Iğdır 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
170300401603	COMPLEX FUNCTIONS THEORY II	Compulsory	3	6	5

Level of Course Unit

First Cycle

Objectives of the Course

To define the field of complex numbers, to introduce complex valued functions of one complex variable; to reintroduce limit; continuity and differentiability for real valued functions of two real variables and to define these for complex valued functions and illustrate the applications of these concepts in the theory of real valued functions of two real variables; to show that many ideas of reel analysis, such as convergence of series, have their most natural setting in the complex analysis and to emphasize difference; contour integration; Cauchy's Theorems; Taylor and Laurent series; ResidueTheorem and Its applications.

Name of Lecturer(s)

Dr. Öğretim Üyesi Hasan KARA

Learning Outcomes

1	make simple arguments concerning limits of real and complex valued functions; show continuity and differentiability in real and complex valued functions; and make simple uses of these
2	calculate contour integrals,Taylor and Laurent expansions and use the calculus of residues to evaluate integrals.

Mode of Delivery

Daytime Class

Prerequisites and co-requisities

none

Recommended Optional Programme Components

none

Course Contents

Week 1 Complex Integrals Week 2 Cauch's Integral Theorems and Results Week 3 Representation of Analytical Functions by Series Week 4 Expansion of Complex Functions to Power Series Week 5 Question Solution Week 6 Classification of Singular Points Week 7 Calculation of Remains Week 8 Calculation of Remains Week 9 Midterm Week 10 Calculation of Certain Real Integrals Week 11 Limits and Continuity of Complex Functions Week 12 Calculation of Trigonometric Integrals Week 13 Improper Integrals and Cauchy Principal Values Week 14 Conformity Transformations

Weekly Detailed Course Contents

Week	Theoretical	Practice	Laboratory
1	Complex Integrals
2	Cauch's Integral Theorems and Results
3	Representation of Analytical Functions by Series
4	Expansion of Complex Functions to Power Series
5	Question Solution
6	Classification of Singular Points
7	Calculation of Remains
8	Calculation of Remains
9	Mid-term exam
10	Calculation of Certain Real Integrals
11	Limits and Continuity of Complex Functions
12	Calculation of Trigonometric Integrals
13	Improper Integrals and Cauchy Principal Values
14	Conformity Transformations

Recommended or Required Reading

Planned Learning Activities and Teaching Methods

Assessment Methods and Criteria

Term (or Year) Learning Activities	Quantity	Weight
Midterm Examination	1	100
SUM		100
End Of Term (or Year) Learning Activities	Quantity	Weight
Final Examination	1	100
SUM		100
Term (or Year) Learning Activities		40
End Of Term (or Year) Learning Activities		60
SUM		100

Language of Instruction

Work Placement(s)

none

Workload Calculation

Activities	Number	Time (hours)	Total Work Load (hours)
Midterm Examination	1	1	1
Final Examination	1	1	1
Self Study	14	3	42
Individual Study for Mid term Examination	14	3	42
Individual Study for Final Examination	14	5	70
TOTAL WORKLOAD (hours)			156

Contribution of Learning Outcomes to Programme Outcomes

	PO 1	PO 2	PO 3	PO 4	PO 5	PO 6	PO 7	PO 8	PO 9	PO 10
LO1	5	4	1	2	4	4	3
LO2	5	5	3	4	4	3	4

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