Course Information
SemesterCourse Unit CodeCourse Unit TitleL+PCreditNumber of ECTS Credits
7MATH407CONFORMAL MAPPINGS3+036

Course Details
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. Christofel-Schwarz conformal mappings. Conformal metric and geometry. Boundary value problems. Electrostatics and hydrodynamics.
Course Methods and Techniques
Prerequisites and co-requisities 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

Course Category

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
In-Term Studies Quantity Percentage
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 Quantity Duration 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:
NoLearning 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
WeekTopicsStudy MaterialsMaterials
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. Christoffel-Schwarz problem.
10 2nd Midterm
11 Christoffel-Schwarz principle
12 Flow around cylınder
13 Aerodynamic profiles
14 Atlas of conformal mappings


Contribution of Learning Outcomes to Programme Outcomes
P1 P2 P3 P4 P5 P6 P7 P8 P9 P10 P11 P12 P13 P14
All 4 4 3 4 3 3 3 2 3 3 4
C1 4 4 3 4 3 3 3 2 3 3 4
C2 4 4 3 4 3 3 3 2 3 3 4
C3 4 4 3 4 3 3 3 2 3 3 4
C4 4 4 3 4 3 3 3 2 3 3 4
C5 4 4 3 4 3 3 3 2 3 3 4
C6 4 4 3 4 3 3 3 2 3 3 4
C7 4 4 3 4 3 3 3 2 3 3 4

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