| Course Title | Code | Semester | L+U Hour | Credits | ECTS |
|---|---|---|---|---|---|
| Geometric Functions I | MAT545 | 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 |
| Instructors |
Fatih HEZENCİ |
| Assistants | |
| Goals | Introduce Univalent functions and examine the properties and theorems related to these functions |
| Course Content | Univalent functions; Elementary properties of univalent functions; The area theorem Growth, covering and distortion results in the class S; The maximum modulus of univalent functions; Subclasses of univalent functions in the unit disc;Functions with positive real part. Subordination and the Herglotz formula; Starlike and convex functions;Starlikeness and convexity of order α; Close-to-convexity, spirallikeness and ɸ-likeness in the unit disc; The Loewner theory; Loewner chains and the Loewner differential equation;Kernel convergence |
| Learning Outcomes |
| Week | Topics | Learning Methods |
|---|---|---|
| 1. Week | Univalent functions | |
| 2. Week | Elementary properties of univalent functions | |
| 3. Week | The area theorem | |
| 4. Week | Growth, covering and distortion results in the class S | |
| 5. Week | The maximum modulus of univalent functions | |
| 6. Week | Subclasses of univalent functions in the unit disc | |
| 7. Week | Functions with positive real part | |
| 8. Week | Midterm | |
| 9. Week | Subordination and the Herglotz formula | |
| 10. Week | Starlike and convex functions | |
| 11. Week | Starlikeness and convexity of order α | |
| 12. Week | Close-to-convexity, spirallikeness and ɸ-likeness in the unit disc | |
| 13. Week | The Loewner theory | |
| 14. Week | Loewner chains and the Loewner differential equation |
| Geometric Function Theory and In One and Hıgher Dımensıons,Ian Graham-Gabrıela Kohr 2003 |
| Program Requirements | Contribution Level | Measurement Method |
|---|---|---|
| PY1 | 4 | 60 |
| PY2 | 5 | 60 |
| PY3 | 2 | 60 |
| PY4 | 1 | 60 |
| PY5 | 5 | - |
| PY6 | 4 | 60 |
| PY7 | 3 | 60 |
| PY8 | 3 | 60 |
| PY9 | 4 | 60 |
| PY10 | 3 | 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 |
| Midterm 2 | 1 | 2 | 2 |
| Homework 1 | 14 | 3 | 42 |
| Homework 2 | 14 | 2 | 28 |
| Quiz 1 | 1 | 2 | 2 |
| Quiz 2 | 1 | 2 | 2 |
| Final | 1 | 2 | 2 |
| Practice | 6 | 6 | 36 |
| Classroom Activities | 14 | 1 | 14 |
| Total Workload | 200 | ||
| ECTS Credit of the Course | 8.0 | ||
