SOFTWARE ENGINEERING
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)	Be able to specify functional and non-functional attributes of software projects, processes and products.
2)	Be able to design software architecture, components, interfaces and subcomponents of a system for complex engineering problems.
3)	Be able to develop a complex software system with in terms of code development, verification, testing and debugging.
4)	Be able to verify software by testing its program behavior through expected results for a complex engineering problem.
5)	Be able to maintain a complex software system due to working environment changes, new user demands and software errors that occur during operation.
6)	Be able to monitor and control changes in the complex software system, to integrate the software with other systems, and to plan and manage new releases systematically.
7)	Be able to identify, evaluate, measure, manage and apply complex software system life cycle processes in software development by working within and interdisciplinary teams.
8)	Be able to use various tools and methods to collect software requirements, design, develop, test and maintain software under realistic constraints and conditions in complex engineering problems.
9)	Be able to define basic quality metrics, apply software life cycle processes, measure software quality, identify quality model characteristics, apply standards and be able to use them to analyze, design, develop, verify and test complex software system.
10)	Be able to gain technical information about other disciplines such as sustainable development that have common boundaries with software engineering such as mathematics, science, computer engineering, industrial engineering, systems engineering, economics, management and be able to create innovative ideas in entrepreneurship activities.
11)	Be able to grasp software engineering culture and concept of ethics and have the basic information of applying them in the software engineering and learn and successfully apply necessary technical skills through professional life.
12)	Be able to write active reports using foreign languages and Turkish, understand written reports, prepare design and production reports, make effective presentations, give clear and understandable instructions.
13)	Be able to have knowledge about the effects of engineering applications on health, environment and security in universal and societal dimensions and the problems of engineering in the era and the legal consequences of engineering solutions.