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

Complex analysis (1)
Code
Semes-
ter
Hours: C+S+L
Credits
Type
Section
MT003
3
2+2+0
6
compulsory
Matematică
MT003
3
2+2+0
6
compulsory
Matematică-Informatică
MT003
3
2+2+0
6
compulsory
Matematici Aplicate
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 complex plane. Stereographic projection.
2. Holomorhic functions:derivatives, Cauchy-Riemann conditions, examples, applications.
3. Integration for complex functions
4. Sequences and series of holomorphic functions. Weierstrass Theorem. Power series. Maximum Modulus Theorem. Laurent series. Singular points. Meromorphic functions. Residues Theorem. Applications.
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. N. Boboc, Functii complexe, Ed.Did.Ped., 1969.
4. Gh. Calugareanu, Elemente de teoria functiilor de o variabila complexa, Ed.Did.Ped., 1963.
5. S. Stoilow, Teoria functiilor de o variabila complexa, vol.I,II, Ed. Acad., 1954-1958.
6. O. Mayer, Teoria functiilor de o variabila complexa, vol.I,II, Ed.Acad., 1981-1990.
7. T. Bulboaca, Nemeth S., Komplex Analizis, Editura Abel (Erdely Tankonyvtanacs), Cluj-Napoca, 2001
8. T. Bulboaca, Salamon J., Komplex Analizis II. Feladatok es megoldasok, Editura Abel (Erdely Tankonyvtanacs), Cluj-Napoca, 2002
9. D. Gaspar, N. Suciu, Analiza complexa, Ed. Acad. Romane, Bucuresti, 1999.
10. J.B. Conway, Functions of One Complex Variable II, Graduate Texts in Mathematics, 159, Springer Verlag, New York, 1996.
11. S. Krantz, Handbook of Complex Variables, Birkhauser, Boston, Basel, Berlin, 1999.
Assessment
Exam.