BAHÇEŞEHİR UNIVERSITY BİLGİ PAKETİ / DERS KATALOĞU
| MATHEMATICS (TURKISH, PHD) | |||||
| PhD | TR-NQF-HE: Level 8 | QF-EHEA: Third Cycle | EQF-LLL: Level 8 | ||
Course Introduction and Application Information
| Course Code | Course Name | Semester | Theoretical | Practical | Credit | ECTS |
| MAT6012 | Univalent Function Theory | Fall Spring |
3 | 0 | 3 | 8 |
| This catalog is for information purposes. Course status is determined by the relevant department at the beginning of semester. |
Basic information
| Language of instruction: | Turkish |
| Type of course: | Departmental Elective |
| Course Level: | |
| Mode of Delivery: | Face to face |
| Course Coordinator : | Assoc. Prof. ERSİN ÖZUĞURLU |
| Recommended Optional Program Components: | None |
| Course Objectives: | In this course the basic results of the univalent functions theory, such as: the area theorem, Koebes one-quarter theorem and the growth and distortion theorems and proof of the famous Bieberbach conjecture by dBranges , will be learned. |
Learning Outcomes
|
The students who have succeeded in this course; 1 Explain the area theorem and Koebe one-quarter theorem 2 Explain growth and distortion theorems about univalent functions. 3 Explain the proof of the famous Bieberbach Conjecture given by deDranges. |
Course Content
| Week 1 Fundamental Distortion Theorems for Univalent Functions Week 2 Fundamental Inequalities of Coefficient for Univalent Functions. Week 3 Some Special Classes of Univalent Functions. Week 4 Parametric Representation of Loewner. Week 5 Faber Polynomials and Generalization of Area Principle. Week 6 Midterm Exam Week 7 Faber Transform. Week 8 Subordination. Week 9 Integral Means. Week 10 Variational Tecniques. Week 11 Midterm Exam Week 12 Extreme points of Some Special Class of Functions. Week 13 Proof of Bieberbach Conjecture. Week 14 Proof of Bieberbach Conjecture. Week 15 General review. Week 16 Final exam. |
Weekly Detailed Course Contents
| Week | Subject | Related Preparation |
| 1) | Fundamental Distortion Theorems for Univalent Functions | |
| 2) | Fundamental Inequalities of Coefficient for Univalent Functions. | |
| 3) | Some Special Classes of Univalent Functions. | |
| 4) | Parametric Representation of Loewner. | |
| 5) | Faber Polynomials and Generalization of Area Principle. | |
| 6) | Faber polynomials and the generalization of field principle (continued) | |
| 7) | Faber Transform. | |
| 8) | Subordination. | |
| 9) | Integral Means. | |
| 10) | Extreme points of Some Special Class of Functions. | |
| 11) | Extreme points of some special class of functions | |
| 12) | Variational Tecniques. | |
| 13) | Proof of Bieberbach Conjecture. | |
| 14) | Proof of Bieberbach Conjecture. |
Sources
| Course Notes / Textbooks: | P.L. Duren, Univalent Functions, Springer Verlag, New York, 1983. |
| References: | A.W. Goodman, Univalent Functions, Vol I, II, Mariner Pub., Tampa, Florida, 1983. |
Evaluation System
| Semester Requirements | Number of Activities | Level of Contribution |
| Quizzes | 3 | % 10 |
| Midterms | 2 | % 50 |
| Final | 1 | % 40 |
| Total | % 100 | |
| PERCENTAGE OF SEMESTER WORK | % 60 | |
| PERCENTAGE OF FINAL WORK | % 40 | |
| Total | % 100 | |
ECTS / Workload Table
| Activities | Number of Activities | Duration (Hours) | Workload |
| Course Hours | 14 | 3 | 42 |
| Study Hours Out of Class | 14 | 4 | 56 |
| Quizzes | 3 | 15 | 45 |
| Midterms | 2 | 19 | 38 |
| Final | 1 | 19 | 19 |
| Total Workload | 200 | ||
Contribution of Learning Outcomes to Programme Outcomes
| No Effect | 1 Lowest | 2 Low | 3 Average | 4 High | 5 Highest |
| Program Outcomes | Level of Contribution |