Complex Functions II (MAE712)
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General
| School |
School of Science |
|---|---|
| Academic Unit |
Department of Mathematics |
| Level of Studies |
Undergraduate |
| Course Code |
ΜΑΕ712 |
| Semester |
7 |
| Course Title |
Complex Functions II |
| Independent Teaching Activities |
Lectures (Weekly Hours: 3, Credits: 6) |
| Course Type |
Special Background |
| Prerequisite Courses | None. |
| Language of Instruction and Examinations |
Greek |
| Is the Course Offered to Erasmus Students |
No |
| Course Website (URL) | See eCourse, the Learning Management System maintained by the University of Ioannina. |
Learning Outcomes
| Learning outcomes |
The course deepens further into the study of the properties of complex, and in particular holomorphic and meromorphic, functions, aiming to derive characteristic results for them which distinguish them from real functions. The students apply the results and techniques they obtained from the introductory course in order to derive more involved results on the one hand within Complex Analysis and on the other hand in relation to its connections with other areas of Mathematics, as for instance Geometry, Topology and Partial Differential Equations, and are trained in the composition of simpler results in order to derive deeper ones. |
|---|---|
| General Competences |
|
Syllabus
The course is a continuation of the introductory compulsory course Complex Functions I. It considers classical theoretical results which are characteristic of Complex Analysis and that highlight its connections with other areas of Mathematics. The following topics are mentioned indicatively: Conformal mappings. Harmonic Functions. Homotopy. Analytic Continuation. Homologically simply connected domains. Generalization of Cauchy’s Integral Theorem. Maximum Principle. Schwarz’ Lemma. Convergence theorems for sequences of holomorphic functions. Partial fraction decomposition. Infinite Products. Riemann Mapping Theorem.
Teaching and Learning Methods - Evaluation
| Delivery |
Face-to-face | ||||||||
|---|---|---|---|---|---|---|---|---|---|
| Use of Information and Communications Technology |
Use of ICT for the presentation and communication for submission of the exercises | ||||||||
| Teaching Methods |
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| Student Performance Evaluation |
xxx |
Attached Bibliography
See the official Eudoxus site or the local repository of Eudoxus lists per academic year, which is maintained by the Department of Mathematics. Books and other resources, not provided by Eudoxus:
- L. V. Ahlfors. Complex Analysis. Third Edition. McGraw-Hill, 1979.
- K. Jaenich. Funktionentheorie. Eine Einfuehrung. Sechste Auflage. Springer, 2011.
- S. Lang. Complex Analysis. Fourth Edition. Springer, 1999.
- Σ. Κ. Μερκουράκης, Τ. Ε. Χατζηαφράτης. Εισαγωγή στη Μιγαδική Ανάλυση. Εκδόσεις Συμμετρία, 2005.
- R. Remmert. Theory of Complex Functions. Springer, 1998.
- R. Remmert. Classical Topics in Complex Function Theory. Springer, 1998.