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 |
MAT6014 | Conformal Mappings | 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: | To determine to which region one transformation transforms the unit disc and to form the transformation that transforms the unit disc to a certain region. |
The students who have succeeded in this course; 1 He/she determines the conformal mappings 2 He/she uses the properties of the conformal mappings 3 He/she determines to which region any given transformation transforms the unit disc 4 He/she determines the Rieman Transformation Theorem 5 He/she knows the rational linear transformations. 6 He/she the principle of symmetry. 7 He/she the conformal mapping who maps one region to another region. 8 He/she applies the Schwarz Christoffel Formula 9 He/she learns the relation between the analytic univalent functions and conformal mappings. 10 He/she knows the univalent functions in the unit disc |
1 The Complex Transformations 2 The geometrical study of the conformal mappings 3 The relation between the analytical univalent functions and conformal mappings 4 The Riemann Mapping Theorem and results 5 The rational linear transformations 6 The principle of symmetry 7 The formation of the simple conformal mappings 8 Some special transformations 9 Midterm Exam evaluation 10 The finding of the linear transformation that draws one region to another region 11 Schwarz Christoffel Formula 12 The class of the univalent functions in the unit disc 13 The function examples belonging to S class 14 Some properties of the analytic univalent functions in the unit disc. 15 General review 16 Final Exam |
Week | Subject | Related Preparation |
1) | The Complex Transformations | |
2) | The geometrical study of the conformal mappings | |
3) | The relation between the analytical univalent functions and conformal mappings | |
4) | The Riemann Mapping Theorem and results | |
5) | The rational linear transformations | |
6) | The principle of symmetry | |
7) | The formation of the simple conformal mappings | |
8) | Some special transformations | |
9) | Midterm Exam evaluation | |
10) | The finding of the linear transformation that draws one region to another region | |
11) | Schwarz Christoffel Formula | |
12) | The class of the univalent functions in the unit disc | |
13) | The function examples belonging to S class | |
14) | Some properties of the analytic univalent functions in the unit disc. |
Course Notes / Textbooks: | Complex Analysis And Applications Second Edition, William R. Derric, 1984. |
References: | . |
Semester Requirements | Number of Activities | Level of Contribution |
Homework Assignments | 1 | % 20 |
Midterms | 1 | % 30 |
Final | 1 | % 50 |
Total | % 100 | |
PERCENTAGE OF SEMESTER WORK | % 50 | |
PERCENTAGE OF FINAL WORK | % 50 | |
Total | % 100 |
Activities | Number of Activities | Duration (Hours) | Workload |
Course Hours | 14 | 3 | 42 |
Study Hours Out of Class | 14 | 5 | 70 |
Homework Assignments | 1 | 25 | 25 |
Midterms | 1 | 30 | 30 |
Final | 1 | 33 | 33 |
Total Workload | 200 |
No Effect | 1 Lowest | 2 Low | 3 Average | 4 High | 5 Highest |
Program Outcomes | Level of Contribution |