Course Code	Semester	Course Name	LE/RC/LA	Course Type	Language of Instruction	ECTS
MB0044		Complex Analysis II	2/2/0	DE	Turkish	5

Course Goals	Making computation of residue with the assistance of determined series representation for analytic functions in Complex Analysis I, calculate some complex and real integrals by using Residue Theorem and giving complementary some special topics  of Complex Analysis.
Prerequisite(s)	None
Corequisite(s)	None
Special Requisite(s)	The lesson Complex Analysis I is the basis of this lesson.
Instructor(s)
Course Assistant(s)	None
Schedule	Monday, 11:00-13:00, Ataköy Campus, classroom 3C-07/09, Tuesday, 13:00-15:00, Ataköy Campus, classroom 3C-04/06.
Office Hour(s)	Tuesday, 15:00-17:00, Ataköy Campus, Office Number 3A-03/05.
Teaching Methods and Techniques	Oral presentations, solving homework problems
Principle Sources	James Ward Brown, Ruel V. Churchill, Complex Variables and Applications, Mc Graw Hill Science, 1995.
Other Sources	Lars V. Alfhors, Complex Analysis: An Introduction to the Theory of Analytic Functions of One Complex Variable, McGraw-Hill, 1996

Course Schedules
Week	Contents	Learning Methods
1. Week	Residue Theorem, Argument Principle, Rouche's Theorem	Oral represantation
2. Week	Evaluation of improper real integrals	Oral represantation
3. Week	Improper integrals involving sines and cosines	Oral represantation
4. Week	Definite integrals involving sines and cosines	Oral represantation
5. Week	Integration through a branch cut, Problems	Oral represantation
6. Week	Open Mapping Theorem, Inverse Function Theorem	Oral represantation
7. Week	Winding number notion, Schwarz Lemma	Oral represantation
8. Week	Midterm exam	-
9. Week	Analytic continuation	Oral represantation
10. Week	Conformal mapping, Riemann Mapping Theorem	Oral represantation
11. Week	The Schwarz-Chirstoffel Formula	Oral represantation
12. Week	Lineer fractional transformations, Möbius transformation	Oral represantation
13. Week	Affine transformasyonu	Oral represantation
14. Week	Some special transformations, Gamma function, Zeta function	Oral represantation
15. Week	Final exam	-
16. Week	Final exam	-
17. Week	Final exam	-

Assessments
Evaluation tools	Quantity	Weight(%)
Midterm(s)	2	60
Final Exam	1	40

Program Outcomes PO-1 Interpreting advanced theoretical and applied knowledge in Mathematics and Computer Science. PO-2 Critiquing and evaluating data by implementing the acquired knowledge and skills in Mathematics and Computer Science. PO-3 Recognizing, describing, and analyzing problems in Mathematics and Computer Science; producing solution proposals based on research and evidence. PO-4 Understanding the operating logic of computer and recognizing computational-based thinking using mathematics as a discipline. PO-5 Collaborating as a team-member, as well as individually, to produce solutions to problems in Mathematics and Computer Science. PO-6 Communicating in a foreign language, and interpreting oral and written communicational abilities in Turkish. PO-7 Using time effectively in inventing solutions by implementing analytical thinking. PO-8 Understanding professional ethics and responsibilities. PO-9 Having the ability to behave independently, to take initiative, and to be creative. PO-10 Understanding the importance of lifelong learning and developing professional skills continuously. PO-11 Using professional knowledge for the benefit of the society.

Learning Outcomes LO-1 Understanding Residue and Rouche' Theorems and making calculate residue by using series expansions of functions. LO-2 Calculating some type of definite integrals with assistance of Residue Theorem. LO-3 Understanding Schwarz Lemma. LO-4 Understanding winding number notion and solving problems involving these. LO-5 Understanding the Inverse Function Theorem and the Open Mapping Theorem. LO-6 Understanding the Riemann Mapping Theorem and the Schwarz-Chirstoffel Formula. LO-7 Learning linear fractional transformations and solving problems on some kind of these transformations. LO-8 Learning Gamma and Zeta Functions.

Course Assessment Matrix:

	PO 1	PO 2	PO 3	PO 4	PO 5	PO 6	PO 7	PO 8	PO 9	PO 10	PO 11
LO 1
LO 2
LO 3
LO 4
LO 5
LO 6
LO 7
LO 8