Nizovi i redovi funkcija

master's thesis

• Author: Danijela Piškor
• Mentor: Ljiljana Arambašić (mentor)
• Committee member: Ljiljana Arambašić (predsjednik povjerenstva)
• Committee member: Boris Guljaš (član povjerenstva)
• Committee member: Zvonimir Tutek (član povjerenstva)
• Committee member: Dijana Ilišević (član povjerenstva)
• Granter: University of Zagreb; Faculty of Science; (Department of Mathematics); Zagreb
• Defense date and country: 2016-09-27, Croatia
• Scientific / art field, discipline and subdiscipline: NATURAL SCIENCES; Mathematics

Abstract

U ovom diplomskom radu proučavamo nizove i redove funkcija. U prvom poglavlju navodimo osnovne činjenice o nizovima i redovima realnih brojeva. Drugo poglavlje detaljnije proučava dvije osnovne vrste konvergencije nizova funkcija, konvergenciju po točkama i uniformnu konvergenciju. Navodimo osnovni kriterij uniformne konvergencije i proučavamo svojstva funkcija koja čuva uniformna konvergencija. Sljedeće poglavlje bavi se redovima funkcija; primjenjujemo rezultate prethodnog poglavlja kako bismo dobili analogne rezultate za redove funkcija. Posljednje poglavlje bavi se specijalnim oblicima redova funkcija, redovima potencija. Proučavamo radijus konvergencije, kao i aritmetičke operacije s redovima potencija. Na kraju poglavlja definirani su Taylorovi redovi, te su dane neke primjene Taylorovih redova.

Abstract (english)

In this thesis we study sequences and series of functions. In the first chapter we present basic facts about sequences and series of numbers. The second chapter considers two basic types of convergence of sequences of functions, pointwise and uniform convergence. We present several test for uniform convergence and study properties of functions that uniform convergence preserves. The next chapter deals with series of functions; we apply results from the previous chapter to obtain analogous results for series of functions. The last chapter considers the special forms of series of functions, power series. We study the radii of convergence as well as arithmetic operations on power series. At the end of this chapter we define Taylor series and give some applications.

• Keywords: nizovi funkcija; redovi funkcija; redovi potencija; Taylorovi redovi
• Keywords (english): sequences of functions; series of functions; power series; Taylor series
• Language: croatian
• URN:NBN: urn:nbn:hr:217:778499
• Study programme: Title: Mathematics Education; specializations in: Mathematics Education; Course: Mathematics Education; Study programme type: university; Study level: graduate; Academic / professional title: magistar/magistra edukacije matematike (magistar/magistra edukacije matematike)
• Type of resource: Text
• File origin: Born digital
• Access conditions: Open access
• Created on: 2019-01-30 09:36:10