Complex Analysis (AN3)
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General
| School | School of Science |
|---|---|
| Academic Unit | Department of Mathematics |
| Level of Studies | Graduate |
| Course Code | AN3 |
| Semester | 2 |
| Course Title | Complex Analysis |
| Independent Teaching Activities | Lectures (Weekly Teaching Hours: 3, Credits: 7.5) |
| Course Type | General Background |
| Prerequisite Courses |
Introduction to Complex Analysis (undergraduate) |
| Language of Instruction and Examinations |
Greek |
| Is the Course Offered to Erasmus Students |
Yes (in English) |
| Course Website (URL) | See eCourse, the Learning Management System maintained by the University of Ioannina. |
Learning Outcomes
| Learning outcomes |
The course aims, firstly, to provide a more complete picture of the subject matter of Complex Analysis, and, secondly, to highlight the impact of its results concerning the properties of various functions of real variables and its relation – mainly through the notion of a harmonic function - to other areas of Mathematics, such as Harmonic Analysis, Geometry and Partial Differential Equations, but also to present some applications of Complex Analysis within various fields of the Natural Sciences. Concerning the skills and competences which the students will acquire, the subject is especially suitable for highlighting the connections between various mathematical areas, the power of generalization of a notion in order to understand the properties of a certain subcase of it, and the usefulness of looking at a subject from different points of view. |
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| General Competences |
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Syllabus
Holomorphic, entire, and meromorphic functions. Conformal mappings. Analytic continuation. Weierstrass’ Convergence Theorem. The Gamma function. Infinite Products. The Riemann Mapping Theorem. Harmonic functions and applications.
Teaching and Learning Methods - Evaluation
| Delivery |
Face-to-face | ||||||||||
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| Use of Information and Communications Technology | - | ||||||||||
| Teaching Methods |
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| Student Performance Evaluation |
The evaluation is carried out as a combination of
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Attached Bibliography
- J. Bak and D. J. Newman, Complex Analysis (3rd ed.), Springer, 2010.
- S. Lang, Complex Analysis (4th ed.), Springer, 1999.
- I. Markushevich, Theory of Functions of a Complex Variable (2nd ed.), Vol. 1-3, AMS Chelsea, 2011.
- I. Markushevich, The Theory of Analytic Functions: A Brief Course, Mir Publishers, 1983.
- R. Remmert, Theory of Complex Functions, Springer, 1990.
- R. Remmert, Classical Topics in Complex Function Theory, Springer, 1998.
- K. Jänich, Funktionentheorie (6te Aufl.), Springer, 2011.