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. |
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 |
Geometric Function Theory and In One and Hıgher Dımensıons,Ian Graham-Gabrıela Kohr 2003 |
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 |
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 |
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 |