# Complex Functions I (MAY611)

### General

School School of Science Department of Mathematics Undergraduate MAΥ611 6 Complex Functions I Presentations, exercises, lectures (Weekly Teaching Hours: 5, Credits: 7.5) General Background - Greek Yes See eCourse, the Learning Management System maintained by the University of Ioannina.

### Learning Outcomes

Learning outcomes It is the most basic introductory course of Mathematical Analysis of the complex space. The student begins to understand the notion of complex numbers and their properties. He/she learns about the use of the complex numbers field in solving some real numbers problems. The student learns about the elementary complex functions and then he/she learns about the line integral as well as the complex integral of such functions. Especially, the advantage of such integrals and their important properties are emphasized. Finally, the student learns the use of complex integrals in computing improper integrals of real functions. Working independently Team work Working in an international environment Working in an interdisciplinary environment Production of new research ideas

### Syllabus

The complex plane, Roots, Lines, Topology, Convergence, Riemann sphere, analytic properties of complex functions, Power series, elementary functions (rational, exp, log, trigonometric functions, hyperbolic, functions), line integrals, curves, conformal mappings, homotopic curves, local properties of complex functions, basic theorems, rotation index, General results, singularities, Laurent series, Residuum, Cauchy Theorem, Applications.

### 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
Lectures 65
Home exercises 22.5
Independent study 100
Course total 187.5
Student Performance Evaluation

Greek. Written exam (100%) on the theory and solving problems.

### 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:

• Jeff Achter, Introduction to Complex Variables, Colorado State University, 2006.
• Lars V. Ahlfors, Complex Analysis, McGraw-Hill, 1966.
• Walter Rudin, Real and Complex Analysis, 2nd ed., McGraw-Hill, New York, 1974.