1. komponenta

Lecture type	Total
Lectures	30
Exercises	30

* Load is given in academic hour (1 academic hour = 45 minutes)

COURSE AIMS AND OBJECTIVES:
The students are introduced to the basic notions and techniques of the theory of functions of a complex variable.

COURSE DESCRIPTION AND SYLLABUS:
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.

Enrollment :
Passed : Fundamentals of mathematical analysis

Izborni matematički predmet 3 - Regular study - Mathematics and Physics Education

Izborni matematički predmet 5 - Regular study - Mathematics and Physics Education