MT505 Complex Analysis

6 ECTS - 3-0 Duration (T+A)- . Semester- 3 National Credit

Information

Code MT505
Name Complex Analysis
Term 2024-2025 Academic Year
Semester . Semester
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 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

Update Time: 09.05.2024 11:48