Babes-Bolyai University of Cluj-Napoca
Faculty of Mathematics and Computer Science
Study Cycle: Graduate

SUBJECT

Code
Subject
MMC0001 Complex Analysis
Section
Semester
Hours: C+S+L
Category
Type
Mathematics
3
2+2+0
speciality
compulsory
Mathematics and Computer Science
3
2+2+0
speciality
compulsory
Applied Mathematics
3
2+2+0
speciality
compulsory
Teaching Staff in Charge
Prof. SALAGEAN Grigore Stefan, Ph.D.,  salageanmath.ubbcluj.ro
Prof. BULBOACA Teodor, Ph.D.,  bulboacamath.ubbcluj.ro
Asist. NECHITA Veronica Oana,  vnechitamath.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), 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.
Links: Syllabus for all subjects
Romanian version for this subject
Rtf format for this subject