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2021S, VO, 3.0h, 4.5EC

## Properties

• Semester hours: 3.0
• Credits: 4.5
• Type: VO Lecture
• Format: Distance Learning

## Learning outcomes

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 integral curves and flows and formulate and explain the main theorem about flows.
• ... 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.

## Subject of course

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

## Teaching methods

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

## Mode of examination

Oral

The course lectures are every

Thursday, 1.00 to 2.30 p.m.

via GoToMeeting (start March, 11th)

https://global.gotomeeting.com/join/698883469

oral exam

Not necessary

## Literature

Es wird ein Skriptum zur Vorlesung geben.

German