Electrical and Electronic Engineering (English) Preview
Bachelor	TR-NQF-HE: Level 6	QF-EHEA: First Cycle	EQF-LLL: Level 6

Course Introduction and Application Information

Course Code:

MATH215

Course Name:

Complex Variables

Semester:

Fall

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:

Prof. Dr. ŞÜKRÜ YALÇINKAYA

Course Lecturer(s):

Assist. Prof. Dr. Barış Efe

Course Assistants:

Course Objective and Content

Course Objectives:

To provide an introduction to the theory of functions of complex variable via teaching fundamental arithmetic with complex numbers and geometry of complex numbers, continuing with analytic functions, Cauchy-Riemann equations, Cauchy integral formula, power series representations of analytic functions and the Residue theorem, completing the course with Fourier series and transform.

Course Content:

Complex numbers, functions of a complex variable, limit, continuity, derivative, analytic functions, Cauchy-Riemann equations, harmonic functions, elementary functions of complex variables, contour integrals, Cauchy's integral theorem, sequences and series of analytic functions, Taylor series, power series, Laurent series, zeros and singularities, the point at infinity, Residue theorem, Fourier series, Fourier transform.

Learning Outcomes

The students who have succeeded in this course;
1) Perform arithmetic operations on complex numbers, given in rectangular or polar form.
2) Understand the concept of complex functions, domain and range; analyze the limit and continuity of a complex function.
3) Define analytic and harmonic functions; calculate the derivative of a complex function using Cauchy Riemann conditions and rules of taking derivative.
4) Analyze the properties of exponential, logarithmic, trigonometric and hyperbolic complex-valued functions.
5) Take simple integrals of complex functions; give an admissible parametrization of smooth curves; evaluate contour integrals and apply Cauchy's integral formula for analytic functions.
6) Gain knowledge on Taylor and Laurent series and their domain of convergence.
7) Understand and apply residue theorem; understand Fourier series and Fourier transform.

Course Flow Plan

Week	Subject	Related Preparation
1)	The algebra of complex numbers, point representation of complex numbers, vectors and polar forms
2)	The complex exponential, powers and roots, the Riemann sphere and stereographic projection
3)	Functions of a complex variable, limits and continuity, derivatives of complex variable functions, analyticity
4)	Cauchy-Riemann equations, harmonic functions
5)	Polynomials and rational functions
6)	The exponential, trigonometric, hyperbolic and logarithmic functions
7)	Contours, contour integrals, independence of path
8)	Midterm Exam
9)	Cauchy's integral theorem
10)	Sequences and series of analytic functions, Taylor series
11)	Power series, Laurent series
12)	Zeros and singularities, the point at infinity
13)	Residue Theorem
14)	Fourier series, Fourier transform

Sources

Course Notes / Textbooks:	Fundamentals of Complex Analysis Engineering, Science, and Mathematics, Edward B. Saff Arthur David Snider, 3rd Edition.
References:	Mathematical Methods in Electrical Engineering, Thomas B. A. Senior, Cambridge University Press.

Course - Program Learning Outcome Relationship

Course Learning Outcomes	1	2	3	4	5	6	7
Program Outcomes
1) Has sufficient knowledge in mathematics and natural sciences.	3	3	3	3	3	3	3
2) Has sufficient knowledge in Electrical and Electronics engineering–specific subjects.
3) Has the ability to apply theoretical and practical knowledge of mathematics, natural sciences, and Electrical and Electronics engineering to solve complex engineering problems.
4) Has the ability to identify, formulate, and solve complex engineering problems, and to select and apply appropriate analysis and modeling methods for this purpose.
5) Has the ability to design complex systems, processes, devices, or products under realistic constraints and conditions to meet specific requirements, and to apply modern design methods for this purpose.
6) Has the ability to select and use modern techniques and tools required for the analysis and solution of complex engineering problems encountered in engineering practice, and to use information technologies effectively.
7) Has the ability to design and conduct experiments, collect data, analyze and interpret results for the investigation of complex engineering problems or Electrical and Electronics engineering–specific research topics.
8) Has the ability to work effectively in disciplinary teams.
9) Has the ability to work effectively in multidisciplinary teams.
10) Has the ability to work individually.
11) Has the ability to communicate effectively in oral and written form; has knowledge of at least one foreign language; writes effective reports, understands written reports, prepares design and production reports, makes effective presentations, and gives and receives clear and understandable instructions.
12) Has awareness of the necessity for lifelong learning; accesses information, follows developments in science and technology, and continuously renews oneself.
13) Acts in accordance with ethical principles; has knowledge of professional and ethical responsibilities and of the standards used in engineering practices.
14) Has knowledge of business practices such as project management, risk management, and change management.
15) Has awareness of entrepreneurship and innovation.
16) Has knowledge of sustainable development.
17) Has knowledge of the impacts of engineering practices on health, environment, and safety on a universal and societal scale, and awareness of contemporary issues reflected in the field of engineering.
18) Has awareness of the legal consequences of engineering solutions.

Course - Learning Outcome Relationship

No Effect	1 Lowest	2 Average	3 Highest

	Program Outcomes	Level of Contribution
1)	Has sufficient knowledge in mathematics and natural sciences.	3
2)	Has sufficient knowledge in Electrical and Electronics engineering–specific subjects.
3)	Has the ability to apply theoretical and practical knowledge of mathematics, natural sciences, and Electrical and Electronics engineering to solve complex engineering problems.
4)	Has the ability to identify, formulate, and solve complex engineering problems, and to select and apply appropriate analysis and modeling methods for this purpose.
5)	Has the ability to design complex systems, processes, devices, or products under realistic constraints and conditions to meet specific requirements, and to apply modern design methods for this purpose.
6)	Has the ability to select and use modern techniques and tools required for the analysis and solution of complex engineering problems encountered in engineering practice, and to use information technologies effectively.
7)	Has the ability to design and conduct experiments, collect data, analyze and interpret results for the investigation of complex engineering problems or Electrical and Electronics engineering–specific research topics.
8)	Has the ability to work effectively in disciplinary teams.
9)	Has the ability to work effectively in multidisciplinary teams.
10)	Has the ability to work individually.
11)	Has the ability to communicate effectively in oral and written form; has knowledge of at least one foreign language; writes effective reports, understands written reports, prepares design and production reports, makes effective presentations, and gives and receives clear and understandable instructions.
12)	Has awareness of the necessity for lifelong learning; accesses information, follows developments in science and technology, and continuously renews oneself.
13)	Acts in accordance with ethical principles; has knowledge of professional and ethical responsibilities and of the standards used in engineering practices.
14)	Has knowledge of business practices such as project management, risk management, and change management.
15)	Has awareness of entrepreneurship and innovation.
16)	Has knowledge of sustainable development.
17)	Has knowledge of the impacts of engineering practices on health, environment, and safety on a universal and societal scale, and awareness of contemporary issues reflected in the field of engineering.
18)	Has awareness of the legal consequences of engineering solutions.

Assessment & Grading

Semester Requirements	Number of Activities	Level of Contribution
Quizzes	4	% 20
Midterms	1	% 30
Final	1	% 50
total		% 100
PERCENTAGE OF SEMESTER WORK		% 50
PERCENTAGE OF FINAL WORK		% 50
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	3		39
Study Hours Out of Class	13	0	4		52
Quizzes	4	2	1		12
Midterms	1	13	2		15
Final	1	18	2		20
Total Workload					138