MATHEMATICS (TURKISH, PHD) | |||||
PhD | TR-NQF-HE: Level 8 | QF-EHEA: Third Cycle | EQF-LLL: Level 8 |
Course Code | Course Name | Semester | Theoretical | Practical | Credit | ECTS |
MAT6012 | Univalent Function Theory | Fall Spring |
3 | 0 | 3 | 8 |
The course opens with the approval of the Department at the beginning of each semester |
Language of instruction: | Tr |
Type of course: | Departmental Elective |
Course Level: | |
Mode of Delivery: | Face to face |
Course Coordinator : | Assoc. Prof. ERSİN ÖZUĞURLU |
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. |
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. |
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. |
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. |
Course Notes: | P.L. Duren, Univalent Functions, Springer Verlag, New York, 1983. |
References: | A.W. Goodman, Univalent Functions, Vol I, II, Mariner Pub., Tampa, Florida, 1983. |
Semester Requirements | Number of Activities | Level of Contribution |
Attendance | % 0 | |
Laboratory | % 0 | |
Application | % 0 | |
Field Work | % 0 | |
Special Course Internship (Work Placement) | % 0 | |
Quizzes | 3 | % 10 |
Homework Assignments | % 0 | |
Presentation | % 0 | |
Project | % 0 | |
Seminar | % 0 | |
Midterms | 2 | % 50 |
Preliminary Jury | % 0 | |
Final | 1 | % 40 |
Paper Submission | % 0 | |
Jury | % 0 | |
Bütünleme | % 0 | |
Total | % 100 | |
PERCENTAGE OF SEMESTER WORK | % 60 | |
PERCENTAGE OF FINAL WORK | % 40 | |
Total | % 100 |
Activities | Number of Activities | Duration (Hours) | Workload |
Course Hours | 14 | 3 | 42 |
Laboratory | 0 | 0 | 0 |
Application | 0 | 0 | 0 |
Special Course Internship (Work Placement) | 0 | 0 | 0 |
Field Work | 0 | 0 | 0 |
Study Hours Out of Class | 14 | 4 | 56 |
Presentations / Seminar | 0 | 0 | 0 |
Project | 0 | 0 | 0 |
Homework Assignments | 0 | 0 | 0 |
Quizzes | 3 | 15 | 45 |
Preliminary Jury | 0 | ||
Midterms | 2 | 19 | 38 |
Paper Submission | 0 | ||
Jury | 0 | ||
Final | 1 | 19 | 19 |
Total Workload | 200 |
No Effect | 1 Lowest | 2 Low | 3 Average | 4 High | 5 Highest |
Program Outcomes | Level of Contribution |