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Information
| Unit | INSTITUTE OF NATURAL AND APPLIED SCIENCES |
| MATHEMATICS (MASTER) (WITH THESIS) | |
| Code | MT505 |
| Name | Complex Analysis |
| Term | 2018-2019 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 |
The current term course schedule has not been prepared yet.
|
Course Goal / Objective
To grasp the fundamental properties of complex functions
Course Content
Complez analytic functions, moromorphic functions. Their properties. Elliptic functions
Course Precondition
Resources
Notes
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. | |
| 2 | Limit, continuity, derivative | Studying the relevant parts of the course materials. | |
| 3 | Analytic functions. Cauchy- Riemann conditions | Studying the relevant parts of the course materials. | |
| 4 | Cauchy- Goursat Theorem. Cauchy integral formula | Studying the relevant parts of the course materials. | |
| 5 | Liouville s theorem. Fundamental Theorem of Algebra | Studying the relevant parts of the course materials. | |
| 6 | Analytic functions and Taylos series. | Studying the relevant parts of the course materials. | |
| 7 | Isolated singular points. Poles and essential singularities | Studying the relevant parts of the course materials. | |
| 8 | Mid-Term Exam | Solve the homework problems. | |
| 9 | Schwarz s Lemma. Mobius transformations | Studying the relevant parts of the course materials. | |
| 10 | Hadamard s three circle Theorem | Studying the relevant parts of the course materials. | |
| 11 | Open mapping property. Morera teoremi. Differentiability of the inverse function. | Studying the relevant parts of the course materials. | |
| 12 | Field of meromorphic functions on the Riemann sphere. | Studying the relevant parts of the course materials. | |
| 13 | Doubly periodic functions. Their properties. | Studying the relevant parts of the course materials. | |
| 14 | Properties of the Weierstrass s function. Differential equaiton | Studying the relevant parts of the course materials. | |
| 15 | Field of meromorphic functions on the torus. | Studying the relevant parts of the course materials. | |
| 16 | Term Exams | Solve the homework problems. | |
| 17 | Term Exams | Solve the homework problems. |
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 | ||