Elementary Differential Geometry

Module MA2204

This Module is offered by TUM Department of Mathematics.

This module handbook serves to describe contents, learning outcome, methods and examination type as well as linking to current dates for courses and module examination in the respective sections.

Basic Information

MA2204 is a semester module in German language at Bachelor’s level which is offered in summer semester.

Total workloadContact hoursCredits (ECTS)
150 h 45 h 5 CP

Content, Learning Outcome and Preconditions


Grundlagen der Differentialgeometrie von Kurven und Flächen in der Ebene und im Raum. Krümmungsbegriffe in Ebene und Raum. Vierscheitelsatz, Torsion, Tangentialraum, kovariante Richtungsableitungen, geodätische Linien, Krümmungsgrößen. Ausblicke auf höhere Dimensionen, Riemannsche Mannigfaltigkeiten, Minimalflächen.

Learning Outcome

Nach dem erfolgreichen Abschluss des Moduls ist der Studierende in der Lage, gekrümmte Objekte in der Ebene und im Raum sowie im Ansatz auch gekrümmte Räume mit analytischen Methoden zu behandeln.


MA1001 Analysis 1, MA1002 Analysis 2, MA1101 Lineare Algebra 1, MA1102 Lineare Algebra 2, MA2203 Geometriekalküle

Courses, Learning and Teaching Methods and Literature

Courses and Schedule

Learning and Teaching Methods

Vorlesung, Übung, Übungsaufgaben zum Selbststudium




W. Kühnel: Differentialgeometrie: Kurven - Flächen - Mannigfaltigkeiten, 4. Auflage, Vieweg, 2008, ISBN: 3834804118. M. P. do Carmo: Differentialgeometrie von Kurven und Flächen, Vieweg, 1983.

Module Exam

Description of exams and course work


Exam Repetition

There is a possibility to take the exam at the end of the semester.

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