LAW
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)	List the relations between concepts and institutions related to various legal disciplines and this concepts and institutions.
2)	Have the knowledge of legal methodology and methods of comment.
3)	Comment the modern legal gains with the historical knowledge.
4)	Have the knowledge of philosophical currents of thought which are the bases of legal rules.
5)	Have the knowledge of legal regulations, judicial decisions and the scientific evaluations related to them.
6)	Resolve the juridical disagreements in light of legal acts, juridical decisions and doctrine.
7)	Use at least one foreign language as scientific language.
8)	Have the knowledge of the political and juridical foundation of the state.
9)	Have the knowledge of the historical development of the rights of individuals and societies and of the basic documents which are accepted throughout this development.
10)	Have the ability to resolve the disagreements which can violate the social order in national or international level.
11)	Have the ability to prevent the juridical disagreements between individuals.
12)	Have the knowledge of international and comparative law systems.
13)	Have the knowledge of the construction and the conduct of the national and international commercial relations.
14)	Use Turkish in an efficient way both verbal and written.
15)	Have the professional and ethical responsibility.
16)	Have the knowledge on the European Union’s legislation and institutions.
17)	Have the knowledge on juridical regulations and applications related to economical and financial mechanisms.
18)	Have the knowledge of the operation of the national and the international judicial bodies.