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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 be able to apply theoretical concepts related to mass communication, consumer behavior, psychology, persuasion,sociology, marketing, and other related fields to understand how advertising and brand communication works in a free-market economy.	2
2)	To be able to critically discuss and interpret theories, concepts, methods, tools and ideas in the field of advertising.	2
3)	To be able to research, create, design, write, and present an advertising campaign and brand strategies of their own creation and compete for an account as they would at an advertising agency.	2
4)	To be able to analyze primary and secondary research data for a variety of products and services.	2
5)	To be able to develop an understanding of the history of advertising as it relates to the emergence of mass media outlets and the importance of advertising in the marketplace.	2
6)	To be able to follow developments, techniques, methods, as well as research in advertising field; and to be able to communicate with international colleagues in a foreign language. (“European Language Portfolio Global Scale”, Level B1)	2
7)	To be able to take responsibility in an individual capacity or as a team in generating solutions to unexpected problems that arise during implementation process in the Advertising field.	3
8)	To be able to understand how advertising works in a global economy, taking into account cultural, societal, political, and economic differences that exist across countries and cultures.	2
9)	To be able to approach the dynamics of the field with an integrated perspective, with creative and critical thinking, develop original and creative strategies.	2
10)	To be able to to create strategic advertisements for print, broadcast, online and other media, as well as how to integrate a campaign idea across several media categories in a culturally diverse marketplace.	2
11)	To be able to use computer software required by the discipline and to possess advanced-level computing and IT skills. (“European Computer Driving Licence”, Advanced Level)	2
12)	To be able to identify and meet the demands of learning requirements.	2
13)	To be able to develop an understanding and appreciation of the core ethical principles of the advertising profession.	2