Module MA4801-KP05

Duration

1 Semester

Turnus of offer

irregularly

Credit points

5

Course of studies, specific fields and terms:

• Master CLS 2023, optional subject, mathematics
• Bachelor CLS 2023, optional subject, mathematics
• Master CLS 2016, optional subject, mathematics
• Bachelor CLS 2016, optional subject, mathematics

Classes and lectures:

• Elliptic Functions and Function Theory (exercise, 1 SWS)
• Elliptic Functions and Function Theory (lecture, 2 SWS)

Workload:

• 30 hours work on project
• 45 hours in-classroom work
• 60 hours private studies
• 15 hours exam preparation

Contents of teaching:

• Complex analysis
• Periodic functions and lattices
• Simple and double periods
• Liouville Theorem, residue theorem
• Weierstrass P-, Zeta- and Sigma-function
• The field of elliptic functions
• Elliptic integrals
• Moduls of elliptic functions

Qualification-goals/Competencies:

• Getting familiar with and developing skills in concepts and techiques in complex analysis
• Extension of the background for different applications, e.a. signal processing, to develop problem solving strategies
• Getting familiar with Mathematica in the considered topic
• Developing competencies for self-sufficient problem solving
• Gaining experience in project work in the field

Grading through:

• exercises, project, oral or written exam

Responsible for this module:

• Prof. Dr. Reinhard Schuster

Teacher:

• Institute for Mathematics
• Prof. Dr. Reinhard Schuster

Literature:

• Andrews, G. E., Askey, R. and Roy, R. : Special Functions Cambridge University Press 1999
• Armitage, J. V. and Eberlein, W. F. : Elliptic Functions Cambridge University Press 2006
• Hurwitz, A. : Vorlesungen über Allgemeine Funktionentheorie und Elliptische Funktionen Springer 2000
• Koecher, M und Krieg, A. : Elliptische Funktionen und Modulformen Springer 2007
• Stramp, W., Ganzha, V. und Vorozhtsov, E. : Höhere Mathematik mit Mathematica Vieweg 1997
• Werner, A. : Elliptische Kurven in der Kryptographie Springer 2002
• Whittaker, E. T. and Watson, G. N. : A course of modern analysis Cambridge University Press 1902 (Reprinted 1999)

Language:

• offered only in German

Notes:

Last Updated:

22.02.2022