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Information
| Code | MT505 |
| Name | Complex Analysis |
| Term | 2024-2025 Academic Year |
| Term | Fall |
| Duration (T+A) | 3-0 (T-A) (17 Week) |
| ECTS | 6 ECTS |
| National Credit | 3 National Credit |
| Teaching Language | Türkçe |
| Level | Yüksek Lisans Dersi |
| Type | Normal |
| Mode of study | Yüz Yüze Öğretim |
| Catalog Information Coordinator | Prof. Dr. DOĞAN DÖNMEZ |
| Course Instructor |
1 |
Course Goal / Objective
To grasp the fundamental properties of complex functions
Course Content
Complex analytic functions, meromorphic functions. Their properties. Elliptic functions
Course Precondition
None.
Resources
Complex Analysis, Theodore W. Gamelin, Springer New York, NY, 2001.
Notes
None.
Course Learning Outcomes
| Order | Course Learning Outcomes |
|---|---|
| LO01 | Understands analytic functions |
| LO02 | Understands Cauchy integral formulas |
| LO03 | Understands Taylor s and Laurent s series |
| LO04 | Understands the fundamental properties of analytic functions |
| LO05 | Understands the fundamental properties of meromorphic functions |
| LO06 | Understands elliptic functions. |
Relation with Program Learning Outcome
| Order | Type | Program Learning Outcomes | Level |
|---|---|---|---|
| PLO01 | Bilgi - Kuramsal, Olgusal | Knows in detail the relationship between the results in her area of expertise and other areas of mathematics. | 5 |
| PLO02 | Bilgi - Kuramsal, Olgusal | Knows in detail the relationship between the results in his area of expertise and other areas of mathematics. | 4 |
| PLO03 | Bilgi - Kuramsal, Olgusal | Establishes new mathematical models with the help of the knowledge gained in the field of specialization. | 5 |
| PLO04 | Bilgi - Kuramsal, Olgusal | Has basic knowledge in all areas of mathematics. | 4 |
| PLO05 | Bilgi - Kuramsal, Olgusal | It presents the knowledge gained in different fields of mathematics and their relations with each other in the simplest and most understandable way. | |
| PLO06 | Bilgi - Kuramsal, Olgusal | Effectively uses the technical equipment needed to express mathematics. | 5 |
| PLO07 | Bilgi - Kuramsal, Olgusal | poses original problems related to field and presents different solution techniques. | |
| PLO08 | Bilgi - Kuramsal, Olgusal | carries out original and qualified scientific studies on the subject related to its field. | 4 |
| PLO09 | Bilgi - Kuramsal, Olgusal | Analyzes existing mathematical theories and develops new theories. | 3 |
| PLO10 | Beceriler - Bilişsel, Uygulamalı | Knows the teaching-learning techniques in areas of mathematics that require expertise and uses these techniques effectively at every stage of education. | 2 |
| PLO11 | Yetkinlikler - Bağımsız Çalışabilme ve Sorumluluk Alabilme Yetkinliği | To have knowledge of a foreign language at a level to be able to follow foreign sources related to the field and to communicate verbally and in writing with foreign stakeholders. | 4 |
| PLO12 | Yetkinlikler - Bağımsız Çalışabilme ve Sorumluluk Alabilme Yetkinliği | presents and publishes its original works within the framework of scientific ethical rules for the benefit of its stakeholders. | |
| PLO13 | Yetkinlikler - Öğrenme Yetkinliği | Adheres to the ethical rules required by its scientific title | 4 |
Week Plan
| Week | Topic | Preparation | Methods |
|---|---|---|---|
| 1 | Complex numbers and properties of the argument function | Studying the relevant parts of the course materials. | Öğretim Yöntemleri: Anlatım |
| 2 | Limit, continuity, derivative | Studying the relevant parts of the course materials. | Öğretim Yöntemleri: Anlatım |
| 3 | Analytic functions. Cauchy- Riemann conditions | Studying the relevant parts of the course materials. | Öğretim Yöntemleri: Anlatım |
| 4 | Cauchy- Goursat Theorem. Cauchy integral formula | Studying the relevant parts of the course materials. | Öğretim Yöntemleri: Anlatım |
| 5 | Liouville s theorem. Fundamental Theorem of Algebra | Studying the relevant parts of the course materials. | Öğretim Yöntemleri: Anlatım |
| 6 | Analytic functions and Taylos series. | Studying the relevant parts of the course materials. | Öğretim Yöntemleri: Anlatım |
| 7 | Isolated singular points. Poles and essential singularities | Studying the relevant parts of the course materials. | Öğretim Yöntemleri: Anlatım |
| 8 | Mid-Term Exam | Solve the homework problems. | Ölçme Yöntemleri: Ödev |
| 9 | Schwarz s Lemma. Mobius transformations | Studying the relevant parts of the course materials. | Öğretim Yöntemleri: Anlatım |
| 10 | Hadamard s three circle Theorem | Studying the relevant parts of the course materials. | Öğretim Yöntemleri: Anlatım |
| 11 | Open mapping property. Morera teoremi. Differentiability of the inverse function. | Studying the relevant parts of the course materials. | Öğretim Yöntemleri: Anlatım |
| 12 | Field of meromorphic functions on the Riemann sphere. | Studying the relevant parts of the course materials. | Öğretim Yöntemleri: Anlatım |
| 13 | Doubly periodic functions. Their properties. | Studying the relevant parts of the course materials. | Öğretim Yöntemleri: Anlatım |
| 14 | Properties of the Weierstrass s function. Differential equaiton | Studying the relevant parts of the course materials. | Öğretim Yöntemleri: Anlatım |
| 15 | Field of meromorphic functions on the torus. | Studying the relevant parts of the course materials. | Öğretim Yöntemleri: Anlatım |
| 16 | Term Exams | Solve the homework problems. | Ölçme Yöntemleri: Ödev |
| 17 | Term Exams | Solve the homework problems. | Ölçme Yöntemleri: Ödev |
Student Workload - ECTS
| Works | Number | Time (Hour) | Workload (Hour) |
|---|---|---|---|
| Course Related Works | |||
| Class Time (Exam weeks are excluded) | 14 | 3 | 42 |
| Out of Class Study (Preliminary Work, Practice) | 14 | 5 | 70 |
| Assesment Related Works | |||
| Homeworks, Projects, Others | 0 | 0 | 0 |
| Mid-term Exams (Written, Oral, etc.) | 1 | 15 | 15 |
| Final Exam | 1 | 30 | 30 |
| Total Workload (Hour) | 157 | ||
| Total Workload / 25 (h) | 6,28 | ||
| ECTS | 6 ECTS | ||