Course Information

Course Information
Course Title Code Semester L+U Hour Credits ECTS
Geometric Functions II MAT546 3 + 0 3.0 8.0
Prerequisites None
Language of Instruction Turkish
Course Level Graduate
Course Type
Mode of delivery Lecturing
Course Coordinator Assoc. Prof. Dr. Fatih HEZENCİ
Instructor(s) Fatih HEZENCİ
Assistants
Goals Introduce Univalent functions and examine the properties and theorems related to these functions
Course Content The Loewner theory;Subordination chains and kernel convergence; Loewner's differential equation; Remarks on Bieberbach's conjecture; Applications of Loewner's differential equation to the study of univalent functions; Becker's univalence criteria; Univalence criteria involving the Schwarzian derivative;Preliminaries concerning Bloch functions;Distortion results for locally univalent Bloch functions; The case of convex functions; Linear invariance in the unit disc; General ideas concerning linear-invariant families; Extremal problems and radius of univalence
Learning Outcomes - Students will learn theoretical concepts in mathematics.
- Students will learn how to read academical journals.
Weekly Topics (Content)
Week Topics Learning Methods
1. Week The Loewner theory
2. Week Kernel convergence
3. Week Loewner's differential equation
4. Week Remarks on Bieberbach's conjecture
5. Week Applications of Loewner's differential equation
6. Week Becker's univalence criteria
7. Week Univalence criteria involving the Schwarzian derivative
8. Week Midterm
9. Week Preliminaries concerning Bloch functions
10. Week Distortion results for locally univalent Bloch functions
11. Week The case of convex functions
12. Week Linear invariance in the unit disc
13. Week General ideas concerning linear-invariant families
14. Week Extremal problems and radius of univalence
Recommended Sources
Geometric Function Theory and In One and Hıgher Dımensıons,Ian Graham-Gabrıela Kohr 2003
Relations with Education Attainment Program Course Competencies
Program Requirements Contribution Level DK1 DK2 Measurement Method
PY1 3 0 0 60
PY2 4 0 0 60
PY3 2 0 0 60
PY4 4 0 0 60
PY5 3 0 0 60
PY6 5 0 0 60
PY7 2 0 0 60
PY8 5 0 0 60
PY9 4 0 0 60
PY10 3 0 0 60
*DK = Course's Contrubution.
0 1 2 3 4 5
Course's Level of contribution None Very Low Low Fair High Very High
Method of assessment/evaluation Written exam Oral Exams Assignment/Project Laboratory work Presentation/Seminar
ECTS credits and course workload
Event Quantity Duration (Hour) Total Workload (Hour)
Course Hours 14 3 42
Research 14 2 28
Midterm 1 1 2 2
Homework 1 14 2 28
Homework 2 14 2 28
Final 1 2 2
Practice 6 6 36
Classroom Activities 14 3 42
Total Workload 208
ECTS Credit of the Course 8.0