Complex analysis, extension

Mathematics BSc
Course description
2013.

Eötvös Loránd University
Faculty of Science
Institute of Mathematics

Borromean Rings

All courses
Core courses
- Algebra, number theory
- Analysis
- Geometry
  - Geometry 1
- Discrete mathematics
  - Discrete mathematics 1
  - Discrete mathematics 2
- Elementary mathematics
  - Elementary mathematics 1
- Informatics
  - Prog. fundamentals
Pure mathematics
- Algebra, number theory
- Analysis
  - Analysis 3
  - Analysis 4
  - Applied analysis
    - Numerical analysis
    - Appl. anal. comp.
  - Differential equations
    - Differential equations
    - Partial diff. equations
  - Topology
    - Introduction
    - Algebraic topology
  - Complex analysis
  - Functional analysis
  - Function series
- Geometry
- Operations research
  - Operations research 1
  - Operations research 2
- Probability theory
- Informatics
- Computer science
- Foundations of math.
  - Set theory
  - Mathematical logic
Applied mathematics
- Analysis
  - Analysis 3
  - Analysis 4
  - Analysis 5
  - Applied analysis
  - Differential equations
    - Differential equations
    - Partial diff. equations
  - Complex analysis
  - Functional analysis
- Geometry
- Operations research
  - Operations research 1
  - Operations research 2
- Probability theory
- Applied modules
- Informatics
- Algorithms
- Algebra
- Elementary mathematics
  - Elementary mathematics 2
  - Elementary mathematics 3
- Foundations of math.
BSc: general information
Studies

Complex analysis, extension

Hours lect+pc	Credits lect+pc	Assessment	Specialization	Course code lect/pc	Semester	Status
1 + 0	1 + 0	exam	pure math.	mm1c1fk5m	5	recommended

Course coordinator

Róbert Szőke
Department of Analysis
Institute of Mathematics

Strong	Weak	Prerequisites
Lecture
Lecture		Weak: Complex analysisL-p (mm1c1kf5m)

Remarks

This course is a recommended extension of Complex analysis, taught in parallel.

Syllabus designed by:

Gábor Halász, Department of Analysis, Institute of Mathematics.

Literature

L.V. Ahlfors: Complex Analysis. McGraw–Hill Book Company, 1979.

Syllabus

The general form of Cauchy's fundamental theorem. Sequences of holomorphic functions. Local value distribution. The Caratheodory theorem.
Subharmonic functions. The maximum principle. The mean value property.
On the values of entire functions. The Picard theorem. The order of an entire function. The subordination. The generalization of the Schwarz lemma.
The Mittag-Leffler theorem. The Weierstrass factorization theorem. Canonical representation of entire functions of finite order. Borel's quantitative version of Picard's theorem.