Analysing and synthesizing the concepts of harmonic and analytic functions in the complex plane, the complex integral calculus and conformal mapping of simply-connected domains.
Prerequisite(s)
None
Corequisite(s)
None
Special Requisite(s)
To have general knowledge about the basic topics of complex analysis.
Instructor(s)
Assist. Prof. Dr. Uğur GÖNÜLLÜ
Course Assistant(s)
None
Schedule
To be announced
Office Hour(s)
Details will be announced. Office number AK / 3-A-03/05
Teaching Methods and Techniques
Lectures, homeworks.
Principle Sources
Z. Nehari, Conformal Mapping, Dover Pub., New York, 1952.
Other Sources
R.E. Greene, S.G. Krantz, Function Theory of One Complex Variable, Third Ed., American Math. Soc. Rhode Island, 2006.
L. Ahlfors, Complex Analysis, McGraw-Hill, 3 edition, 1979.
Cengiz Ulucay, Fonksiyonlar teorisi ve Riemann yüzeyleri, T.C. Karadeniz Teknik Üniversitesi, Temel Bilimler Fakültesi Yayınları, Trabzon, 1978.
Course Schedules
Week
Contents
Learning Methods
1. Week
Harmonic Functions
Lectures
2. Week
Harmonic Functions
Lectures
3. Week
Harmonic Functions
Lectures
4. Week
Analytic Functions
Lectures
5. Week
Analytic Functions
Lectures
6. Week
Analytic Functions
Lectures
7. Week
The Complex Integral Calculus
Lectures
8. Week
The Complex Integral Calculus
Lectures
9. Week
The Complex Integral Calculus
Lectures
10. Week
Families of Analytic Functions
Lectures
11. Week
Families of Analytic Functions
Lectures
12. Week
Conformal Mapping of Simply-Connected Domains
Lectures
13. Week
Conformal Mapping of Simply-Connected Domains
Lectures
14. Week
Conformal Mapping of Simply-Connected Domains
Lectures
15. Week
Final Week
Exams
16. Week
Final Week
Exams
17. Week
Final Week
Exams
Assessments
Evaluation tools
Quantity
Weight(%)
Homework / Term Projects / Presentations
1
50
Final Exam
1
50
Program Outcomes
PO-1
Have scientific research in mathematics and computer science in the level of theoretical and practical knowledge.
PO-2
On the basis of undergraduate level qualifications, develop and deepen the same or a different areas of information at the level of expertise, and analyze and interpret by using statistical methods
PO-3
Develop new strategic approaches for the solution of complex problems encountered in applications related to the field and unforeseen and take responsibility for the solution.
PO-4
Evaluate critically skills acquired in the field of information in the level of expertise and assess the learning guides.
PO-5
Transfer current developments in the field and their work to the groups inside and outside the area supporting with quantitative and qualitative datas as written, verbal and visual by a systematic way.
PO-6
Use information and communication technologies with computer software in advanced level.
PO-7
Develop efficient algorithms by modeling problems faced in the field and solve such problems by using actual programming languages.
PO-8
Respect to social, scientific, cultural and ethical values at the stages of data collection related to the field, interpretation, and implementation.
PO-9
To solve problems related to the field, establish functional interacts by using strategic decision making processes.
PO-10
Establish and discuss in written, oral and visual communication in an advanced level by using at least one foreign language.
Learning Outcomes
LO-1
Analysing the harmonic functions in the complex plane.
LO-2
Analysing and synthesizing the theory of analytic functions.
LO-3
Analysing and applying the concept of complex integration.
LO-4
Having knowledge on families of analytic functions.
LO-5
Analysing and synthesizing the theory of conformal mapping of simply-connected domains.
