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Complex analysis

Code: 33083
ECTS: 6.0
Lecturers in charge: prof. dr. sc. Pavle Pandžić
Lecturers: dr. sc. Barbara Bošnjak - Exercises
Karmen Grizelj , mag. math. - Exercises
English level:


All teaching activities will be held in Croatian. However, foreign students in mixed groups will have the opportunity to attend additional office hours with the lecturer and teaching assistants in English to help master the course materials. Additionally, the lecturer will refer foreign students to the corresponding literature in English, as well as give them the possibility of taking the associated exams in English.

1. komponenta

Lecture typeTotal
Lectures 30
Exercises 30
* Load is given in academic hour (1 academic hour = 45 minutes)
The students are introduced to the basic notions and techniques of the theory of functions of a complex variable.

Subjects by weeks:
1. Complex numbers and functions. Graphical presentation of complex functions. Continuity and limits of complex function.
2. Holomorphic functions. Exponential and logarithmic function.
3. Integral of a complex function. Indedx of a closed curve.
4. Square root. Cauchy's theorem.
5. Cauchy's integral formula. Morera's theorem.
6. Sequences and series of functions. Power series.
7. Taylor series. Uniqueness of holomorpic function. Liouville's theorem. First fundamental theorem of algebra.
8. Laurent series. Isolated singularities.
9. Residue theorem and applications to evaluating integrals.
10. Aplications of residue theorem to series, partial fractions and infinite products. Gamma function.
11. Zeros and poles of meromorphic functions. Argument principle.
12. Rouche's theorem. Second fundamental theorem of algebra. Weierstrass' preparatory theorem.
13. Open mapping theorem. Holomorphic isomorphism theorem. Maximal module principal. Schwarz lemma.
  1. M. Rao, H. Stetkoer: Complex Analysis: An Invitation
  2. Š. Ungar: Matematička analiza 4
  3. L. V. Ahlfors: Complex Analysis
  4. H. Kraljević, S. Kurepa: Matematička analiza 4/I: Funkcije kompleksne varijable
  5. W. Rudin: Real and Complex Analysis
Prerequisit for:
Enrollment :
Passed : Integral calculus of functions of several variables
6. semester
Mandatory course - Regular study - Mathematics
Consultations schedule:


Link to the course web page: https://web.math.pmf.unizg.hr/nastava/kompa/