Differentiable Manifolds
A First Course
Seiten
1994
Birkhauser Boston Inc (Verlag)
978-0-8176-3626-5 (ISBN)
Birkhauser Boston Inc (Verlag)
978-0-8176-3626-5 (ISBN)
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This text is based on the full-year PhD qualifying course on differentiable manifolds, global calculus, differential geometry and related topics, given by the author at Washington University. It presupposes a good grounding in general topology and modern algebra.
This text is based on the full-year PhD qualifying course on differentiable manifolds, global calculus, differential geometry and related topics, given by the author at Washington University. It presupposes a good grounding in general topology and modern algebra, especially linear algebra and analogous theory of modules over a commutative, unitary ring.
This text is based on the full-year PhD qualifying course on differentiable manifolds, global calculus, differential geometry and related topics, given by the author at Washington University. It presupposes a good grounding in general topology and modern algebra, especially linear algebra and analogous theory of modules over a commutative, unitary ring.
1. Topological Manifolds.- 2. Local Theory.- 3. Global Theory.- 4. Flows and Foliation.- 5. Lie Groups.- 6. Covectors and 1-Forms.- 7. Multilinear Algebra.- 8. Integration and Cohomology.- 9. Forms and Foliations.- 10. Riemannian Geometry.- Appendix A. Vector Fields on Spheres.- Appendix B. Inverse Function Theorem.- Appendix C. Ordinary Differential Equations.- C.1. Existence and uniqueness of solutions.- C.2. A digression concerning Banach spaces.- C.3. Smooth dependence on initial conditions.- C.4. The Linear Case.- Appendix D. Sard’s Theorem.- Appendix E. de Rham-?ech Theorem.- E.1. ?ech cohomology.- E.2. The de Rham-?ech complex.
| Erscheint lt. Verlag | 1.2.1994 |
|---|---|
| Reihe/Serie | Birkhäuser Advanced Texts Basler Lehrbücher |
| Zusatzinfo | 23 illustrations |
| Verlagsort | Secaucus |
| Sprache | englisch |
| Maße | 167 x 241 mm |
| Themenwelt | Mathematik / Informatik ► Mathematik ► Analysis |
| Mathematik / Informatik ► Mathematik ► Geometrie / Topologie | |
| ISBN-10 | 0-8176-3626-9 / 0817636269 |
| ISBN-13 | 978-0-8176-3626-5 / 9780817636265 |
| Zustand | Neuware |
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