Babes-Bolyai University of Cluj-Napoca
Faculty of Mathematics and Computer Science
Study Cycle: Graduate
SUBJECT

Code	Subject	
MMC0001	Complex Analysis	

Section	Sem.	Hours: C+S+L	Category	Type	
Mathematics	3	2+2+0	speciality	compulsory	
Mathematics and Computer Science	3	2+2+0	speciality	compulsory	

Teaching Staff in Charge	Prof. SALAGEAN Grigore Stefan, Ph.D., salagean@math.ubbcluj.ro
Prof. BULBOACA Teodor, Ph.D., bulboaca@math.ubbcluj.ro	
Aims	Appropriation of the basic knowledge of the theory of complex functions of a complex variable and the presentation of some applications of this theory.	
Content	1. Complex numbers. The extended complex plane. Stereographic projection.
2. Holomorhic functions. Derivatives of a complex function of one variable. Cauchy - Riemann conditions. Geometric interpretation of the derivative. Examples of holomorphic functions. Homographic functions. Applications.
3. Integration for complex functions. Cauchy Integral. Cauchy's Theorem. Cauchy's formulas.
4. Sequences and series of holomorphic functions. Weierstrass Theorem. Power series. The analyticity of holomorphic functions. Zeroes of holomorphic functions. Identity's Theorem of holomorphic functions. Maximum modulus Theorem. Laurent series. Singular points. Meromorphic functions.
5. Residues Theorem. Applications.	
Bibliography	1. HAMBURG, PETRE - MOCANU, PETRU - NEGOESCU, NICOLAE : Analiză matematică (Funcţii complexe), Bucureşti: Editura Didactică şi Pedagogică, 1982.
2. GAŞPAR, DUMITRU - SUCIU, NICOLAE : Analiză complexă, Bucureşti, Editura Academiei Române, 1999.
3. KRANTZ, STEVEN : Handbook of complex variables, Boston, Basel, Berlin: Birkhauser Verlag, 1999.
4. CONWAY, J. B. : Functions of one complex variable II, Graduate Texts in Mathematics, 159, New York: Springer Verlag, 1996.
5. BULBOACĂ, TEODOR - NÉMETH, SÁNDOR : Komplex Analizis, Cluj-Napoca, Editura Abel (Erdely Tankönyvtanács), 2004.
6. BULBOACĂ, TEODOR - SALAMON, JULIA : Komplex Analizis II. Feladatok és megoldások, Cluj-Napoca, Editura Abel (Erdely Tankönyvtanács), 2002.
7. MAYER, OCTAV : Teoria funcţiilor de o variabilă complexă (vol. I, II), Bucureşti, Editura Academiei Române, 1981-1990.
8. STOILOV, SIMION : Teoria funcţiilor de o variabilă complexă (vol. I, II), Bucureşti, Editura Academiei Române, 1954-1958.
9. CĂLUGĂREANU, GHEORGHE : Elemente de teoria funcţiilor de o variabilă complexă, Bucureşti, Editura Didactică şi Pedagogică, 1963.
10. MOCANU, PETRU : Funcţii complexe, Cluj-Napoca, Lit. Univ. Cluj, 1972.	
Assessment	Exam. Student tests during the semester; their average represents 1/3 from the final score.