Verižni ulomki in neskončne vrste : diplomsko delo

Skubic, Katja (author), Slapar, Marko (mentor), Starčič, Tadej (co-mentor)

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.

• Language: Slovenian
• Keywords: neskončni verižni ulomek, konvergenca, Taylorjeva vrsta
• Work type: Bachelor thesis/paper
• Typology: 2.11 - Undergraduate Thesis
• Organization: PEF - Faculty of Education
• Publisher: [K. Skubic]
• Year: 2014
• Number of pages: 32 str.
• PID: 20.500.12556/RUL-69033
• UDC: 517.524(043.2)
• COBISS.SI-ID: 10216009
• Publication date in RUL: 10.07.2015

Secondary language

• Language: Slovenian
• Title: Continued fractions and infinite series

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.