104.278 AKANA Analysis on manifolds
This course is in all assigned curricula part of the STEOP.
This course is in at least 1 assigned curriculum part of the STEOP.

2023W, UE, 1.0h, 1.5EC


  • Semester hours: 1.0
  • Credits: 1.5
  • Type: UE Exercise
  • Format: Presence

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 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.

Subject of course

Exercise classes for the corresponding course

Teaching methods

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

Mode of examination


Additional information

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



Course dates

Fri12:00 - 14:0019.01.2024Sem.R. DB gelb 05 B Replacement class

Examination modalities

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

Course registration

Not necessary


Study CodeObligationSemesterPrecon.Info
860 GW Optional Courses - Technical Mathematics Not specified


No lecture notes are available.