Bifurcation Theory - Interactive curriculae of TU Ilmenau
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| module properties module number 5826 - common information | |
|---|---|
| module number | 5826 |
| department | Department of Mathematics and Natural Sciences |
| ID of group | 2416 (Analysis and Dynamical Systems) |
| module leader | Dr. Jürgen Knobloch |
| language | Deutsch |
| term | Wintersemester |
| previous knowledge and experience | Analysis I-II, Gewöhnliche Differentialgleichungen |
| learning outcome | Die Studierenden kennen wesentliche Methoden der Bifurkationstheorie und sind in der Lage, diese auf konkrete Problemstellungen aus Naturwissenschaft und Technik anzuwenden. |
| content | Analytische Bifurkationstheorie, Bifurkationspunkte, Liapunov/Schmidt Reduktion, Bifurkationstheoreme, Anwendungen auf Differential- und Integralgleichungen, Topologische Bifurkationstheorie, Abbildungsgrad und Fixpunktindex, Satz von Crandall/Rabiniwitz, Morselemma, Indexsprungprinzip, Lokale und globale Bifurkation, Anwendung auf Gleichungssysteme und Randwertprobleme, Singularitätentheorie (universelle Entfaltungen), Kodimension-1 Entfaltungen. |
| media of instruction and technical requirements for education and examination in case of online participation | Tafel, Folien, Skript, Übungsaufgaben |
| literature / references | S.-N. Chow, J.K. Hale: Methods of Bifurcation Theory. Grundlehren der Math. Wiss. 251. Springer-Verlag New York 1982. Deimling: Nichtlineare Gleichungen und Abbildungsgrade. Springer-Verlag 1974 Guckenheimer, J.; Holmes, P.: Nonlinear Oscillations, Dynamical Systems and Bifurcation of Vector Fields. Applied Mathematical Sciences 42. Springer-Verlag New York 1983. Krasnoselski, M. etal.: Näherungsverfahren zur Lösung von Operatorgleichungen}. Akademie-Verlag, Berlin 1973. Wainberg, M. M.; Trenogin, W. A.: Theorie der L"osungsverzweigung bei nichtlinearen Gleichungen. Akademie-Verlag Berlin 1973. E. Zeidler: Nonlinear Functional Analysis and its Applications. Teil I. Springer-Verlag 1990. |
| evaluation of teaching | |
| Details reference subject | |
|---|---|
| module name | Bifurcation Theory |
| examination number | 2400187 |
| credit points | 4 |
| SWS | 3 |
| on-campus program (h) | 33.75 |
| self-study (h) | 86.25 |
| obligation | elective module |
| exam | oral examination performance, 30 minutes |
| details of the certificate | |
| link to Moodle course | |
| teacher | |
| signup details for alternative examinations | |
| maximum number of participants | |
| Details in degree program Master Technische Kybernetik und Systemtheorie 2014 | |
|---|---|
| module name | Bifurcation Theory |
| examination number | 2400187 |
| credit points | 5 |
| on-campus program (h) | 34 |
| self-study (h) | 116 |
| obligation | elective module |
| exam | oral examination performance, 30 minutes |
| details of the certificate | |
| link to Moodle course | |
| signup details for alternative examinations | |
| maximum number of participants | |
| Details in degree program Master Mathematik und Wirtschaftsmathematik 2013 (WM), Master Mathematik und Wirtschaftsmathematik 2013 (AM) | |
|---|---|
| module name | Bifurcation Theory |
| examination number | 2400187 |
| credit points | 4 |
| on-campus program (h) | 34 |
| self-study (h) | 86 |
| obligation | elective module |
| exam | oral examination performance, 30 minutes |
| details of the certificate | |
| link to Moodle course | |
| signup details for alternative examinations | |
| maximum number of participants | |