PERFORMING ARTS
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 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)	They acquire theoretical, historical and aesthetic knowledge specific to their field by using methods and techniques related to performing arts (acting, dance, music, etc.).	2
2)	They have knowledge about art culture and aesthetics and they provide the unity of theory and practice in their field.	2
3)	They are aware of national and international values in performing arts.	2
4)	Abstract and concrete concepts of performing arts; can transform it into creative thinking, innovative and original works.	1
5)	They have the sensitivity to run a business successfully in their field.	3
6)	Develops the ability to perceive, think, design and implement multidimensional from local to universal.	3
7)	They have knowledge about the disciplines that the performing arts field is related to and can evaluate the interaction of the sub-disciplines within their field.	2
8)	They develop the ability to perceive, design, and apply multidimensionality by having knowledge about artistic criticism methods.	3
9)	They can share original works related to their field with the society and evaluate their results and question their own work by using critical methods.	1
10)	They follow English language resources related to their field and can communicate with foreign colleagues in their field.	1
11)	By becoming aware of national and international values in the field of performing arts, they can transform abstract and concrete concepts into creative thinking, innovative and original works.	3
12)	They can produce original works within the framework of an interdisciplinary understanding of art.	2
13)	Within the framework of the Performing Arts Program and the units within it, they become individuals who are equipped to take part in the universal platform in their field.	3
14)	Within the Performing Arts Program, according to the field of study; have competent technical knowledge in the field of acting and musical theater.	2
15)	They use information and communication technologies together with computer software that is at least at the Advanced Level of the European Computer Use License as required by the field.	3