Verižni ulomki in neskončne vrste

diplomsko delo

Katja Skubic (Author), Marko Slapar (Mentor), Tadej Starčič (Co-mentor)

Abstract

V diplomskem delu bom skušala razumljivo predstaviti koncept splošnih verižnih ulomkov, njihovo povezavo s številskimi vrstami oziroma nekaterimi analitičnimi funkcijami. Pri tem si bom pobližje ogledala tudi osnovne koncepte neskončnih vrst, ustavila pa se bom tudi pri zgodovini verižnih ulomkov, saj njihovi zametki segajo daleč v zgodovino matematike in so povezani s številnimi pomembnimi matematičnimi imeni. Na koncu pa se bom posvetila še dobro znanim matematičnima konstantama, ki nas spremljata že skozi dolga stoletja. To sta števili pi in e. Raziskovanje bo namenjeno predvsem njuni predstavitvi z verižnimi ulomki ob pomoči izpeljav iz neskončnih vrst.

Keywords

neskončni verižni ulomek;konvergenca;Taylorjeva vrsta;

Data

Language:	Slovenian
Year of publishing:	2014
Typology:	2.11 - Undergraduate Thesis
Organization:	UL PEF - Faculty of Education
Publisher:	[K. Skubic]
UDC:	517.524(043.2)
COBISS:	10216009
Views:	1126
Downloads:	157
Average score:	0 (0 votes)
Metadata:

Other data

Secondary language:	English
Secondary title:	Continued fractions and infinite series
Secondary abstract:	The intention of this diploma is to present the concept of continued fractions, their conection with infinite series and some analitical functions. There will be also presented the concept of numerical series. There is a lot of history behind the continued fractions. I will only mention a few most important names which are linked with beginnings of continued fractions. At the end I will present two most known constants, numbers pi and e. I will try to write them with continued fractions using infinite series because of their close connection.
Secondary keywords:	mathematics;matematika;
File type:	application/pdf
Type (COBISS):	Bachelor thesis/paper
Thesis comment:	Univ. Ljubljana, Pedagoška fak., Matematika in računalništvo
Pages:	32 str.
ID:	8707989