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School of Science
Department of Mathematics
|Level of Studies||
Complex Functions I
|Independent Teaching Activities||
Presentations, exercises, lectures (Weekly Teaching Hours: 5, Credits: 7.5)
|Language of Instruction and Examinations||
|Is the Course Offered to Erasmus Students||
|Course Website (URL)||See eCourse, the Learning Management System maintained by the University of Ioannina.|
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.
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
|Use of Information and Communications Technology||
Use of ICT for the presentation and communication for submission of the exercises
|Student Performance Evaluation||
Greek. Written exam (100%) on the theory and solving problems.
- 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.