MAT6014 Conformal MappingsBahçeşehir UniversityDegree Programs MATHEMATICS (TURKISH, PHD)General Information For StudentsDiploma SupplementErasmus Policy StatementNational QualificationsBologna Commission
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 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