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 |
This catalog is for information purposes. Course status is determined by the relevant department at the beginning of semester. |
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. |
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 / 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. |
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 |
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 |
No Effect | 1 Lowest | 2 Low | 3 Average | 4 High | 5 Highest |
Program Outcomes | Level of Contribution | |
1) | Ability to assimilate mathematic related concepts and associate these concepts with each other. | 5 |
2) | Ability to gain qualifications based on basic mathematical skills, problem solving, reasoning, association and generalization. | 5 |
3) | Be able to organize events, for the development of critical and creative thinking and problem solving skills, by using appropriate methods and techniques. | 5 |
4) | Ability to make individual and team work on issues related to working and social life. | |
5) | Ability to transfer ideas and suggestions, related to topics about his/her field of interest, written and verball. | 4 |
6) | Ability to use mathematical knowledge in technology. | |
7) | To apply mathematical principles to real world problems. | 3 |
8) | Ability to use the approaches and knowledge of other disciplines in Mathematics. | 3 |
9) | Be able to set up and develope a solution method for a problem in mathematics independently, be able to solve and evaluate the results and to apply them if necessary. | 5 |
10) | To be able to link abstract thought that one has to concrete events and to transfer the solutions and examine and interpret the results scientifically by forming experiments and collecting data. | 5 |
11) | To be able to conduct a research either as an individual or as a team member, and to be effective in each related step of the project, to take role in the decision process, to plan and manage the project by using time effectively. | 5 |
12) | To be able to acquire necessary information and to make modeling in any field that mathematics is used and to improve herself/himself. | 5 |