Subject: Complex Analysis	Code: MMC0001	

Semester	 Hours: C+S+L	Type	 Section	
3	2+2+0	compulsory	Mathematics	
3	2+2+0	compulsory	Mathematics and Computer Science	
3	2+2+0	compulsory	Applied Mathematics	

Teaching Staff in Charge	Prof. SALAGEAN Grigore Stefan, Ph.D., salagean@math.ubbcluj.ro
Prof. BULBOACA Teodor, Ph.D., bulboaca@math.ubbcluj.ro
Asist. NECHITA Veronica Oana, vero@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	
Selective References	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