Ordu University Lifelong Learning Programme

Description of Individual Course Units

Course Unit Code	Course Unit Title	Type of Course Unit	Year of Study	Semester	Number of ECTS Credits
MAT30820121310	THEORY OF COMPLEX FUNCTIONS- II	Compulsory	3	6	5

Level of Course Unit

First Cycle

Objectives of the Course

To teach the basic concepts of complex analysis.

Name of Lecturer(s)

DOÇ.DR. ERHAN SET

Learning Outcomes

1	Students who successfully complete this course : will develop the right thinking and the ability to comment and students will gain basic knowledge about mathematics.

Mode of Delivery

Formal Education

Prerequisites and co-requisities

None

Recommended Optional Programme Components

None

Course Contents

Integral representations for analytic functions and applications. Sequences and series, power series, uniform convergence, Taylor series representations, representations of Laurent series, singularities, zeros and poles. Residue theorem, calculation of residues, trigonometric integrals, generalized integrals of rational functions, generalized integrals containing trigonometric functions, integrals involving multi-valued functions, the argument principle and Rouche's theorem.

Weekly Detailed Course Contents

Week	Theoretical	Practice	Laboratory
1	Integral representations for analytic functions and applications
2	Sequences and series
3	Power series
4	Uniform convergence
5	Taylor series representations, representations of Laurent series
6	Singularities, zeros and poles
7	Residue theorem, calculation of residues
8	Midterm exam
9	Trigonometric integrals
10	Generalized integrals of rational functions
11	Generalized integrals containing trigonometric functions
12	Integrals involving multi-valued functions
13	The argument principle and Rouche's theorem
14	Simply connected region. Cauchy's Inequality
15	Liouville's Theorem, the Fundamental Theorem of Algebra. Morera's Theorem
16	Final exam

Recommended or Required Reading

Turgut Başkan, Kompleks fonksiyonlar Teorisi, Uludağ Üniversitesi Yayınları 2000. R.V. Churchill, Complex Variable and Applications, McGraw-Hill , Inc. Ali Dönmez, Karmaşık Fonksiyonlar Kuramı, Dicle Üni., 1985 Marsden, J.E., Basic Complex Analysis, W.H.F. and Conpany, 1973.

Planned Learning Activities and Teaching Methods

Assessment Methods and Criteria

Term (or Year) Learning Activities	Quantity	Weight
SUM		0
End Of Term (or Year) Learning Activities	Quantity	Weight
SUM		0
Yarıyıl (Yıl) İçi Etkinlikleri		40
Yarıyıl (Yıl) Sonu Etkinlikleri		60
SUM		100

Language of Instruction

Work Placement(s)

None

Workload Calculation

Activities	Number	Time (hours)	Total Work Load (hours)
Midterm Examination	1	2	2
Final Examination	1	2	2
Attending Lectures	14	4	56
Self Study	14	4	56
Individual Study for Mid term Examination	2	8	16
Individual Study for Final Examination	2	9	18
TOTAL WORKLOAD (hours)			150

Contribution of Learning Outcomes to Programme Outcomes

	PO 1	PO 2	PO 3	PO 4	PO 5	PO 6	PO 7
LO1	4	3	4	5	5	5	4

* Contribution Level : 1 Very low 2 Low 3 Medium 4 High 5 Very High