Semester  Course Unit Code  Course Unit Title  L+P  Credit  Number of ECTS Credits 
7  MATH407  CONFORMAL MAPPINGS  3+0  3  6 
Language of Instruction

English

Level of Course Unit

First Cycle

Department / Program

MATHEMATICS

Mode of Delivery

Face to Face

Type of Course Unit

Elective

Objectives of the Course

Study conformal transformations and applications to geometry and the boundary value problems of electrostatics and hydrodynamics

Course Content

Analytic functions. Geometrical interpretation. Conformal transformations. Mobius transformations. ChristofelSchwarz conformal mappings. Conformal metric and geometry. Boundary value problems. Electrostatics and hydrodynamics.

Course Methods and Techniques


Prerequisites and corequisities

None

Course Coordinator

None

Name of Lecturers

Prof.Dr. Oktay Pashaev Associate Prof.Dr. Fatih Erman

Assistants

None

Work Placement(s)

No

Recommended or Required Reading
Resources

V. I. Ivanov, V. Yu. Popov. "Conformal mapping and applications", Moscow University 2002 M.A. Lavrentyev "Conformal mappings with applications to some problems of mechanics", Leningrad, 1946


conformal transformations and applications to geometry and the boundary value problems of electrostatics and hydrodynamics


1


2


3


Planned Learning Activities and Teaching Methods
Activities are given in detail in the section of "Assessment Methods and Criteria" and "Workload Calculation"
Assessment Methods and Criteria
InTerm Studies

Midterm exams

2

%
50

Quizzes

0

%
0

Homeworks

0

%
0

Other activities

0

%
0

Laboratory works

0

%
0

Projects

0

%
0

Final examination

1

%
50

Total

3

%
100

ECTS Allocated Based on Student Workload
Activities

Total Work Load

Weekly Course Time

1

72

72

Outside Activities About Course (Attendance, Presentation, Midterm exam,Final exam, Quiz etc.)

1

42

42

Exams and Exam Preparations

1

72

72

Total Work Load
 

Number of ECTS Credits 6
186

Course Learning Outcomes: Upon the successful completion of this course, students will be able to:
No  Learning Outcomes 
1
 To understand how conformal mappings contribute to studying geometrical objects 
2
 To be able to solve typical problems assocoated with this theory 
3
 The abılıty to understand and apply mathematıcal techniques for solvıng problems. (PO 1) 
4
 To distinguish mathematical language to solve concrete problems. (PO 2) 
5
 To be able to write and speak about subjects. (PO 3) 
6
 The abılıty to demonstrate knowledge of basıc mathematical theorems . (PO 5) 
7
 Th be able to prove basic mathematical theorems. (PO 11) 
Weekly Detailed Course Contents
Week  Topics  Study Materials  Materials 
1 
Analytic functions. Harmonic functions.



2 
Basic principles of conformal mappings. Boundaries and symmetries.


Ivanov V, Popov V. Conformal mapping and applications

3 
Planar harmonic vector fields. Complex potential.



4 
Conformal mapping by elementary functions



5 
1st Midterm



6 
The Mobius transformation. Conformal mappings of circular domains.



7 
Vortices and sources of vector field



8 
Vortex lattices



9 
Polygons. ChristoffelSchwarz problem.



10 
2nd Midterm



11 
ChristoffelSchwarz principle



12 
Flow around cylınder



13 
Aerodynamic profiles



14 
Atlas of conformal mappings



Contribution of Learning Outcomes to Programme Outcomes
Contribution: 0: Null 1:Slight 2:Moderate 3:Significant 4:Very Significant
https://obs.iyte.edu.tr/oibs/bologna/progCourseDetails.aspx?curCourse=163245&lang=en