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master's thesis
Elementarni aspekti diferencijabilnosti
Zagreb: University of Zagreb, Faculty of Science, 2018. urn:nbn:hr:217:288985
Protulipac, Alena
University of Zagreb
Faculty of Science
Department of Mathematics

Institutional repository: Repository of the Faculty of Science

Cite this document

Protulipac, A. (2018). Elementarni aspekti diferencijabilnosti (Master's thesis). Zagreb: University of Zagreb, Faculty of Science. Retrieved from https://urn.nsk.hr/urn:nbn:hr:217:288985

Protulipac, Alena. "Elementarni aspekti diferencijabilnosti." Master's thesis, University of Zagreb, Faculty of Science, 2018. https://urn.nsk.hr/urn:nbn:hr:217:288985

Protulipac, Alena. "Elementarni aspekti diferencijabilnosti." Master's thesis, University of Zagreb, Faculty of Science, 2018. https://urn.nsk.hr/urn:nbn:hr:217:288985

Protulipac, A. (2018). 'Elementarni aspekti diferencijabilnosti', Master's thesis, University of Zagreb, Faculty of Science, accessed 30 November 2024, https://urn.nsk.hr/urn:nbn:hr:217:288985

Protulipac A. Elementarni aspekti diferencijabilnosti [Master's thesis]. Zagreb: University of Zagreb, Faculty of Science; 2018 [cited 2024 November 30] Available at: https://urn.nsk.hr/urn:nbn:hr:217:288985

A. Protulipac, "Elementarni aspekti diferencijabilnosti", Master's thesis, University of Zagreb, Faculty of Science, Zagreb, 2018. Available at: https://urn.nsk.hr/urn:nbn:hr:217:288985

Metadata
TitleElementarni aspekti diferencijabilnosti
AuthorAlena Protulipac
MentorZvonko Iljazović (mentor)
Committee memberZvonko Iljazović (predsjednik povjerenstva)
Committee memberJuraj Šiftar (član povjerenstva)
Committee memberTina Bosner (član povjerenstva)
Committee memberMaja Resman (član povjerenstva)
GranterUniversity of Zagreb
Faculty of Science
(Department of Mathematics)
Zagreb
Defense date and country2018-07-17, Croatia
Scientific / art field,
discipline and subdiscipline		NATURAL SCIENCES
Mathematics
Abstract
U prvom poglavlju se definira neprekidnost funkcije u točki te je dan primjer funkcije koja je neprekidna u svakoj točki osim u jednoj. Zatim se definira gomilište skupa i limes funkcije te su navedeni primjeri vezani uz to. Navedeni su rezultati koji povezuju neprekidnost funkcije i limes funkcije. Zatim se definira niz u \(\mathbb{R}\) te konvergencija nizova. Iskazane su i dokazane neke propozicije vezane uz konvergenciju nizova. Na kraju poglavlja dokazano je da su zbroj i umnožak neprekidnih funkcija neprekidne funkcije. Drugo poglavlje počinje definicijom i primjerima derivabilnosti funkcije. Slijede iskazi i dokazi propozicija o derivaciji zbroja, umnoška i kvocijenta funkcija te iskazi i dokazi propozicija koje povezuju neprekidnost i derivabilnost funkcija te konvergenciju nizova. Nakon toga se dokažu propozicije o neprekidnosti i derivabilnosti kompozicije funkcija. Zatim slijede svojstva inverznih funkcija.
Abstract (english)
In the first chapter we study the notion of continuous function. Then we examine accumulation points of a set and limits of function. We also give results about the relationship between the continuity of a function and a limit of a function. We study convergent sequences in \(\mathbb{R}\). At the end of the first chapter we prove that the sum and the product of continuous functions are continuous functions. In the second chapter we study derivable functions. We examine derivability of the sum, the product and the quotient of the functions and we prove some results which connect continuity and derivability of functions and convergent sequences. We examine continuity and derivability of the composition of functions. We also examine derivability of inverse functions.
Keywords
Keywords (english)
Languagecroatian
URN:NBNurn:nbn:hr:217:288985
Study programmeTitle: 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 resourceText
File originBorn digital
Access conditionsOpen access
Terms of useLicence In copyright icon
Created on2019-06-13 10:21:14