Differential calculus on manifolds
Code | Completion | Credits | Range | Language |
---|---|---|---|---|
01DPV | ZK | 2 | 2+0 | Czech |
- Lecturer:
- Severin Pošta (gar.), Matěj Tušek
- Tutor:
- Severin Pošta (gar.), Matěj Tušek
- Supervisor:
- Department of Mathematics
- Synopsis:
-
Smooth manifold, tangent space differential forms, tensors, Riemannian metrics and manifold, covariant derivative, parallel transport, orientation of manifold, itegration on manifold and Stokes theorem.
- Requirements:
-
Basic course in Calculus and Linear Algebra and topology (in the extent of the courses 01MA1, 01MAA2-4, 01LA1, 01LAA2, 01TOP held at the FNSPE CTU in Prague).
- Syllabus of lectures:
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1. Smooth manifolds 2. Tangent and cotangent space 3. Tensors, differential forms 4. Orientation of manifold, integration on manifold 5. Stokes theorem 6. Riemannian manifold.
- Syllabus of tutorials:
- Study Objective:
-
Knowledge: To get acquainted with basic notions of differential geometry with emphasis on mathematical details.
Abilities: Consequently, to be able to self-study advanced physical (not only) literature.
- Study materials:
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key references:
[1] J.M. Lee: Introduction to Smooth Manifolds, Springer, 2003.
recommended references:
[2] J. M Lee: Riemannian Manifolds: An Introduction to Curvature, Springer, 1997.
[3] M. Spivak: Calculus on Manifolds, Addison-Wesley Publishing Company, 1965.
[4] F. Morgan: Riemannian Geometry: A Begginer's Guide, Jones and Bartlett Publishers, 1993.
- Note:
- Time-table for winter semester 2011/2012:
- Time-table is not available yet
- Time-table for summer semester 2011/2012:
- Time-table is not available yet
- The course is a part of the following study plans: