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Bachelor	TR-NQF-HE: Level 6	QF-EHEA: First Cycle	EQF-LLL: Level 6

Course Introduction and Application Information

Course Code	Course Name	Semester	Theoretical	Practical	Credit	ECTS
MAT4051	Advanced Complex Analysis	Spring	3	0	3	6

This catalog is for information purposes. Course status is determined by the relevant department at the beginning of semester.

Basic information

Language of instruction:	English
Type of course:	Non-Departmental Elective
Course Level:	Bachelor’s Degree (First Cycle)
Mode of Delivery:	Face to face
Course Coordinator :
Recommended Optional Program Components:	There is none.
Course Objectives:	To study advanced studies and applications in the theory of functions of a complex variable.

Learning Outcomes

The students who have succeeded in this course;
Grap residue theorem and its applications in evaluation of reel integrals

Explain general principles of theory of conformal mappings.

Grab Laplace and Fourier Transforms.

Course Content

Concept of Residue, Residue Theorem.
Applications of Residue Theorem to Real Integrals.
Argument Principle, Rouche and Hurwitz Theorems.
Infınıte Products, Weierstrass Formula.
Representation Entire and Meromorphic Functions as an Infınıte Product, Mittag-Leffler Formula.
Concept of Analytic Continuity, Analytic Continuity of an Analytic Function.
Weierstrass Method of Analytic Continuity.
General Principle of Conformal Mappings.
Riemann Mapping Theorem.
Riemann-Schwarz Symmetry Principle, Christoffel-Schwarz Formula.
Functions Denoted by Cauchy Kernel.
Regularity of an Integral Depending on a Parameter.
Laplace Transform.
Fourier Transform.

Weekly Detailed Course Contents

Week	Subject	Related Preparation
1)	Concept of Residue, Residue Theorem.
2)	Applications of Residue Theorem to Real Integrals.
3)	Argument Principle, Rouche and Hurwitz Theorems.
4)	Infınıte Products, Weierstrass Formula.
5)	Representation Entire and Meromorphic Functions as an Infınıte Product, Mittag-Leffler Formula.
6)	Concept of Analytic Continuity, Analytic Continuity of an Analytic Function.
7)	Weierstrass Method of Analytic Continuity.
8)	General Principle of Conformal Mappings.
9)	Riemann Mapping Theorem.
10)	Riemann-Schwarz Symmetry Principle, Christoffel-Schwarz Formula.
11)	Functions Denoted by Cauchy Kernel.
12)	Regularity of an Integral Depending on a Parameter.
13)	Laplace Transform.
14)	Fourier Transform.

Sources

Course Notes / Textbooks:	A.I. Markushevich “Theory of Functions of a Complex Variable” Ruel V. Churchill, James Ward Brown, “Complex variables and applications”
References:	.

Evaluation System

Semester Requirements	Number of Activities	Level of Contribution
Attendance	16	% 0
Homework Assignments	7	% 10
Midterms	2	% 50
Final	1	% 40
Total		% 100
PERCENTAGE OF SEMESTER WORK		% 60
PERCENTAGE OF FINAL WORK		% 40
Total		% 100

ECTS / Workload Table

Activities	Number of Activities	Duration (Hours)	Workload
Course Hours	14	3	42
Study Hours Out of Class	14	2	28
Homework Assignments	7	2	14
Midterms	2	10	20
Final	1	21	21
Total Workload			125

Contribution of Learning Outcomes to Programme Outcomes

No Effect	1 Lowest	2 Low	3 Average	4 High	5 Highest

	Program Outcomes	Level of Contribution
1)	To prepare students to become communication professionals by focusing on strategic thinking, professional writing, ethical practices, and the innovative use of both traditional and new media	2
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8)	To analyze and develop solutions to problems encountered in the practical field of advertising