Complex analysis (2) |
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Teaching Staff in Charge |
Prof. BULBOACA Teodor, Ph.D., bulboaca@math.ubbcluj.ro Assoc.Prof. KOHR Gabriela, Ph.D., gkohr@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. 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. Analytic continuation. Regular points and singular points. Continuation along curves. The Picard theorem. 6. Infinite series and products. The theorems of Weierstrass and Mittag-Leffler. 7. Harmonic functions. Poisson representation of harmonic functions. |
References |
1. P. Mocanu, Functii complexe, Lit.Univ.Cluj, 1972.
2. P. Hamburg, P. Mocanu, N. Negoescu, Analiza matematica (Functii complexe), Ed. Did. Ped., 1982. 3. B. Chabat, Introduction a l@Analyse Complexe, vol. II, Ed. Mir, Moscou, 1990. 4. J.B. Conway, Functions of One Complex Variable II, Graduate Texts in Mathematics, 159, Springer Verlag, New York, 1996. 5. S. Krantz, Handbook of Complex Variables, Birkhauser, Boston, Basel, Berlin, 1999. 6. O. Mayer, Teoria functiilor de o variabila complexa, vol. I, II, Ed. Acad. Romane, Bucuresti, 1981-1990. 7. T. Bulboaca, Nemeth S., Komplex Analizis, Ed. Abel, Cluj-Napoca, 2001. 8. T. Bulboaca, Salamon J., Komplex Analizis II. Feladatok es megoldasok, Ed. Abel, Cluj-Napoca, 2002. 9. D. Gaspar, N. Suciu, Analiza complexa, Ed. Acad. Romane, Bucuresti, 1999. |
Assessment |
Exam. |