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undergraduate thesis
Nizovi
Osijek: Josip Juraj Strossmayer University of Osijek, School of Applied Mathematics and Informatics, 2024. urn:nbn:hr:126:639233
Barunović, Barbara
Josip Juraj Strossmayer University of Osijek
School of Applied Mathematics and Informatics

Institutional repository: Repository of School of Applied Mathematics and Computer Science

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Barunović, B. (2024). Nizovi (Undergraduate thesis). Osijek: Josip Juraj Strossmayer University of Osijek, School of Applied Mathematics and Informatics. Retrieved from https://urn.nsk.hr/urn:nbn:hr:126:639233

Barunović, Barbara. "Nizovi." Undergraduate thesis, Josip Juraj Strossmayer University of Osijek, School of Applied Mathematics and Informatics, 2024. https://urn.nsk.hr/urn:nbn:hr:126:639233

Barunović, Barbara. "Nizovi." Undergraduate thesis, Josip Juraj Strossmayer University of Osijek, School of Applied Mathematics and Informatics, 2024. https://urn.nsk.hr/urn:nbn:hr:126:639233

Barunović, B. (2024). 'Nizovi', Undergraduate thesis, Josip Juraj Strossmayer University of Osijek, School of Applied Mathematics and Informatics, accessed 16 July 2024, https://urn.nsk.hr/urn:nbn:hr:126:639233

Barunović B. Nizovi [Undergraduate thesis]. Osijek: Josip Juraj Strossmayer University of Osijek, School of Applied Mathematics and Informatics; 2024 [cited 2024 July 16] Available at: https://urn.nsk.hr/urn:nbn:hr:126:639233

B. Barunović, "Nizovi", Undergraduate thesis, Josip Juraj Strossmayer University of Osijek, School of Applied Mathematics and Informatics, Osijek, 2024. Available at: https://urn.nsk.hr/urn:nbn:hr:126:639233

Metadata
TitleNizovi
Title (english)Sequences
AuthorBarbara Barunović
MentorDragana Jankov Maširević (mentor)
GranterJosip Juraj Strossmayer University of Osijek
School of Applied Mathematics and Informatics
Osijek
Defense date and country2024-06-25, Croatia
Scientific / art field,
discipline and subdiscipline		NATURAL SCIENCES
Mathematics
Mathematical Analysis
Abstract
U ovom radu bavimo se nizovima realnih brojeva te navodimo bitna svojstva nizova. Najprije je definiran pojam niza i podniza. Većina rada se bavi konvergencijom niza što je jedan od osnovnih pojmova realne analize. Definiran je limes, ograničenost i monotonost niza te su dokazani bitni teoremi koji povezuju te pojmove s konvergencijom. Pomoću konvergencije niza u metričkom prostoru okarakterizirali smo zatvarač skupa. Pokazano je da definicija broja e proizlazi iz konvergencije niza. Zatim je uveden pojam Cauchyjevog niza i dokazana su bitna svojstva Cauchyjevog niza. Na samom kraju rada bavili smo se nizovima funkcija i konvergencijom po točkama
Abstract (english)
In this paper, we deal with sequences of real numbers and highlight important properties of sequences. First, the concepts of a sequences and a subsequences is defined. Most of the paper is focused on the convergence of sequences, which is one of the fundamental concepts of real analysis. The limit, boundedness, and monotonicity of sequences are defined, and essential theorems that connect these concepts with convergence are proven. Using the convergence of a sequence in a metric space, we characterized the closure of a set. It has been shown that the concept of a Cauchy sequence was introduced and important properties of Cauchy sequences were proven. At the very end of the paper, we dealt with sequences of functions and pointwise convergence.
Keywords
Keywords (english)
Languagecroatian
URN:NBNurn:nbn:hr:126:639233
Study programmeTitle: University Bachelor of Mathematics (univ. bacc. math.)
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
Created on2024-07-09 06:34:57