Numerics for Invariant Manifolds - Interactive curriculae of TU Ilmenau
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| module properties module number 5828 - common information | |
|---|---|
| module number | 5828 |
| department | Department of Mathematics and Natural Sciences |
| ID of group | 2413 (Numerical Analysis and Information Processing) |
| module leader | Prof. Dr. Hans Babovsky |
| language | Deutsch |
| term | Sommersemester |
| previous knowledge and experience | Dynamische Systeme 1, 2 |
| learning outcome | Den Studierenden wird der aktuelle Wissensstand (State of the Art) zur numerischen Approximation invarianter Mannigfaltigkeiten bei dynamischen Systemen vermittelt und insbesondere die stabile Diskretisierung von 2-Tori diskutiert. Die Themenwahl soll zu einer ganzheitlichen Sicht komplizierter Bifurkationsphänomene der Praxis beitragen. |
| content | Approximation implizit definierter k-Mannigfaltigkeiten (PC-Methoden, Kurvenverfolgung, Moving Frame Algorithm, PL-Approximation k-dimensionaler Mannigfaltigkeiten) Approximation stabiler und instabiler Invarianzkurven (Numerische Approximation von Poincare-Abbildungen, Verfolgung der Invarianzkurven von Poincare-Abbildungen, Einzugsbereiche von Lösungen und Separatrizen) Approximation invarianter k-Tori (Toruslösungen und quasi-periodische Orbits, diskretisierte 2-Tori, numer. Stabilität und Konvergenz, Spektralmethoden und Pseudospektralmethoden für 2-Tori, Numerische Fortsetzungsverfahren für 2-Tori). |
| media of instruction and technical requirements for education and examination in case of online participation | Folie, Tafel, Beamer, Computerunterstützung |
| literature / references | (1) Hoffmann, A.; Marx, B.; Vogt, W.: Mathematik für Ingenieure - Theorie und Numerik. Band 2, Pearson, Studium München 2006 (2) Samoilenko, A.M.: Elements of the Mathematical Theory of Multi-Frequency Oscillations. Kluwer, Dordrecht 1991. (3) Doedel, E.; Tuckerman, L.S. (Hrsg.): Numerical Methods for Bifurcation Problems and Large-Scale Dynamical Systems. Springer, New York 2000 |
| evaluation of teaching | |
| Details reference subject | |
|---|---|
| module name | Numerics for Invariant Manifolds |
| examination number | 2400195 |
| 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 Mathematik und Wirtschaftsmathematik 2013 (WM), Master Mathematik und Wirtschaftsmathematik 2013 (AM) | |
|---|---|
| module name | Numerics for Invariant Manifolds |
| examination number | 2400195 |
| 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 | |