COURSE SYLLABUS

COMPLEX FUNCTIONS THEORY I

1	Course Title:	COMPLEX FUNCTIONS THEORY I
2	Course Code:	MAT3011
3	Type of Course:	Compulsory
4	Level of Course:	First Cycle
5	Year of Study:	3
6	Semester:	5
7	ECTS Credits Allocated:	7
8	Theoretical (hour/week):	2
9	Practice (hour/week) :	2
10	Laboratory (hour/week) :	0
11	Prerequisites:	None
12	Recommended optional programme components:	None
13	Language:	Turkish
14	Mode of Delivery:	Face to face
15	Course Coordinator:	Prof. Dr. AHMET TEKCAN
16	Course Lecturers:	Analiz ve Fonksiyonlar Teorisi Anabilim Dalı öğretim üyeleri
17	Contactinformation of the Course Coordinator:	Bursa Uludağ Üniversitesi, Fen Edebiyat Fakültesi, Matematik Bölümü, Bursa 224 294 17 51 tekcan@uludag.edu.tr
18	Website:
19	Objective of the Course:	The conceptions of limit,continuity,complex differentation and entire functions and theorems related with these and applications. Complex sequences and series. Fundamental functions and to analysis their properties. To teach he basic concepts of complex integrals.
20	Contribution of the Course to Professional Development	To help the learn informations on complex function theory 1.

Learning Outcomes:

1	He/she distinguishes the relationship between the complex and real numbers. ;
2	He/she interprets the topology of complex plane;
3	He/she expresses the complex sequences and series;
4	He/she applies the rules of limit, continuity and the complex differentation;
5	He/she interprets the holomorphic functions;
6	He/she applies the complex functions properties;
7	He/she explains the complex numbers and their properties;
8	He/she interprets complex integral;

22	Course Content:

Week	Theoretical	Practical
1	Algebra and geometry of complex numbers.	The solution of problems related
2	The logarithm of complex numbers and the complex power of complex numbers.	The solution of problems related
3	Functions of complex variables	The solution of problems related
4	Introduction to topology of the complex plane	The solution of problems related
5	Limits and continuity, connectedness and compactness	The solution of problems related
6	Derivatives and analytic functions of complex	The solution of problems related
7	Cauchy-Riemann equations and results	The solution of problems related
8	Exponential functions	The solution of problems related
9	Trigonometric and inverse trigonometric functions	The solution of problems related
10	Curves in the complex plane	The solution of problems related
11	Line integrals and their properties	The solution of problems related
12	Cauchy teoremi integral ve ilkel fonksiyon	The solution of problems related
13	Index numbers and Cauchy's integral and the derivative formula	The solution of problems related
14	The results of Cauchy's integral formula: maximum Module and the fundamental theorem of algebra, Schwarz Lemma.	The solution of problems related

23	Textbooks, References and/or Other Materials:	[1] T. BAŞKAN: Kompleks Fonksiyonlar Teorisi, Vipaş A.Ş. 2007. [2] B.P. PALKA: An Introduction to Complex Function Theory, Springer-Verlag,1991. [3] J. H. MATHEWS & R.W.HOWELL: Complex Analysis, Jones and Bartlett Pub. 1997.
24	Assesment

TERM LEARNING ACTIVITIES	NUMBER	PERCENT
Midterm Exam	1	40
Quiz	0	0
Homeworks, Performances	0	0
Final Exam	1	60
Total	2	100
Contribution of Term (Year) Learning Activities to Success Grade		40
Contribution of Final Exam to Success Grade		60
Total		100
Measurement and Evaluation Techniques Used in the Course	The system of relative evaluation is applied.
Information

ECTS / WORK LOAD TABLE

CONTRIBUTION OF LEARNING OUTCOMES TO PROGRAMME QUALIFICATIONS

LO: Learning Objectives

PQ: Program Qualifications

Contribution Level:

1 Very Low

2 Low

3 Medium

4 High

5 Very High