Course Information

Course Title	Code	Semester	L+U Hour	Credits	ECTS
THEORY OF FUNCTIONS	801500715610		3 + 0	3.0	8.0

Prerequisites

None

Language of Instruction	Turkish
Course Level	Graduate Degree
Course Type	Compulsory
Mode of delivery
Course Coordinator
Instructors	Ayhan ŞERBETÇİ
Assistants
Goals	Complex numbers, power series, analytic functions, harmonic functions, Cauchy's theorem and the results, singularities and residues, the argument principle, the maximum module principle, Schwarz's lemma .
Course Content	Complex numbers, power series, analytic functions, harmonic functions, Cauchy's theorem and the results, singularities and residues, the argument principle, the maximum module principle, Schwarz's lemma .
Learning Outcomes	1) Knows the basic properties of complex numbers. 2) Knows the basic properties of power series and establishes the relationship with analytic functions. 3) Explain the results of the Cauchy theorem. 4) Knows singularities and residues and makes applications. 5) Knows the principle of argumentation and maximum module.

Week	Topics	Teaching and Learning Methods and Techniques	Study Materials
1. Week	Complex numbers	Lecture	Presentation (Including Preparation Time)
2. Week	Complex numbers	Lecture	Presentation (Including Preparation Time)
3. Week	Power series	Lecture	Presentation (Including Preparation Time)
4. Week	Power series	Lecture	Presentation (Including Preparation Time)
5. Week	Analytic functions	Lecture	Presentation (Including Preparation Time)
6. Week	Analytic functions	Lecture	Presentation (Including Preparation Time)
7. Week	Harmonic functions	Lecture	Presentation (Including Preparation Time)
8. Week	Cauchy theorem and its consequences	Lecture	Presentation (Including Preparation Time)
9. Week	Cauchy theorem and its consequences	Lecture	Presentation (Including Preparation Time)
10. Week	Singularities and residues	Lecture	Presentation (Including Preparation Time)
11. Week	Singularities and residues	Lecture	Presentation (Including Preparation Time)
12. Week	Argüment Principle	Lecture	Presentation (Including Preparation Time)
13. Week	Maksimum modulu Principle	Lecture	Presentation (Including Preparation Time)
14. Week	Schwarz lemma	Lecture	Presentation (Including Preparation Time)

Recommended Sources

Churchill, R.V. and Brown, J.W. (2008), Complex variables and applications, 8. edition. McGraw-Hill Book Co., New York.

Hahn L, and Epstein B., (1996), Classical Complex Analysis, Jones and Bartlett Publishers.

Mathews, J.H., Howell, R.W. (2001), Compleks Analysis, Jones And Bartlett Publishers, Boston.

Saff, E.B. and Snider, A.D. (2000), Fundamentals of Complex Analysis with Applications, Prentice Hall, NJ.

*DK = Course's Contrubution.

	0	1	2	3	4	5
Level of contribution	None	Very Low	Low	Fair	High	Very High

Event	Quantity	Duration (Hour)	Total Workload (Hour)
Course Duration (Total weeks*Hours per week)	14	3	42
Work Hour outside Classroom (Preparation, strengthening)	14	6	84
Homework	3	15	45
Presentation (Including Preparation Time)	1	21	21
Midterm Exam	1	1.5	1.5
Final Exam	1	2	2
Time to prepare for Final Exam	1	45	45
Total Workload
Total Workload / 30 (s)
ECTS Credit of the Course			30