SOCIOLOGY
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	Fall	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 learn and compare major sociology perspectives, both classical and contemporary, and apply all of them to analysis of social conditions.
2)	To be able to identify the basic methodological approaches in building sociological and anthropological knowledge at local and global levels
3)	To be able to use theoretical and applied knowledge acquired in the fields of statistics in social sciences.
4)	To have a basic knowledge of other disciplines (including psychology, history, political science, communication studies and literature) that can contribute to sociology and to be able to make use of this knowledge in analyzing sociological processes
5)	To have a knowledge and practice of scientific and ethical principles in collecting, interpreting and publishing sociological data also develop ability how to share this data with experts and lay people, using effective communication skills
6)	To develop competence in analyzing and publishing sociological knowledge by using computer software for quantitative and qualitative analysis; and develop an attitute for learning new techniques in these fields.
7)	To identify and to have a knowledge of the theories related to urban and rural sociology and demography, and political sociology, sociology of gender, sociology of body, visual sociology, sociology of work, sociology of religion, sociology of knowledge and sociology of crime.
8)	To have knowledge of how sociology is positioned as a scientific discipline from a philosophical and historical perspective
9)	To have the awareness of social issues in Turkish society, to develop critical perspective in analysing these issues and to have a knowledge of the works of Turkish sociologists and to be able to transfer this knowledge
10)	To have the awareness of social issues and global societal processes and to apply sociological analysis to development and social responsibility projects
11)	To have the ability to define a research question, design a research project and complete a written report for various fields of sociology, either as an individual or as a team member.
12)	To be able to transfer the knowledge gained in the areas of sociology to the level of secondary school.