Analysing and synthesizing the theory of geometric and univalent functions and their related fundamental topics.
Prerequisite(s)
None
Corequisite(s)
None
Special Requisite(s)
To have general knowledge about the basic topics of complex analysis.
Instructor(s)
Assoc. Prof. Emel Yavuz
Course Assistant(s)
None
Schedule
To be announced
Office Hour(s)
Details will be announced. Office number AK / 3-A-03/05
Teaching Methods and Techniques
Lectures, homeworks.
Principle Sources
P.L. Duren, Univalent Functions, Springer Verlag, New York, 1983.
Other Sources
A.W. Goodman, Univalent Functions, Vol I, II, Mariner Pub., Tampa, Florida, 1983.
Course Schedules
Week
Contents
Learning Methods
1. Week
Geometric Function Theory
Lectures
2. Week
Geometric Function Theory
Lectures
3. Week
Geometric Function Theory
Lectures
4. Week
Elementary Theory of Univalent Functions
Lectures
5. Week
Elementary Theory of Univalent Functions
Lectures
6. Week
Elementary Theory of Univalent Functions
Lectures
7. Week
Elementary Theory of Univalent Functions
Lectures
8. Week
Parametric Representation of Slit Mappings
Lectures
9. Week
Parametric Representation of Slit Mappings
Lectures
10. Week
Parametric Representation of Slit Mappings
Lectures
11. Week
Generalizations of the Area Principle
Lectures
12. Week
Generalizations of the Area Principle
Lectures
13. Week
Generalizations of the Area Principle
Lectures
14. Week
Generalizations of the Area Principle
Lectures
15. Week
Final Week
Exams
16. Week
Final Week
Exams
17. Week
Final Week
Exams
Assessments
Evaluation tools
Quantity
Weight(%)
Midterm(s)
2
30
Homework / Term Projects / Presentations
2
20
Final Exam
1
50
Program Outcomes
PO-1
Have scientific research in mathematics and computer science in the level of theoretical and practical knowledge.
PO-2
On the basis of undergraduate level qualifications, develop and deepen the same or a different areas of information at the level of expertise, and analyze and interpret by using statistical methods
PO-3
Develop new strategic approaches for the solution of complex problems encountered in applications related to the field and unforeseen and take responsibility for the solution.
PO-4
Evaluate critically skills acquired in the field of information in the level of expertise and assess the learning guides.
PO-5
Transfer current developments in the field and their work to the groups inside and outside the area supporting with quantitative and qualitative datas as written, verbal and visual by a systematic way.
PO-6
Use information and communication technologies with computer software in advanced level.
PO-7
Develop efficient algorithms by modeling problems faced in the field and solve such problems by using actual programming languages.
PO-8
Respect to social, scientific, cultural and ethical values at the stages of data collection related to the field, interpretation, and implementation.
PO-9
To solve problems related to the field, establish functional interacts by using strategic decision making processes.
PO-10
Establish and discuss in written, oral and visual communication in an advanced level by using at least one foreign language.
Learning Outcomes
LO-1
Analysing and synthesizing the theory of geometric functions.
LO-2
Analysing and synthesizing the elementary theory of univalent functions.
LO-3
Analysing the parametric representation of slit mappings.
LO-4
Analysing generalizations of the area principle.
LO-5
Estimating and understanding of fundamental inequalities of univalent functions.
