cohomology The Long Exact Sequence in Cohomology The Mayer-Vietoris Sequence Homotopy Invariance Computation of de Rham Cohomology Proof of Homotopy Invariance.
- Euclidean Spaces
- Smooth Functions on a Euclidean Space
- Tangent Vectors in Rn as Derivations
- Alternating k-Linear Functions
- Differential Forms on Rn
- Manifolds
- Manifolds
- Smooth Maps on a Manifold
- Quotients
- Lie Groups and Lie Algebras
- The Tangent Space
- Submanifolds
- Categories and Functors
- The Rank of a Smooth Map
- The Tangent Bundle
- Bump Functions and Partitions of Unity
- Vector Fields
- Lie Groups and Lie Algebras
- Lie Groups
- Lie Algebras
- Differential Forms
- Differential 1-Forms
- Differential k-Forms
- The Exterior Derivative
- Integration
- Orientations
- Manifolds with Boundary
- Integration on a Manifold
- De Rham Theory
- De Rham Cohomology
- The Long Exact Sequence in Cohomology
- The Mayer Vietoris Sequence
- Homotopy Invariance
- Computation of de Rham Cohomology
- Proof of Homotopy Invariance