Course MAT-40-21-K-6
Manifolds (4V+2U, 9.0 LP)
Course Type
SWS | Type | Course Form | CP (Effort) | Presence-Time / Self-Study | |
---|---|---|---|---|---|
- | K | Lecture with exercise classes (V/U) | |||
4 | V | Lecture | 6.0 CP | 56 h | 124 h |
2 | U | Exercise class (in small groups) | 3.0 CP | 28 h | 62 h |
(4V+2U) | 9.0 CP | 84 h | 186 h |
Basedata
Possible Study achievement
- Verification of study performance: proof of successful participation in the exercise classes (ungraded)
- Details of the examination (type, duration, criteria) will be announced at the beginning of the course.
Contents
- Concept of manifold, in particular differentiable manifold,
- tangential and other vector bundles to manifolds,
- partition of unity,
- orientation
- differential equations on manifolds, Ehresmann's fibration theorem,
- differential forms and integration, general theorem of Stokes,
- special structures on manifolds (e.g. basic concepts of complex, Riemannian and symplectic manifolds).
Literature
- T. Bröcker, K. Jänich: Introduction to Differential Topology,
- K. Jänich: Vector Analysis,
- S. Lang: Introduction to Differentiable Manifolds,
- J.M. Lee: Introduction to Smooth Manifolds,
- M. Spivak: Calculus on Manifolds: A Modern Approach to Classical Theorems of Advanced Calculus.
Materials
Further literature will be announced in the lecture; Exercise material is provided.
Registration
Registration for the exercise classes via the online administration system URM (https://urm.mathematik.uni-kl.de)
Requirements for attendance (informal)
Additional knowledge from the courses [MAT-12-25-K-3] and [MAT-12-27-K-3] is useful but not necessarily required.
Modules:
Courses
Requirements for attendance (formal)
None
References to Course [MAT-40-21-K-6]
Module | Name | Context | |
---|---|---|---|
[MAT-40-21-M-6] | Manifolds | P: Obligatory | 4V+2U, 9.0 LP |
Course-Pool | Name | ||
[MAT-40-4V-KPOOL-4] | Elective Courses Algebra, Geometry and Computeralgebra (4V, B.Sc.) | ||
[MAT-70-4V-KPOOL-4] | Elective Courses Analysis and Stochastics (4V, B.Sc.) |