Complex Functions I (MAY611)
Undergraduate Courses Outlines - Department of Mathematics
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) |
http://www.math.uoi.gr/GR/studies/undergraduate/courses/perigr /MAE_611.pdf |
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 |
|
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 |
| ||||||||||
| Student Performance Evaluation |
Greek. Written exam (100%) on the theory and solving problems. |
Attached Bibliography
See Eudoxus. Additionally:
- 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.