Module MA4804-KP05
Special Functions (SpFunkKP05)
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
- Minor in Teaching Mathematics, Master of Education 2023, optional subject, mathematics
- Minor in Teaching Mathematics, Master of Education 2017, optional subject, mathematics
- Master CLS 2016, optional subject, mathematics
- Bachelor CLS 2016, optional subject, mathematics
Classes and lectures:
- Special Functions (lecture, 2 SWS)
- Special Functions (exercise, 1 SWS)
Workload:
- 15 hours exam preparation
- 60 hours private studies
- 45 hours in-classroom work
- 30 hours work on project
Contents of teaching:
- Algebraic operations with complex numbers
- Exponential function, angle functions, hyperbolic angle functions, derived functions
- Gamma and beta functions
- Hypergeometric function
- Bessel function, Legendre function, Laguerre function, Tscheybyscheff function, Hermite function, Jacobi hypergeometric function
- Elliptic functions, theta functions
- Number theoretic functions
- Riemann zeta function
- Used mathematical theories and concepts:
- Complex function theory
- Infinite products
- Differential equations (ordinary, partial)
- Functional equations
- Integral representation
- Taylor series expansions for eigenvalues and eigenfunctions (using space and time, defined on geometric objects)
- Producing functions (a Taylor series in two variables is considered as a series in one variable and the coefficients are special functions in the other variable)
- Addition theorems
- Fourier transformations
- Transformation groups, matrix groups
Qualification-goals/Competencies:
- Theoretical knowlege of the mentioned topics
- Historical and latest questions
- Solve questions in this field
- Recognize interdisciplinary aspects
Grading through:
- exercises, project, oral or written exam
Responsible for this module:
Literature:
- Andrews G.E., Askey R., Roy R. : Special Functions.Encyclopedia of Mathematics and its Application 71 Cambridge University Press 2006
- Courant, R., Hilbert, D. : Methoden der mathematischen Physik Springer 1993
- Erdélyi, A. , Magnus, W., Oberhettinger, F., Tricomi, F. : Higher Transcendental Functions McGraw-Hill, New York, 1953
- Fichtenholz, G.M. : Differential- und Integralrechnung, Band 1-3 H. Deutsch 1997
- Hurwitz, A., Courant, R. : Vorlesungen über Allgemeine Funktionentheorie und Elliptische Funktionen Springer 2000
- Stegun, I. A., Abramowitz, M. : Handbook of Mathematical Functions Dover Press
- Strampp, W., Ganzha, V., Vorozhtsov, E. : Höhere Mathematik mit Mathematica, Bd.4, Funktionentheorie, Fouriertransformationen und Laplacetransformationen: Funktionentheorie, Fourier- und Laplacetransformation Vieweg 1997
- Wawrzynczyk, A. : Group Representations and Special Functions Reidel Publishing Company 1983
- Whittaker, E. T., Watson, G. N. : A Cource of Modern Analysis Cambridge University Press 1902 ... 1999
Language:
- offered only in German
Notes:
Admission requirements for taking the module:- None (The competencies of the modules listed under 'Requires' are needed for this module, but are not a formal prerequisite)
Admission requirements for participation in module examination(s):
- Successful completion of homework assignments as specified at the beginning of the semester
Module exam(s):
- MA4804-L1: Special Functions, written exam (90 min) or oral exam (30 min), 100 % of module grade
Last Updated:
22.02.2022