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undergraduate thesis
Nizovi funkcija
Osijek: Josip Juraj Strossmayer University of Osijek, Department of Mathematics, 2021. urn:nbn:hr:126:033134
Majdenić, Jelena
Josip Juraj Strossmayer University of Osijek
Department of Mathematics
Chair of Pure Mathematics
Algebra and Calculus Research Group

Cite this document

Majdenić, J. (2021). Nizovi funkcija (Undergraduate thesis). Retrieved from https://urn.nsk.hr/urn:nbn:hr:126:033134

Majdenić, Jelena. "Nizovi funkcija." Undergraduate thesis, Josip Juraj Strossmayer University of Osijek, Department of Mathematics, 2021. https://urn.nsk.hr/urn:nbn:hr:126:033134

Majdenić, Jelena. "Nizovi funkcija." Undergraduate thesis, Josip Juraj Strossmayer University of Osijek, Department of Mathematics, 2021. https://urn.nsk.hr/urn:nbn:hr:126:033134

Majdenić, J. (2021). 'Nizovi funkcija', Undergraduate thesis, Josip Juraj Strossmayer University of Osijek, Department of Mathematics, accessed 30 March 2023, https://urn.nsk.hr/urn:nbn:hr:126:033134

Majdenić J. Nizovi funkcija [Undergraduate thesis]. Osijek: Josip Juraj Strossmayer University of Osijek, Department of Mathematics; 2021 [cited 2023 March 30] Available at: https://urn.nsk.hr/urn:nbn:hr:126:033134

J. Majdenić, "Nizovi funkcija", Undergraduate thesis, Josip Juraj Strossmayer University of Osijek, Department of Mathematics, Osijek, 2021. Available at: https://urn.nsk.hr/urn:nbn:hr:126:033134

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Metadata
TitleNizovi funkcija
Title (english)Sequences of Functions
AuthorJelena Majdenić
MentorDragan Jukić (mentor)
GranterJosip Juraj Strossmayer University of Osijek
Department of Mathematics
(Chair of Pure Mathematics)
(Algebra and Calculus Research Group)
Osijek
Defense date and country2021-09-15, Croatia
Scientific / art field,
discipline and subdiscipline		NATURAL SCIENCES
Mathematics
Mathematical Analysis
Abstract
U ovom završnom radu proučavat ćemo konvergenciju nizova funkcija. Najprije ćemo navesti konvergenciju po točkama kao očitu definiciju konvergencije niza funkcija i pokazati da ta konvergencija nema dobro ponašanje. Zbog toga, kao jači pojam konvergencije, definirat ćemo uniformnu konvergenciju niza funkcija. Navest ćemo teoreme koji nam govore da uniformna konvergencija čuva omeđenost, neprekidnost te osigurava integrabilnost granične funkcije, a onda i time komutiranje limesa i integrala. Pokazat ćemo kada imamo derivabilnost granične funkcije, te komutiranje derivacije i limesa niza funkcija.
Abstract (english)
In this bachelor’s thesis we will study the convergence of sequences of functions. Firstly we will state the pointwise convergence as an obvious way to define the convergence of functions and we will show that it is not as well-behaved. As a stronger definition of convergence, we will define uniform convergence. We will state theorems which proves that uniform convergence preserve boundedness, continuity and ensures integrability of limit function as well as commutation of limit and integration. Thesis will show when is limit function derivable along with commutation of derivation and limit of sequence of functions.
Keywords
Keywords (english)
Languagecroatian
URN:NBNurn:nbn:hr:126:033134
Study programmeTitle: University undergraduate study programme in mathematics
Study programme type: university
Study level: undergraduate
Academic / professional title: sveučilišni/a prvostupnik/prvostupnica (baccalaureus/baccalaurea) matematike (sveučilišni/a prvostupnik/prvostupnica (baccalaureus/baccalaurea) matematike)
Type of resourceText
File originBorn digital
Access conditionsOpen access
Terms of useLicence In copyright icon
RepositoryRepository of Department of Mathematics Osijek
Created on2021-09-22 10:05:17