104.276 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, VO, 3.0h, 4.5EC


  • 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


Additional information

The course lectures are every

Thursday, 1.00 to 2.30 p.m.

via GoToMeeting (start March, 11th)




Examination modalities

oral exam

Course registration

Not necessary



Es wird ein Skriptum zur Vorlesung geben.