Complex Functions I (MAY611)

• Ελληνική Έκδοση
• Undergraduate Courses Outlines
• Outline Modification (available only for faculty members)
• Department of Mathematics
• Save as PDF or Print (to save as PDF, pick the corresponding option from the list of printers, located in the window which will popup)

General

School	School of Science
Academic Unit	Department of Mathematics
Level of Studies	Undergraduate
Course Code	MAΥ611
Semester	6
Course Title	Complex Functions I
Independent Teaching Activities	Presentations, exercises, lectures (Weekly Teaching Hours: 5, Credits: 7.5)
Course Type	General Background
Prerequisite Courses	-
Language of Instruction and Examinations	Greek
Is the Course Offered to Erasmus Students	Yes
Course Website (URL)	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.

General Competences

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	Activity Semester Workload 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:

• Γιαννούλης, Ι. (2024). Μιγαδική Ανάλυση [Προπτυχιακό εγχειρίδιο]. Κάλλιπος, Ανοικτές Ακαδημαϊκές Εκδόσεις. http://dx.doi.org/10.57713/kallipos-408
• R. Remmert. Theory of Complex Functions. Springer, 1998.
• S. Lang. Complex Analysis. Fourth Edition. Springer, 1999.