COURSE SYLLABUS

UNIVALENT FUNCTIONS I

1	Course Title:	UNIVALENT FUNCTIONS I
2	Course Code:	MAT6105
3	Type of Course:	Optional
4	Level of Course:	Third Cycle
5	Year of Study:	1
6	Semester:	1
7	ECTS Credits Allocated:	6
8	Theoretical (hour/week):	3
9	Practice (hour/week) :	0
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. SİBEL YALÇIN TOKGÖZ
16	Course Lecturers:	Doç. Dr. Elif Yaşar
17	Contactinformation of the Course Coordinator:	syalcin@uludag.edu.tr, 0(224)2941758, B.U.Ü. Fen Edebiyat Fakültesi Matematik Bölümü, 16059 BURSA
18	Website:
19	Objective of the Course:	To teach the basic subjects of the Geometric Functions Theory
20	Contribution of the Course to Professional Development	Knows the basic properties of analytic univalent functions.

Learning Outcomes:

1	He/she learns the basic properties of the univalent functions;
2	He/she uses the area theorem in the solution of the coefficient problem;
3	He/she relates between the univalent functions having a pole and the analytic univalent functions;
4	He/she solves the extremal problems fort he subclasses of the analytic univalent functions.;
5	He/she solves the radius problems;
6	He/she gets the integral represents of the functions with positive real part.;
7	He/she the relation between convex and starlike functions.;
8	He/she knows the relation between typically real functions and the functions with positive real part.;
9	He/she gets the inequalities of coefficient of the typically real functions;
10	He/she defines the new classes of the univalent functions.;

22	Course Content:

Week	Theoretical	Practical
1	The basic properties of the univalent functions
2	Some Area Theorems
3	The bounded univalent functions
4	The univalent functions having a pole
5	Transformation of the range from the unit disk to right half plane problems
6	The distortion Theorems, Robertson Conjecture
7	The functions with positive real part
8	The convex and starlike functions and their properties.
9	The extremal problems and radius problems
10	Alpha convex and alpha starlike functions
11	Alpha spiral functions and their properties
12	The typically real functions and some of their properties
13	The definiton studies of the sbclasses of the univalent functions.
14	The provision studies the properties of the new classes defined.

23	Textbooks, References and/or Other Materials:	1-) Peter Duren ; Univalent Functions, Springer-Verlag 2-) A.W.Goodman ; Univalent Functions I-II 3-) G.Schober ; Univalent Functions and selected topics, Springer-Verlag 4-) C. Pommerenke ; Univalent Functions , Vandenhoeck & Ruprecht in Göttingen
24	Assesment

TERM LEARNING ACTIVITIES	NUMBER	PERCENT
Midterm Exam	0	0
Quiz	0	0
Homeworks, Performances	0	0
Final Exam	1	100
Total	1	100
Contribution of Term (Year) Learning Activities to Success Grade		0
Contribution of Final Exam to Success Grade		100
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