COMPLEX ANALYSIS
| Title | ΜΙΓΑΔΙΚΗ ΑΝΑΛΥΣΗ / COMPLEX ANALYSIS |
| Code | Θ020 |
| Faculty | Sciences |
| School | Mathematics |
| Cycle / Level | 2nd / Postgraduate |
| Teaching Period | Winter/Spring |
| Coordinator | Dimitrios Betsakos |
| Common | Yes |
| Status | Active |
| Course ID | 600025909 |
Programme of Study: PMS Tmīmatos Mathīmatikṓn (2025-2030)
Registered students: 0
| Orientation | Attendance Type | Semester | Year | ECTS |
|---|---|---|---|---|
| THEŌRĪTIKA MATHĪMATIKA | Elective Courses belonging to the selected specialization | Winter | - | 10 |
| Academic Year | 2025 – 2026 |
| Class Period | Winter |
| Faculty Instructors | |
| Weekly Hours | 3 |
| Total Hours | 39 |
| Class ID | 600268385
|
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/1/600268385
- eLearning:
- 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
Good knowledge of the material of an undergraduate course on Complex Analysis.
Good knowledge of the basic elements of the Topology of the Plane.
Learning Outcomes
Upon successful completion of the course, students will have assimilated the course material, will be able to apply their knowledge to solve exercises, to understand material from other, related courses, and to be able to deepen to the concepts and methods they have learned.Moreover,
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
- Apply knowledge in practice
- Adapt to new situations
- Make decisions
- Work autonomously
- Work in teams
- Generate new research ideas
- Appreciate diversity and multiculturality
- 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
- 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 for examples and exercises. Online exercise hours.
Course Organization
| Activities | Workload | ECTS | Individual | Teamwork | Erasmus |
|---|---|---|---|---|---|
| Lectures | 39 | ✓ | |||
| Reading Assigment | 183 | ✓ | |||
| Tutorial | 13 | ✓ | |||
| Project | 20 | ✓ | |||
| Written assigments | 40 | ✓ | |||
| Exams | 5 | ✓ | |||
| Total | 300 |
Student Assessment
Description
Weekly exercises 30%
Midterm exam 30%
Final Exam 40%
Student Assessment methods
- Written Exam with Extended Answer Questions (Summative)
- Written Assignment (Summative)
- Written Exam with Problem Solving (Summative)
Bibliography
Additional bibliography for study
1. Ahlfors L. V., Complex Analysis, McGraw-Hill 1979.
2. Rudin, W., Real and Complex Analysis, McGraw-Hill 1987.
3. D. Sarason, Complex Function Theory, Second Edition, Amer. Math. Soc. 2007.
4. Saks S. and Zygmund A., Analytic Functions, Elsevier 1971.
Last Update
07-05-2025
