Complex Analysis
| Title | ΜΙΓΑΔΙΚΗ ΑΝΑΛΥΣΗ / Complex Analysis |
| Code | 0641 |
| Faculty | Sciences |
| School | Mathematics |
| Cycle / Level | 2nd / Postgraduate |
| Teaching Period | Winter |
| Coordinator | Dimitrios Betsakos |
| Common | Yes |
| Status | Active |
| Course ID | 40000029 |
Programme of Study: PMS Tmīmatos Mathīmatikṓn (2018-sīmera)
Registered students: 13
| Orientation | Attendance Type | Semester | Year | ECTS |
|---|---|---|---|---|
| THEŌRĪTIKA MATHĪMATIKA | Core Courses A2 | 1 | 1 | 10 |
| Academic Year | 2025 – 2026 |
| Class Period | Winter |
| Faculty Instructors |
|
| Weekly Hours | 3 |
| Total Hours | 39 |
| Class ID | 600290416
|
Course Type 2021
Specialization / Direction
Mode of Delivery
- Face to face
- Distance learning
Digital Course Content
- e-Study Guide https://qa.auth.gr/en/class/1/600290416
- eLearning (Moodle): https://elearning.auth.gr/course/view.php?id=8302
Erasmus
The course is also offered to exchange programme students.
Language of Instruction
- Greek (Instruction, Examination)
Prerequisites
General Prerequisites
General background of the introductory material of an undergraduate course on Complex Analysis
Learning Outcomes
Upon successful completion of the course, students will:
1. have a deep knowledge of the basic notions of Complex Analysis such as the notions: holomorphic function, conformal map, harmonic function, normal family.
2. be able to solve problems related to the above notions and their interrelations.
3. be able to execute calculations on concrete examples
General Competences
- Retrieve, analyse and synthesise data and information, with the use of necessary technologies
- Make decisions
- Work autonomously
- Work in teams
- Work in an international context
- Generate new research ideas
- Be critical and self-critical
- Advance free, creative and causative thinking
Course Content (Syllabus)
Holomorphic functions. General form of Cauchy's theorem. Locally uniform convergenvce, Weierstrass' theorem. Infinite products, Runge's theorem. Normal families, Montel's theorem. Conformal mapping, Riemann mapping theorem. Harmonic and subharmonic functions, Maximum principle, Dirichlet's problem, Schwarz reflection principle. Theorems of Bloch, Schottky, Montel_caratheodory, Picard.
Keywords
Holomorphic functions, normal families, conformal mapping, harmonic functions
Educational Material Types
- Notes
- Slide presentations
- Multimedia
- Book
Use of Information and Communication Technologies
Use of ICT
- Use of ICT in Course Teaching
- Use of ICT in Communication with Students
- Use of ICT in Student Assessment
Description
Use of Mathematica foe examples and exercises. Online exercise hours.
Course Organization
| Activities | Workload | ECTS | Individual | Teamwork | Erasmus |
|---|---|---|---|---|---|
| Lectures | 39 | 1.3 | |||
| Reading Assigment | 183 | 6.1 | |||
| Tutorial | 13 | 0.4 | |||
| Project | 20 | 0.7 | |||
| Written assigments | 40 | 1.3 | |||
| Exams | 5 | 0.2 | |||
| Total | 300 | 10 |
Student Assessment
Description
The final grade for this course will be calculated as follows:
1. First Exam 30%
2. Exercises-Projects-Participation 30%
3. Second Exam 40%
Student Assessment methods
- Written Exam with Short Answer Questions (Formative, Summative)
- Written Exam with Extended Answer Questions (Formative, Summative)
- Written Assignment (Formative, Summative)
- Written Exam with Problem Solving (Formative, Summative)
Bibliography
Additional bibliography for study
1. D. Sarason, Complex Function Theory
2. S. Saks, A. Zygmund, Analytic Functions
3. W. Rudin, Real and Complex Analysis
Last Update
07-05-2025
