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 the notion of integral curves and flows and formulate 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.

Exercise classes for the corresponding course

Exercise will be posted at least a week before class. During class students will present their solutions to the exercises.

Die Übung findet zu folgenden 6 Terminen jeweils Dienstag 8:30 bis 10:00 Uhr im Besprechungsraum im 7. Stock Freihaus (grün) statt:

31. Oktober

14. November

28. November

12. Dezember

9. Jänner

23. Jänner

There will be Problemsheets posted online and grading will be done based on your Solutions to these Problems.