# 104.278 AKANA Analysis on manifolds This course is in all assigned curricula part of the STEOP.\$(function(){PrimeFaces.cw("Tooltip","widget_j_id_21",{id:"j_id_21",showEffect:"fade",hideEffect:"fade",target:"isAllSteop"});});This course is in at least 1 assigned curriculum part of the STEOP.\$(function(){PrimeFaces.cw("Tooltip","widget_j_id_23",{id:"j_id_23",showEffect:"fade",hideEffect:"fade",target:"isAnySteop"});}); 2023W 2021S 2020S 2018W 2016S 2013S 2011W

2023W, UE, 1.0h, 1.5EC

## Properties

• 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

Immanent

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

DayTimeDateLocationDescription
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.

Not necessary

## Curricula

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

## Literature

No lecture notes are available.

German