Robne vrednosti potenčnih vrst

diplomsko delo

Teja Koprivc (Author), Marko Slapar (Mentor), Eva Berdajs (Co-mentor)

Abstract

V diplomskem delu se bom ukvarjala predvsem z območjem konvergence kompleksnih potenčnih vrst. Za potenčne vrste obstaja maksimalen odprti disk, na katerem vrsta konvergira, bolj zapleteno pa je preveriti konvergenco vrste na robu tega diska in določiti točke z roba, v katerih ima vsota vrste lokalno holomorfno razširitev. Ogledali si bomo nekaj zanimivih primerov potenčnih vrst na kompleksnem disku in natančno obravnavali konvergenco na robu konvergenčnega diska. Pri razumevanju konvergence na robu si bomo pomagali z Abelovim izrekom, ki ga bomo v diplomski nalogi tudi dokazali.

Keywords

enakomerna konvergenca;konvergenčni radij;konvergenčni kriteriji;Abelov izrek;

Data

Language:	Slovenian
Year of publishing:	2018
Typology:	2.11 - Undergraduate Thesis
Organization:	UL PEF - Faculty of Education
Publisher:	[T. Koprivc]
UDC:	51(043.2)
COBISS:	12117321
Views:	508
Downloads:	100
Average score:	0 (0 votes)
Metadata:

Other data

Secondary language:	English
Secondary title:	Boundary behavior of power series
Secondary abstract:	This diploma thesis will mostly focus on the problem of convergence of the complex power series. There is a maximum open disk for the power series, which the series converges, however, it is much more complicated to under- stand the convergence at boundary points of this disk and to determine at which points of the boundary has the series has a local holomorphic exten- sion. This thesis includes some interesting examples of the power series on a complex disk and some detailed description of a convergence at boundary points of the disk. For better understanding of the convergence at boundary points, we used and prove Abel’s theorem.
Secondary keywords:	mathematics;matematika;
File type:	application/pdf
Type (COBISS):	Bachelor thesis/paper
Thesis comment:	Univ. v Ljubljani, Pedagoška fak., Dvopredmetni učitelj
Pages:	28 str.
ID:	10973360