"Babes-Bolyai" University of Cluj-Napoca
Faculty of Mathematics and Computer Science

Complex analysis 2
Hours: C+S+L
Matematică informatică
Teaching Staff in Charge
Prof. BULBOACA Teodor, Ph.D.,  bulboacamath.ubbcluj.ro
Assoc.Prof. KOHR Gabriela, Ph.D.,  gkohrmath.ubbcluj.ro
Appropriation of the basic knowledge of the theory of complex functions of a complex variable and the presentation of some applications of this theory.
1. Analytical branches. The index of a path. The homological version of Cauchy's theorem.
2. Residues. Meromorphic functions. The principle of argument's variation. Rouche's theorem. The open mapping theorem.
3. The geometric theory of holomorphic functions: Conformal mappings. Conformal automorphisms of the unit disc and of annuli. Normal families. Montel's and Vitali's theorems. Conformal equivalence of simply connected domains. The Riemann mapping theorem. Continuity at the boundary.
4. Properties of univalent functions on the unit disc. The class S.
5. Infinite series and products. The theorems of Weierstrass and Mittag-Leffler.
6. Harmonic and subharmonic functions. Poisson representation of harmonic functions.
1. HAMBURG, PETRE - MOCANU, PETRU - NEGOESCU, NICOLAE : Analiză matematică (Funcţii complexe), Editura Didactică şi Pedagogică, Bucureşti, 1982.
2. GAŞPAR, DUMITRU - SUCIU, NICOLAE : Analiză complexă, Editura Academiei Române, Bucureşti, 1999.
3. KRANTZ, STEVEN : Handbook of complex variables, Birkhauser Verlag, Boston, Basel, Berlin, 1999.
4. CONWAY, J. B. : Functions of one complex variable II, Graduate Texts in Mathematics, 159, Springer Verlag, New York, 1996.
5. BULBOACĂ, TEODOR - NÉMETH, SÁNDOR : Komplex Analizis, Editura Abel (Erdely Tankönyvtanács), Cluj-Napoca, 2004.
6. BULBOACĂ, TEODOR - SALAMON, JULIA : Komplex Analizis II. Feladatok és megoldások, Editura Abel (Erdely Tankönyvtanács), Cluj-Napoca, 2002.
7. MAYER, OCTAV : Teoria funcţiilor de o variabilă complexă (vol. I, II), Editura Academiei Române, Bucureşti, 1981-1990.
8. STOILOV, SIMION : Teoria funcţiilor de o variabilă complexă (vol. I, II), Editura Academiei Române, Bucureşti, 1954-1958.
9. CĂLUGĂREANU, GHEORGHE : Elemente de teoria funcţiilor de o variabilă complexă, Editura Didactică şi Pedagogică, Bucureşti, 1963.
10. MOCANU, PETRU : Funcţii complexe, Lit. Univ. Cluj, 1972.
Exam. Student tests during the semester; their average represents 1/3 from the final score.