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.

General Competences

Search for, analysis and synthesis of data and information Adapting to new situations Decision-making Working independently Criticism and self-criticism Production of free, creative and inductive thinking

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
Use of Information and Communications Technology	-
Teaching Methods	Activity Semester Workload Lectures 39 Self-study 78 Homework 70.5 Course total 187.5
Student Performance Evaluation	The evaluation is carried out as a combination of Written exam. Assigned homework. Presentation and oral examination.

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.