Riemannov upodobitveni izrek

diplomsko delo

Nina Potočar (Author), Marko Slapar (Mentor)

Abstract

V prvem delu diplomske naloge najprej predstavimo osnovne definicije in lastnosti kompleksne ravnine. V nadaljevanju se osredotočimo na kompleksne funkcije in lomljene linearne transformacije. Eno izmed bolj pomembnih poglavij je tudi Schwarzova lema in avtomorfizmi kroga. V drugem delu predstavimo Riemannov upodobitveni izrek, ki nam pove, da je vsako enostavno povezano območje v ₵, razen cele kompleksne ravnine, biholomorfno ekvivalentno enotskemu disku. Nato razložimo, zakaj izrek ne velja za celotno kompleksno ravnino. Na koncu sledijo primeri uporabe Riemannovega upodobitvenega izreka.

Keywords

holomorfne funkcije;lomljene linearne preslikave;Schwarzova lema;Riemannov upodobitveni izrek;

Data

Language:	Slovenian
Year of publishing:	2017
Typology:	2.11 - Undergraduate Thesis
Organization:	UL PEF - Faculty of Education
Publisher:	[N. Potočar]
UDC:	51(043.2)
COBISS:	11694153
Views:	928
Downloads:	165
Average score:	0 (0 votes)
Metadata:

Other data

Secondary language:	English
Secondary title:	Riemann mapping theorem
Secondary abstract:	In the first part of the thesis, we introduce the basic definitions and properties of the complex plane. We then focus on complex functions and linear fractional transformations. One of the main chapters of the thesis is the one regarding the Schwarz lemma and the automorphisms of the unit disk. In the second part of the diploma thesis we present the Riemann mapping theorey, which states that every simply connected domain in ₵, except for the whole plane, is biholomorphically equivalent to the unit disc. We then explain why the theorey does not apply to the whole complex plane. The final part of the thesis contains examples of the Riemann mapping theorey.
Secondary keywords:	mathematics;matematika;
File type:	application/pdf
Type (COBISS):	Bachelor thesis/paper
Thesis comment:	Univ. v Ljubljani, Pedagoška fak., Dvopredmetni učitelj, Matematika-računalništvo
Pages:	IV, 21 str.
ID:	10864152