Mathematics (English) Preview
Bachelor	TR-NQF-HE: Level 6	QF-EHEA: First Cycle	EQF-LLL: Level 6

Course Introduction and Application Information

Course Code:

MATH352

Course Name:

Complex Analysis

Semester:

Spring

Course Credits:

ECTS

Language of instruction:

English

Course Condition:

Does the Course Require Work Experience?:

Type of course:

Compulsory Courses

Course Level:

Bachelor

TR-NQF-HE:6. Master`s Degree

QF-EHEA:First Cycle

EQF-LLL:6. Master`s Degree

Mode of Delivery:

Face to face

Course Coordinator:

Araş. Gör. GAMZE AKAR UYSAL

Course Lecturer(s):

Prof. Dr. Selçuk Demir

Course Assistants:

Course Objective and Content

Course Objectives:	The course aims to introduce the principal concepts and methods of the theory of functıons of one complex varıable.
Course Content:	The content of the course consists of continuity, differentiation and integration of functions of one complex variable and the most significant results of these.

Learning Outcomes

The students who have succeeded in this course;
1) will be able to apply the algebraic and geometric properties of complex numbers
2) will be able to describe and use an analytic function and the elementary functions
3) will be able to apply the Cauchy-Goursat Theorem and Cauchy's Integral Formula
4) will be able to find Taylor or Laurent expansions and analytic continuation of a function
5) will be able to apply residue theorem.

Course Flow Plan

Week	Subject	Related Preparation
1)	Algebraic and geometric meaning of complex numbers, regions in complex plane
2)	Functions of a complex variable, graphs of mappings, limits, continuity
3)	"Derivatives of functions of a complex variable, the Cauchy-Riemann equations, analytic functions, harmonic functions"
4)	Elementary functions, exponential function, the logarithmic function and its branches
5)	Trigonometric, hyperbolic and inverse trigonometric, inverse hyperbolic functions
6)	Smooth paths, contour integrals, antiderivatives, the Cauchy-Goursat Theorem
7)	Cauchy's Integral Formula
8)	Midterm Exam
9)	Liouville's Theorem and maximum moduli of functions
10)	Series of numbers, power series
11)	Taylor series, Laurent series
12)	Absolute and uniform convergence of power series, integration and differentiation of power series. The uniqueness of Taylor and Laurent series represantations, analytic continuation
13)	The Residue Theorem, isolated singular points, zeros and poles of order m
14)	Applications of residues

Sources

Course Notes / Textbooks:	Mathews, J. H., Howell, R. W., Complex Analysis for Mathematics and Engineering, Jons and Barlett Publishers, 2006
References:	Bak, J., Newman, D. J., Complex Analysis, Springer, 2010

Course - Program Learning Outcome Relationship

Course Learning Outcomes	1	2	3	4	5
Program Outcomes
1) Have the knowledge of the scope, history, applications, problems, methods of mathematics and knowledge that will be beneficial to humanity as both scientific and intellectual discipline.
2) Have the ability to establish a relationship between mathematics and other disciplines and develop mathematical models for interdisciplinary problems.
3) Have the ability to define, formulate and analyze real life problems with statistical and mathematical techniques.
4) Have the ability to think analytically and use the time effectively in the process of deduction.
5) Have the ability to search the literature, understand and interpret scientific articles.
6) Have the knowledge of basic software to be able to work in the related fields of computer science and have the ability to use information technologies at an advanced level of the European Computer Driving License.
7) Have the ability to work efficiently in interdisciplinary teams.
8) Have the ability to communicate effectively in oral and written form, write effective reports and comprehend the written reports, make effective presentations.
9) Have the consciousness of professional and ethical responsibility and acting ethically; have the knowledge about academic standards.
10) Have the ability to use a foreign language at least at B1 level in terms of European Language Portfolio criteria.
11) Are aware of the necessity of lifelong learning; have the ability to access information, to follow developments in science and technology and to constantly renew themselves.

Course - Learning Outcome Relationship

No Effect	1 Lowest	2 Average	3 Highest

	Program Outcomes	Level of Contribution
1)	Have the knowledge of the scope, history, applications, problems, methods of mathematics and knowledge that will be beneficial to humanity as both scientific and intellectual discipline.	2
2)	Have the ability to establish a relationship between mathematics and other disciplines and develop mathematical models for interdisciplinary problems.
3)	Have the ability to define, formulate and analyze real life problems with statistical and mathematical techniques.
4)	Have the ability to think analytically and use the time effectively in the process of deduction.	3
5)	Have the ability to search the literature, understand and interpret scientific articles.
6)	Have the knowledge of basic software to be able to work in the related fields of computer science and have the ability to use information technologies at an advanced level of the European Computer Driving License.
7)	Have the ability to work efficiently in interdisciplinary teams.
8)	Have the ability to communicate effectively in oral and written form, write effective reports and comprehend the written reports, make effective presentations.
9)	Have the consciousness of professional and ethical responsibility and acting ethically; have the knowledge about academic standards.
10)	Have the ability to use a foreign language at least at B1 level in terms of European Language Portfolio criteria.	3
11)	Are aware of the necessity of lifelong learning; have the ability to access information, to follow developments in science and technology and to constantly renew themselves.	3

Assessment & Grading

Semester Requirements	Number of Activities	Level of Contribution
Midterms	1	% 40
Final	1	% 60
total		% 100
PERCENTAGE OF SEMESTER WORK		% 40
PERCENTAGE OF FINAL WORK		% 60
total		% 100

Workload and ECTS Credit Calculation

Activities	Number of Activities	Preparation for the Activity	Spent for the Activity Itself	Completing the Activity Requirements	Workload
Course Hours	13	0	4		52
Application	13	0			0
Study Hours Out of Class	13	0	4		52
Midterms	1	0	15		15
Final	1	0	25		25
Total Workload					144