Complex Functions II (MAE712): Διαφορά μεταξύ των αναθεωρήσεων

Τελευταία αναθεώρηση της 15:42, 15 Ιανουαρίου 2025

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	ΜΑΕ712
Semester	7
Course Title	Complex Functions II
Independent Teaching Activities	Lectures (Weekly Hours: 3, Credits: 6)
Course Type	Special Background
Prerequisite Courses	None.
Language of Instruction and Examinations	Greek
Is the Course Offered to Erasmus Students	No
Course Website (URL)	See eCourse, the Learning Management System maintained by the University of Ioannina.

Learning Outcomes

Learning outcomes	The course deepens further into the study of the properties of complex, and in particular holomorphic and meromorphic, functions, aiming to derive characteristic results for them which distinguish them from real functions. The students apply the results and techniques they obtained from the introductory course in order to derive more involved results on the one hand within Complex Analysis and on the other hand in relation to its connections with other areas of Mathematics, as for instance Geometry, Topology and Partial Differential Equations, and are trained in the composition of simpler results in order to derive deeper ones.
General Competences	Αnalyse and combine data and information using various technologies. Working independently and in groups. Free, creative, analytic, and conclusive thinking. Decision making.

Syllabus

The course is a continuation of the introductory compulsory course Complex Functions I. It considers classical theoretical results which are characteristic of Complex Analysis and that highlight its connections with other areas of Mathematics. The following topics are mentioned indicatively: Conformal mappings. Harmonic Functions. Homotopy. Analytic Continuation. Homologically simply connected domains. Generalization of Cauchy’s Integral Theorem. Maximum Principle. Schwarz’ Lemma. Convergence theorems for sequences of holomorphic functions. Partial fraction decomposition. Infinite Products. Riemann Mapping Theorem.

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
Study in class	39
Other activities determined by the teaching professor	111
Course total	150

Student Performance Evaluation

xxx

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:

L. V. Ahlfors. Complex Analysis. Third Edition. McGraw-Hill, 1979.
K. Jaenich. Funktionentheorie. Eine Einfuehrung. Sechste Auflage. Springer, 2011.
S. Lang. Complex Analysis. Fourth Edition. Springer, 1999.
Σ. Κ. Μερκουράκης, Τ. Ε. Χατζηαφράτης. Εισαγωγή στη Μιγαδική Ανάλυση. Εκδόσεις Συμμετρία, 2005.
R. Remmert. Theory of Complex Functions. Springer, 1998.
R. Remmert. Classical Topics in Complex Function Theory. Springer, 1998.

@@ Γραμμή 1: / Γραμμή 1: @@
-* [[Σεμινάριο Ανάλυσης II (MAE754)|Ελληνική Έκδοση]]
+* [[Μιγαδικές_Συναρτήσεις_II_(MAE712)|Ελληνική Έκδοση]]
 {{Course-UnderGraduate-Top-EN}}
 {{Menu-OnAllPages-EN}}
@@ Γραμμή 20: / Γραμμή 20: @@
 ! Course Code
 |
-ΜΑΕ754
+ΜΑΕ712
 |-
 ! Semester
@@ Γραμμή 28: / Γραμμή 28: @@
 ! Course Title
 |
-Seminar in Analysis II
+Complex Functions II
 |-
 ! Independent Teaching Activities
@@ Γραμμή 39: / Γραμμή 39: @@
 |-
 ! Prerequisite Courses
-| None. However it is desirable to have a strong knowledge of basic notions of differential equations.
+| None.
 |-
 ! Language of Instruction and Examinations
@@ Γραμμή 58: / Γραμμή 58: @@
 ! Learning outcomes
 |
-* The ability to write a complete report on a scientific subject.
+The course deepens further into the study of the properties of complex, and in particular holomorphic and meromorphic, functions, aiming to derive characteristic results for them which distinguish them from real functions. The students apply the results and techniques they obtained from the introductory course in order to derive more involved results on the one hand within Complex Analysis and on the other hand in relation to its connections with other areas of Mathematics, as for instance Geometry, Topology and Partial Differential Equations, and are trained in the composition of simpler results in order to derive deeper ones.
-* The ability to present this report.
-* Working in teams.
-The report can be, but not required to be, original. Further details can be determined by the teaching professor.
 |-
 ! General Competences
@@ Γραμμή 70: / Γραμμή 66: @@
 * Free, creative, analytic, and conclusive thinking.
 * Decision making.
-Further details can be determined by the teaching professor.
 |}
 === Syllabus ===
-In depth study in a scientific subject related to mathematical analysis. Further details can be determined by the teaching professor.
+The course is a continuation of the introductory compulsory course Complex Functions I. It considers classical theoretical results which are characteristic of Complex Analysis and that highlight its connections with other areas of Mathematics. The following topics are mentioned indicatively: Conformal mappings. Harmonic Functions. Homotopy. Analytic Continuation. Homologically simply connected domains. Generalization of Cauchy’s Integral Theorem. Maximum Principle. Schwarz’ Lemma. Convergence theorems for sequences of holomorphic functions. Partial fraction decomposition. Infinite Products. Riemann Mapping Theorem.
 === Teaching and Learning Methods - Evaluation ===
@@ Γραμμή 83: / Γραμμή 77: @@
 ! Delivery
 |
-Details will be determined by the teaching professor. Methods include presentations contacted by the students.
+Face-to-face
 |-
 ! Use of Information and Communications Technology
 |
-Details will be determined by the teaching professor.
+Use of ICT for the presentation and communication for submission of the exercises
 |-
 ! Teaching Methods
@@ Γραμμή 107: / Γραμμή 101: @@
 ! Student Performance Evaluation
 |
-* There is no final exam.
+xxx
-* Each student must write a report on a specific subject.
-* Each student must present the report publically.
-* Students may miss up to 3 lectures.
-Other means of evaluation can be determined by the teaching professor.
 |}
 === Attached Bibliography ===
-Bibliography is suggested by the teaching professor, depending on the subject under study.
+<!-- In order to edit the bibliography, visit the webpage -->
+<!-- https://wiki.math.uoi.gr/index.php/%CE%A0%CF%81%CF%8C%CF%84%CF%85%CF%80%CE%BF:MAE712-Biblio -->
+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:
+{{MAE712-Biblio}}