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 and univalent functions.
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
Subordination Principle
Lectures
2. Week
Subordination Principle
Lectures
3. Week
Subordination Principle
Lectures
4. Week
Integral Means
Lectures
5. Week
Integral Means
Lectures
6. Week
Integral Means
Lectures
7. Week
Some Special Topics on Univalent Functions
Lectures
8. Week
Some Special Topics on Univalent Functions
Lectures
9. Week
Some Special Topics on Univalent Functions
Lectures
10. Week
General Extremal Problems
Lectures
11. Week
General Extremal Problems
Lectures
12. Week
General Extremal Problems
Lectures
13. Week
Boundary Variation
Lectures
14. Week
Boundary Variation
Lectures
15. Week
Final Week
Exams
16. Week
Final Week
Exams
17. Week
Final Week
Exams
Assessments
Evaluation tools
Quantity
Weight(%)
Midterm(s)
2
50
Homework / Term Projects / Presentations
2
20
Final Exam
1
30
Program Outcomes
PO-1
Have ability to develop new mathematical ideas and methods by using high-level mental processes such as creative and critical thinking, problem solving and decision-making.
PO-2
Follow the current developments in the field of mathematics, and make the critical analysis, synthesis and evaluation of new and complex ideas.
PO-3
Understand the interdisciplinary interaction related to Mathematics and play a role in an effective manner in environments that require with the resolution of problems encountered in this process.
PO-4
Defend original views on the discussion of the issues in the field of mathematics with experts and communicate to show competence in oral and written.
PO-5
Do research with high-level national and international scientific working groups, and acquire the responsibility to contribute to the literature by publishing original works in respected scientific journals.
PO-6
Use computer software to solve problems effectively by following the developments in information and communication technologies.
PO-7
Contribute to the solution of social, scientific, cultural and ethical problems encountered issues related to the field and support the development of these values.
PO-8
To solve problems related to the field, establish functional interacts by using strategic decision making processes.
PO-9
Establish and discuss in written, oral and visual communication at an advanced level by using at least one foreign language.
Learning Outcomes
LO-1
Analysing and synthesizing of the subordination principle.
LO-2
Having advanced knowledge on integral means.
LO-3
Having advanced knowledge on bounded univalent functions, convolution of convex functions, criteria of univalence.
