MATHEMATİCS III PROGRAMME COURSE DESCRIPTION

Code	Name of the Course Unit	Semester	In-Class Hours (T+P)	Credit	ECTS Credit
MAT209	MATHEMATİCS III	3	3	3	5

GENERAL INFORMATION
Language of Instruction :	Turkish
Level of the Course Unit :	BACHELOR'S DEGREE, TYY: + 6.Level, EQF-LLL: 6.Level, QF-EHEA: First Cycle
Type of the Course :	Compulsory
Mode of Delivery of the Course Unit	-
Coordinator of the Course Unit	Assist.Prof. PERİ GÜNEŞ
Instructor(s) of the Course Unit	Assist.Prof. TARIK ARABACI
Course Prerequisite	No

OBJECTIVES AND CONTENTS
Objectives of the Course Unit:	Complex analysis is the study of functions of a complex variable, in particular “analytic” or complex differentiable functions. This course develops some of the rich theory of complexanalytic functions of one variable, beginning with the basic arithmetic and geometry of complex numbers and proceeding to the CauchyRiemann equations and Cauchy’s integral formula. It continues with power series representation of analytic functions, the basic theory of residues, and possible further topics.
Contents of the Course Unit:	In this course basic concepts of complex numbers will be discussed. Elementary functions; Derivative and CauchyRiemann equations; Cauchy’s integral theorem; Morera’s theorem; Zeroes of analytic functions; Maximum and minimum principle; Fundamental theorem of algebra; Laurent series; Classification of singular isolated points; residue theorem.

KEY LEARNING OUTCOMES OF THE COURSE UNIT (On successful completion of this course unit, students/learners will or will be able to)
The students will be able to use Derivative and Cauchy Riemann equations.
The students will be able to apply the Line integrals and the Cauchy’s integral theorem.
The students will be able to calculate Cauchy’s integral formula for analytic functions.
The students will be able to use Laurent series.
The students will be able to calculate integrals with the residue theorem.
The students will be able to apply Rouché’s theorem.

WEEKLY COURSE CONTENTS AND STUDY MATERIALS FOR PRELIMINARY & FURTHER STUDY
Week	Preparatory	Topics(Subjects)	Method
1	-	Revisions on complex numbers.	-
2	-	Elementary functions sin z, cos z, sinh z, cosh z, exp(z).	-
3	-	Derivative of complex-valued functions. Cauchy-Riemann equalities.	-
4	-	Line integrals. Primitive function.	-
5	-	Cauchy’s integral theorem, Morera’s theorem.	-
6	-	Taylor series	-
7	-	Complex analysis	-
8	-	MID-TERM EXAM	-
9	-	Complex analysis	-
10	-	Zeros of analytic functions. Laurent Series.	-
11	-	Discrete math	-
12	-	Discrete math	-
13	-	Theory of Residues.	-
14	-	Computation of integrals with Residue Theorem.	-
15	-	Rouché’s theorem.	-
16	-	FINAL EXAM	-
17	-	FINAL EXAM	-

SOURCE MATERIALS & RECOMMENDED READING

ASSESSMENT
Assessment & Grading of In-Term Activities	Number of Activities	Degree of Contribution (%)	Description

Level of Contribution
0	1	2	3	4	5

KNOWLEDGE
Theoretical
	Programme Learning Outcomes	Level of Contribution
		0	1	2	3	4	5
1	Explains the fundamental engineering concepts of electrical and electronics science and relates them to the groundwork of electrical and electronics science.

KNOWLEDGE
Factual
	Programme Learning Outcomes	Level of Contribution
		0	1	2	3	4	5
1	Uses theoretical and practical knowledge coming from electrical and electronics sciences, to find solutions to engineering problems.

SKILLS
Cognitive
	Programme Learning Outcomes	Level of Contribution
		0	1	2	3	4	5
1	Determines the components and the underlying process of a system and designs an appropriate model related to electrical and electronics under reasonable constraints.
2	Designs a model related to electrical and electronics with modern techniques.

SKILLS
Practical
	Programme Learning Outcomes	Level of Contribution
		0	1	2	3	4	5
1	Determines, detects and analyzes the areas of electrical and electronics engineering science applications and develops appropriate solutions.
2	Identifies, models and solveselectrical and electronics engineering problems by applying appropriate analytical methods.
3	Determines and uses the necessary electrical and electronics engineering technologies in an efficient way for engineering applications.

OCCUPATIONAL
Autonomy & Responsibility
	Programme Learning Outcomes	Level of Contribution
		0	1	2	3	4	5
1	Possess the responsibility and ability to design and conduct experiments for engineering problems by collecting, analyzing and interpreting data.
2	Possess the ability to conduct effective individual study.
3	Takes responsibility as a team work and contributes in an effective way.

OCCUPATIONAL
Learning to Learn
	Programme Learning Outcomes	Level of Contribution
		0	1	2	3	4	5
1	Monitors the developments in the field of electrical and electronics engineering technologies by means of books, internet and related journals and possess the required knowledge for the management, control, development and security of information technologies.
2	Develops positive attitude towards lifelong learning.

OCCUPATIONAL
Communication & Social
	Programme Learning Outcomes	Level of Contribution
		0	1	2	3	4	5
1	Communicates effectively by oral and/or written form and uses at least one foreign language.
2	Possess sufficient consciousness about the issues of project management, practical applications and also environmental protection, worker's health and security.

OCCUPATIONAL
Occupational and/or Vocational
	Programme Learning Outcomes	Level of Contribution
		0	1	2	3	4	5
1	Possess professional and ethical responsibility and willingness to share it.
2	Possess sufficient consciousness about the universality of electrical and electronics engineering solutions and applications and be well aware of the importance of innovation.

WORKLOAD & ECTS CREDITS OF THE COURSE UNIT
Workload for Learning & Teaching Activities
Type of the Learning Activites	Learning Activities (# of week)	Duration (hours, h)	Workload (h)
Lecture & In-Class Activities	14	3	42
Preliminary & Further Study	14	3	42
Land Surveying	0	0	0
Group Work	0	0	0
Laboratory	0	0	0
Reading	1	2	2
Assignment (Homework)	8	5	40
Project Work	0	0	0
Seminar	0	0	0
Internship	0	0	0
Technical Visit	0	0	0
Web Based Learning	0	0	0
Implementation/Application/Practice	0	0	0
Practice at a workplace	0	0	0
Occupational Activity	0	0	0
Social Activity	0	0	0
Thesis Work	0	0	0
Field Study	0	0	0
Report Writing	0	0	0
Final Exam	1	1	1
Preparation for the Final Exam	0	0	0
Mid-Term Exam	1	1	1
Preparation for the Mid-Term Exam	0	0	0
Short Exam	0	0	0
Preparation for the Short Exam	0	0	0
TOTAL	39	0	128