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

Complex analysis (2)
Code
Semes-
ter
Hours: C+S+L
Credits
Type
Section
MT004
4
2+1+0
6
compulsory
Matematică
MT004
4
2+1+0
6
optional
Matematică-Informatică
Teaching Staff in Charge
Prof. BULBOACA Teodor, Ph.D.,  bulboacamath.ubbcluj.ro
Assoc.Prof. KOHR Gabriela, Ph.D.,  gkohrmath.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.
References
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.
Assessment
Exam. Student tests during the semester; their average represents 1/3 from the final score.