Complex Functions I (MAY611): Διαφορά μεταξύ των αναθεωρήσεων

Τελευταία αναθεώρηση της 12:23, 15 Ιουνίου 2023

Ελληνική Έκδοση
Undergraduate Courses Outlines
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Department of Mathematics
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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.

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-[[Undergraduate Courses Outlines]] - [https://math.uoi.gr  Department of Mathematics]
+* [[Μιγαδικές Συναρτήσεις I (MAY611)|Ελληνική Έκδοση]]
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 === General ===
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 ! Course Website (URL)
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+| See [https://ecourse.uoi.gr/ eCourse], the Learning Management System maintained by the University of Ioannina.
-http://www.math.uoi.gr/GR/studies/undergraduate/courses/perigr /MAE_611.pdf
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 === Attached Bibliography ===
-See [https://service.eudoxus.gr/public/departments#20 Eudoxus]. Additionally:
+<!-- In order to edit the bibliography, visit the webpage -->
-* Jeff Achter, Introduction to Complex Variables, Colorado State University, 2006.
+<!-- https://wiki.math.uoi.gr/index.php/%CE%A0%CF%81%CF%8C%CF%84%CF%85%CF%80%CE%BF:MAY611-Biblio -->
-* Lars V. Ahlfors, Complex Analysis, McGraw-Hill, 1966.
-* Walter Rudin, Real and Complex Analysis, 2nd ed., McGraw-Hill, New York, 1974.
+See the official [https://service.eudoxus.gr/public/departments#20 Eudoxus site] or the [https://cloud.math.uoi.gr/index.php/s/62t8WPCwEXJK7oL local repository] of Eudoxus lists per academic year, which is maintained by the Department of Mathematics. Books and other resources, not provided by Eudoxus:
+{{MAY611-Biblio}}