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
170300401503	COMPLEX FUNCTIONS THEORY I	Compulsory	3	5	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 Numbers Week 2 Fundamental Concepts and Results in Complex Plane Week 3 Connected Sets and Domains Week 4 Analitic Geometry in Complex Plane Week 5 Extended Complex Plane Week 6 Definition of Complex Functions Week 7 Definitions of Basic Complex Functions and Their Properties Week 8 Sequence of Complex Numbers and Convergence Week 9 Mid-term exam Week 10 Series of Complex Numbers and Convergence, Power Series and Convergence Week 11 Limit of Complex Functions and Continuity Week 12 Differentiablity and Analitcity, Conform Transformations Week 13 Integration on Curves Week 14 Cauchy Theorems and Applications Week 15 Residual Theorems and Applications Week 16 End-of-term exam

Weekly Detailed Course Contents

Week	Theoretical	Practice	Laboratory
1	Complex Numbers
2	Important Concepts and Results at the Complex Plane
3	Connected Sets and Domains
4	Analitic Geometry in Complex Plane
5	Extended Complex Plane
6	Definition of Complex Functions
7	Definitions of Basic Complex Functions and Their Properties
8	Sequence of Complex Numbers and Convergence
9	Mid-term exam
10	Series of Complex Numbers and Convergence, Power Series and Convergence
11	Limit of Complex Functions and Continuity
12	Differentiablity a
13	Cauchy-Riemann equations
14	Calculating Harmonic Functions and Harmonic Conjugates

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