Universitatea Babeş-Bolyai Cluj-Napoca
Facultatea de Matematică şi Informatică
Ciclul de studii: Masterat
Domeniul: Matematica
Programul de studii: Analiză reală şi complexă (în limba engleză)
Limba de predare: Engleză

SYLLABUS

I. General data
Code	Subject	
MT255	Univalent Functions and Differential Subordinations	

Semester	Hours: C+S+L	Category	Status	
1	2+1+1		compulsory	

II. Full status faculty members
Name and	Scientific	Didactic	Chair	Type of activity	
surname	title	title		C	S	L	
SALAGEAN Grigore Stefan	Ph.D.	Prof.	Function Theory	*			

Associated faculty members
Name and	Scientific	Institution	Type of	Type of activity	
surname	title		position	C	S	L	

III. Course objectives
The aim of this course is to realize a deep study of univalent functions, which are essential in geometric function theory.	

IV. Course contents
1. Univalent functions. Area Theorem. Covering and distortion theorems.
2. Holomorphic functions with positive real part. Herglotz formula. Integral representations. Subordination.
3. Classes of univalent functions. Starlike functions, convex functions, alpha-convex functions, spirallike functions, typically real functions. Meromorphic functions.
4. Differential subordinations. Fundamental lemmas. The class of admissible functions. Applications.

V. Bibliography
1. MOCANU, PETRU - BULBOACĂ, TEODOR - SĂLĂGEAN, GR. ŞTEFAN : Teoria geometrică a funcţiilor univalente, Cluj-Napoca: Casa Cărţii de Ştiinţă, 1999.
2. MILLER, SANDFORD S. - MOCANU, PETRU T. : Differential Subordinations. Theory and Applications, New York - Basel: Marcel Dekker Inc., 2000
3. POMMERENKE, CHRISTIAN : Univalent Functions, Göttingen: Vandenhoeck & Ruprecht,  1975
4. GOODMAN, WALTER A. : Univalent functions (vol. I, II), Tampa: Mariner Publishing Co., 1983.
5. GOLUZIN, GHENADII MIHAILOVICI : Geometric theory of functions of a complex variable, New York: Trans. Math. Mon., Amer. Math. Soc., 1969.
6. DUREN, PETER L. : Berlin, Heidelberg: Univalent functions, Springer Verlag,  1984.
7. BULBOACĂ, TEODOR - MOCANU, PETRU : Bevezetés az analitikus függvények geometriai elméletébe, Cluj-Napoca: Ed. Abel (Erdely Tankönyvtanács), 2003.
8. SĂLĂGEAN, GRIGORE STEFAN : Geometria planului complex, Cluj-Napoca: ProMedia Plus,  1997
9. GRAHAM, IAN - KOHR, GABRIELA : Geometric function theory in one and higher dimensions, New York: M. Dekker, 2003.	

VI. Thematic of didactic activities per weeks

VII. Didactic methods used

VIII. Assessment
exam (70%) + home-work (30%)	

IX. Additional references

	Dean,							Chair head,

	Date,							Course responsible,
								Prof. SALAGEAN Grigore Stefan, Ph.D.