MATH 303 | Course Introduction and Application Information - Department of Mathematics

Course Name

Complex Analysis

Code	Semester	Theory (hour/week)	Application/Lab (hour/week)	Local Credits	ECTS
MATH 303	Fall	3	0	3	7

Prerequisites	None
Course Language	English
Course Type	Required
Course Level	First Cycle
Mode of Delivery	face to face
Teaching Methods and Techniques of the Course	Lecture / Presentation
National Occupation Classification	-
Course Coordinator	Doç. Dr. Sevin GÜMGÜM
Course Lecturer(s)	Prof. Dr. Tahsin ÖNER
Assistant(s)	Araş. Gör. Dr. Ayşe BELER Araş. Gör. Merve KAHRAMAN ARİMAN Araş. Gör. Sıla Selenay KOÇ

Course Objectives

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.

Learning Outcomes

#	Content	PC Sub	* Contribution Level
#	Content	PC Sub	1	2	3	4	5
1	will be able to use derivative and Cauchy Riemann equations.
2	will be able to apply the Line integrals and the Cauchy’s integral theorem.
3	will be able to calculate Cauchy’s integral formula for analytic functions.
4	will be able to use Laurent series.
5	will be able to calculate integrals with the residue theorem.
6	will be able to apply Rouché’s theorem.

Course Description

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.

Course Category	Core Courses	X
	Major Area Courses
	Supportive Courses
	Media and Management Skills Courses
	Transferable Skill Courses

Week	Subjects	Related Preparation	Learning Outcome
1	Complex Numbers	James Ward Brown and Ruel V. Churchill “Complex Variables and Applications”, Eighth Edition, MCGraw-Hill Higher Education, 2009. Section 1.
2	Elementary Functions	James Ward Brown and Ruel V. Churchill “Complex Variables and Applications”, Eighth Edition, MCGraw-Hill Higher Education, 2009. Section 3.
3	Analytic Functions	James Ward Brown and Ruel V. Churchill “Complex Variables and Applications”, Eighth Edition, MCGraw-Hill Higher Education, 2009. Section 2.
4	Analytic Functions	James Ward Brown and Ruel V. Churchill “Complex Variables and Applications”, Eighth Edition, MCGraw-Hill Higher Education, 2009. Section 2.
5	Analytic Functions	James Ward Brown and Ruel V. Churchill “Complex Variables and Applications”, Eighth Edition, MCGraw-Hill Higher Education, 2009. Section 2.
6	Integrals	James Ward Brown and Ruel V. Churchill “Complex Variables and Applications”, Eighth Edition, MCGraw-Hill Higher Education, 2009. . Section 4.
7	Integrals	James Ward Brown and Ruel V. Churchill “Complex Variables and Applications”, Eighth Edition, MCGraw-Hill Higher Education, 2009. Section .4
8	Midterm Exam
9	Series	James Ward Brown and Ruel V. Churchill “Complex Variables and Applications”, Eighth Edition, MCGraw-Hill Higher Education, 2009. Section 5.
10	Series	James Ward Brown and Ruel V. Churchill “Complex Variables and Applications”, Eighth Edition, MCGraw-Hill Higher Education, 2009. Section 5.
11	Residues and Poles	James Ward Brown and Ruel V. Churchill “Complex Variables and Applications”, Eighth Edition, MCGraw-Hill Higher Education, 2009. Section 6.
12	Residues and Poles	James Ward Brown and Ruel V. Churchill “Complex Variables and Applications”, Eighth Edition, MCGraw-Hill Higher Education, 2009. . Section 6.
13	Residues and Poles	James Ward Brown and Ruel V. Churchill “Complex Variables and Applications”, Eighth Edition, MCGraw-Hill Higher Education, 2009. Section 6.
14	Conformal Mapping	James Ward Brown and Ruel V. Churchill “Complex Variables and Applications”, Eighth Edition, MCGraw-Hill Higher Education, 2009. Section 9.
15	Semester review
16	Final exam

Course Notes/Textbooks	James Ward Brown and Ruel V. Churchill “Complex Variables and Applications”, Eighth Edition, MCGraw-Hill Higher Education, 2009. ISBN-13: 978-9339205157
Suggested Readings/Materials	S. Ponnusamy and H. Silverman, Birkhäuser, “Complex Variables with Applications”, 2006. ISBN-13: 978-0817644574

Semester Activities	Number	Weighting	LO 1	LO 2	LO 3	LO 4	LO 5	LO 6
Participation
Laboratory / Application
Field Work
Quizzes / Studio Critiques	2	10
Portfolio
Homework / Assignments
Presentation / Jury
Project
Seminar / Workshop
Oral Exams
Midterm	1	40
Final Exam	1	50
Total

Weighting of Semester Activities on the Final Grade	3	50
Weighting of End-of-Semester Activities on the Final Grade	1	50
Total

Semester Activities	Number	Duration (Hours)	Workload
Theoretical Course Hours (Including exam week: 16 x total hours)	16	4	64
Laboratory / Application Hours (Including exam week: '.16.' x total hours)	16		0
Study Hours Out of Class	14	3	42
Field Work			0
Quizzes / Studio Critiques	2	10	20
Portfolio			0
Homework / Assignments			0
Presentation / Jury			0
Project			0
Seminar / Workshop			0
Oral Exam			0
Midterms	1	30	30
Final Exam	1	54	54
		Total	210

#	PC Sub	Program Competencies/Outcomes	* Contribution Level
#	PC Sub	Program Competencies/Outcomes	1	2	3	4	5
1	To be able to have a grasp of basic mathematics, applied mathematics or theories and applications of statistics.		-	-	-	-	X
2	To be able to use advanced theoretical and applied knowledge, interpret and evaluate data, define and analyze problems, develop solutions based on research and proofs by using acquired advanced knowledge and skills within the fields of mathematics or statistics.		-	-	X	-	-
3	To be able to apply mathematics or statistics in real life phenomena with interdisciplinary approach and discover their potentials.		-	-	-	X	-
4	To be able to evaluate the knowledge and skills acquired at an advanced level in the field with a critical approach and develop positive attitude towards lifelong learning.		-	-	-	-	X
5	To be able to share the ideas and solution proposals to problems on issues in the field with professionals, non-professionals.		-	-	-	-	-
6	To be able to take responsibility both as a team member or individual in order to solve unexpected complex problems faced within the implementations in the field, planning and managing activities towards the development of subordinates in the framework of a project.		-	-	-	-	-
7	To be able to use informatics and communication technologies with at least a minimum level of European Computer Driving License Advanced Level software knowledge.		-	-	-	-	-
8	To be able to act in accordance with social, scientific, cultural and ethical values on the stages of gathering, implementation and release of the results of data related to the field.		-	-	-	-	-
9	To be able to possess sufficient consciousness about the issues of universality of social rights, social justice, quality, cultural values and also environmental protection, worker's health and security.		-	-	-	-	-
10	To be able to connect concrete events and transfer solutions, collect data, analyze and interpret results using scientific methods and having a way of abstract thinking.		-	-	-	-	-
11	To be able to collect data in the areas of Mathematics or Statistics and communicate with colleagues in a foreign language.		-	-	-	-	-
12	To be able to speak a second foreign language at a medium level of fluency efficiently.		-	-	-	-	-
13	To be able to relate the knowledge accumulated throughout the human history to their field of expertise.		-	-	-	-	-