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 |
| MAT6014 | Conformal Mappings | 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: | 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. |
Learning Outcomes
|
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 |
Course Content
| 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 |
Weekly Detailed Course Contents
| 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. |
Sources
| Course Notes / Textbooks: | Complex Analysis And Applications Second Edition, William R. Derric, 1984. |
| References: | . |
Evaluation System
| 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 | |
ECTS / Workload Table
| 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 | ||
Contribution of Learning Outcomes to Programme Outcomes
| 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. | 4 |
| 4) | Ability to make individual and team work on issues related to working and social life. | 4 |
| 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. | 4 |
| 7) | To apply mathematical principles to real world problems. | 4 |
| 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. | 3 |
| 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. | 4 |
| 12) | To be able to acquire necessary information and to make modeling in any field that mathematics is used and to improve herself/himself. | 4 |