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master's thesis
Funkcionalne jednadžbe u nastavi matematike
Zagreb: University of Zagreb, Faculty of Science, 2020. urn:nbn:hr:217:727653
Juras, Ružica
University of Zagreb
Faculty of Science
Department of Mathematics

Institutional repository: Repository of the Faculty of Science

Cite this document

Juras, R. (2020). Funkcionalne jednadžbe u nastavi matematike (Master's thesis). Zagreb: University of Zagreb, Faculty of Science. Retrieved from https://urn.nsk.hr/urn:nbn:hr:217:727653

Juras, Ružica. "Funkcionalne jednadžbe u nastavi matematike." Master's thesis, University of Zagreb, Faculty of Science, 2020. https://urn.nsk.hr/urn:nbn:hr:217:727653

Juras, Ružica. "Funkcionalne jednadžbe u nastavi matematike." Master's thesis, University of Zagreb, Faculty of Science, 2020. https://urn.nsk.hr/urn:nbn:hr:217:727653

Juras, R. (2020). 'Funkcionalne jednadžbe u nastavi matematike', Master's thesis, University of Zagreb, Faculty of Science, accessed 23 December 2024, https://urn.nsk.hr/urn:nbn:hr:217:727653

Juras R. Funkcionalne jednadžbe u nastavi matematike [Master's thesis]. Zagreb: University of Zagreb, Faculty of Science; 2020 [cited 2024 December 23] Available at: https://urn.nsk.hr/urn:nbn:hr:217:727653

R. Juras, "Funkcionalne jednadžbe u nastavi matematike", Master's thesis, University of Zagreb, Faculty of Science, Zagreb, 2020. Available at: https://urn.nsk.hr/urn:nbn:hr:217:727653

Metadata
TitleFunkcionalne jednadžbe u nastavi matematike
Title (english)Functional equations in mathematics teaching
AuthorRužica Juras
MentorLjiljana Arambašić (mentor)
Committee memberLjiljana Arambašić (predsjednik povjerenstva)
Committee memberIlja Gogić (član povjerenstva)
Committee memberAna Prlić (član povjerenstva)
Committee memberFranka Miriam Brückler (član povjerenstva)
GranterUniversity of Zagreb
Faculty of Science
(Department of Mathematics)
Zagreb
Defense date and country2020-09-30, Croatia
Scientific / art field,
discipline and subdiscipline		NATURAL SCIENCES
Mathematics
Abstract
Ovaj diplomski rad sastavljen je od četiri poglavlja. U prvom poglavlju dan je povijesni uvod u funkcionalne jednadžbe od njihove prve pojave pa do prvih rješenja, kao i kratke biografije matematičara koji su doprinijeli razvoju teorije funkcionalnih jednadžbi. Funkcionalne jednadžbe dviju varijabli tema su drugog poglavlja ovog diplomskog rada. Tu je proučavana Cauchyjeva funkcionalna jednadžba, Cauchyjeva eksponencijalna funkcionalna jednadžba te Jenesenova jednadžba. Glavna su tema trećeg poglavlja metode rješavanja funkcionalnih jednadžbi s jednom varijablom. Prezentirane su metoda zamjene varijable i metoda linearizacije. U posljednjem poglavlju riječ je o zadacima koji se javljaju u srednjoškolskim udžbenicima matematike ili na matematičkim natjecanjima. Na kraju je navedeno nekoliko primjera problema koji se reduciraju na osnovne funkcionalne jednadžbe, ali taj dio je primjeren za najdarovitije učenike jer je izvan nastavnog sadržaja.
Abstract (english)
This thesis consists of four chapters. In the first chapter, a historical introduction to functional equations from their first occurrences to the first solutions is presented, and short biographies of mathematicians who contributed to the development of theory of functional equations are given. The functional equations of two variables are the topic of the second chapter of this thesis. We studied the Cauchy functional equation, the Cauchy exponential functional equation and the Jensen functional equation. The main topic of the third chapter are the methods of solving functional equations with one variable. We presented the method of substitution and the linearization method. In the last chapter we deal with problems that appear in high school mathematics as well as in mathematical competitions. We end with several examples of problems which reduce to basic functional equations, but this is appropriate only for the most talented students since this is beyond high school curriculum
Keywords
Keywords (english)
Languagecroatian
URN:NBNurn:nbn:hr:217:727653
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 on2021-02-25 14:00:20