Complex analysis

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

Hours lect+pc	Credits lect+pc	Assessment	Specialization	Course code lect/pc	Semester	Status
2 + 2	2 + 3	exam + term grade	pure math.	mm1c1kf5m mm1c2kf5m	5	compulsory

Course coordinator

Róbert Szőke
Department of Analysis
Institute of Mathematics

Strong	Weak	Prerequisites
Practice class
Practice class		Strong: Analysis3L-p (mm1c1an3m)
Lecture
Lecture		Weak: practice class

Remarks

The course Complex analysis, extension is a recommended extension of this course, 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

Complex differentiability, Cauchy-Riemann equations. Complex power series. The complex exponential function and the complex logarithm. Complex trigonometric functions. Complex integration. Cauchy's fundamental theorem, Cauchy-s integral formula. Maximum principle. Schwarz's lemma. Liouville's theorem.
Laurent series. Isolated singularities. Residue theorem and its applications. Rouché's theorem. Conformal mappings. Theorems of Weierstrass, Hurwitz and Montel. Riemann mapping theorem. Reflection principle. Schwarz-Christoffel formula. Harmonic functions. The Poisson kernel.