Complex Analysis - Interactive curriculae of TU Ilmenau
The interactive curriculae provide information on the degree programmes offered by the TU Ilmenau.
Please refer to the respective study and examination rules and regulations for the legally binding curricula (Annex Curriculum).
You can find all details on planned lectures and classes in the course catalogue.
Please note that this page is no longer updated. All modules and study plans from PO version 2021 onwards (Bachelor and Master study programs) are now available on the Campus Portal.
| module properties module number 201250 - common information | |
|---|---|
| module number | 201250 |
| department | Department of Mathematics and Natural Sciences |
| ID of group | 2416 (Analysis and Dynamical Systems) |
| module leader | Prof. Dr. Timo Reis |
| language | Deutsch |
| term | ganzjährig |
| previous knowledge and experience | Analysis 1-4 |
| learning outcome | Nach der Lehrveranstaltung verfügen die Teilnehmer*innen über grundlegende Kenntnisse der Funktionentheorie und auch somit über eine erweiterte Kenntnis der Lösung von Integralen. Die so aufgebaute allgemeine Theorie lässt sich dann mit Erfolg zur Lösung konkreter Probleme, nicht nur der reinen, sondern auch der angewandten Mathematik heranziehen. Nach intensiven Diskussionen und Gruppenarbeit während der Übungen können die Studenten Leistungen ihrer Mitkommilitonen richtig einschätzen und würdigen. Sie berücksichtigen Kritik, beherzigen Anmerkungen und nehmen Hinweise an. After the course, participants will have acquired basic knowledge of Complex Analysis, as well as an extended understanding of solving integrals. The general theory established can then be successfully applied to solve concrete problems, not only in pure mathematics but also in applied mathematics. Through intense discussions and group work during exercises, students are able to accurately assess and appreciate the contributions of their peers. They consider criticism, heed remarks, and accept suggestions. |
| content | Differentiation analytischer Funktionen, Holomorphie, Kurvenintegrale, Cauchyscher Integralsatz, Cauchyscher Integralformeln, Laurentreihen, Singularitäten, Residuensatz Differentiation of analytic functions, holomorphy, curve integrals, Cauchy's integral theorem, Cauchy's integral formulas, Laurent series, singularities, residue theorem. |
| media of instruction and technical requirements for education and examination in case of online participation | Tafel, Folien, Skript, Übungsaufgaben Board, slides, script, exercises |
| literature / references | Jänich, K.: Einführung in die Funktionentheorie. Springer-Verlag 1980. Jeffrey, Alan: Complex analysis and Applications. Chapman & Hall/CRC. 2006. Marsden, J.E.; Hoffman M.J.: Basic Complex Analysis. W.H.Freeman and Co. New York 1999. Remmert, R.: Funktionentheorie. Bd. I, II. Springer-Verlag 1991 |
| evaluation of teaching | |
| Details reference subject | |
|---|---|
| module name | Complex Analysis |
| examination number | 2400910 |
| credit points | 5 |
| SWS | 3 (2 V, 1 Ü, 0 P) |
| on-campus program (h) | 33.75 |
| self-study (h) | 116.25 |
| obligation | obligatory module |
| exam | oral examination performance, 30 minutes |
| details of the certificate | |
| link to Moodle course | |
| teacher | apl. Prof. Dr. Thomas Böhme |
| signup details for alternative examinations | |
| maximum number of participants | |