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.

2021S, UE, 1.0h, 1.5EC


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

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

The exercise course will be held via distance learning.

Meetings online:

  • Wed, April 14 at 2:00 p.m.
  • Wed, April 28 at 2:00 p.m.
  • Wed, May 12 at 2:00 p.m.
  • Wed, May 26 at 2:00 p.m.
  • Wed, Jun    9 at 2:00 p.m.
  • Wed, Jun  23 at 2:00 p.m.

Via GoToMeeting


Now you can find the second exercise sheet in the course material. Please send me an email indicating which exercises you did one day before the meeting. Based on your email, you will be asked to explain some exercises during the online meeting. Exercises that coudn't be solved will also be covered in our meeting but won't be selected as possible questions for you.



Examination modalities

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

Course registration

Begin End Deregistration end
09.03.2021 00:01 06.04.2021 23:59 06.04.2021 23:59



No lecture notes are available.


  • Attendance Required!