Diskretne harmonične in analitične funkcije

diplomsko delo

Maja Hladnik (Author), Marko Slapar (Mentor)

Abstract

V diplomskem delu bomo definirali harmonične in analitične funkcije na diskretnih objektih. Pri tem bomo izhajali iz definicij in izrekov, ki veljajo za običajne harmonične in holomorfne funkcije. Zato bomo v diplomskem delu najprej definirali harmonične funkcije ter pokazali, da je povprečna vrednost harmonične funkcije na poljubni krogli enaka vrednosti te funkcije v središču krogle. Nato bomo definirali holomorfne funkcije in dokazali Morerov izrek. Definirali bomo osnovne pojme iz teorije grafov, v zadnjem delu diplomskega dela pa bomo definirali diskretne harmonične funkcije in diskretne analitične funkcije. Za oboje bomo navedli primere.

Keywords

izrek o povprečni vrednosti;holomorfne funkcije;Morerov izrek;grafi;

Data

Language:	Slovenian
Year of publishing:	2017
Typology:	2.11 - Undergraduate Thesis
Organization:	UL PEF - Faculty of Education
Publisher:	[M. Hladnik]
UDC:	51(043.2)
COBISS:	11701577
Views:	683
Downloads:	165
Average score:	0 (0 votes)
Metadata:

Other data

Secondary language:	English
Secondary title:	Discrete harmonic and analytic functions
Secondary abstract:	In this diploma thesis, we will introduce discrete harmonic and analytic functions. Definitions will be based on definitions and theorems, known for harmonic and holomorphic functions. That is why we will start the diploma thesis by defining harmonic functions. We will show that the average value of a harmonic function over a ball is equal to the value of this function at the center of the ball. We will then define holomorphic functions and prove Morera's theorem. We will define some basic terms in graph theory, and in the last part of the thesis, we will define discrete harmonic and analytic functions. We will give examples for both.
Secondary keywords:	mathematics;matematika;
File type:	application/pdf
Type (COBISS):	Bachelor thesis/paper
Thesis comment:	Univ. v Ljubljani, Pedagoška fak., Dvopredmetni učitelj
Pages:	23 str.
ID:	10864184