Manifolds (4V+2U, 9.0 LP)
|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|
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.
- Concept of manifold, in particular differentiable manifold,
- tangential and other vector bundles to manifolds,
- partition of unity,
- 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).
- 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.
Further literature will be announced in the lecture; Exercise material is provided.
Registration for the exercise classes via the online administration system URM (https://urm.mathematik.uni-kl.de)