After successful completion of the course, students are able to...

• ... recall and motivate the definition of topological and smooth manifolds and to prove some elementary properties of these structures.
• ... define (co-)tangential spaces and (co-)vector fields and to relate these concepts with the differentiation of functions, respectively with differential forms, on smooth manifolds.
• ... distinguish between submersions and immersions and to decide, when an submanifold is called embedded.
• ... define the Lie bracket of vector fields and to explain how the tangentialspace of a smooth manifold is turned into an Lie algebra.
• ... explain how the left cosets of a Lie group with respect to a closed Lie subgroup carry the structure of a homogeneous space.
• ... explain the product of differential forms and the (outer) derivative.
• ... explain how to integrate a differentialform over a manifold and to formulate and prove Stokes' Theorem on smooth manifolds.

Smooth manifolds, tangent vectors, vector fields, integral curves and flows, differential forms, theorem of Stokes

Lecture (a exercise couse will be held as a seperated LVA)

Umstellung auf Fernlehre in Arbeit...

oral exam

Es wird ein Skriptum zur Vorlesung geben.