prikaz prve stranice dokumenta Elementarne nejednakosti i primjene
  Download
PDF 261.52 KB
master's thesis
Elementarne nejednakosti i primjene
Zagreb: University of Zagreb, Faculty of Science, 2023. urn:nbn:hr:217:272015
Razum, Eva
University of Zagreb
Faculty of Science
Department of Mathematics

Institutional repository: Repository of the Faculty of Science

Cite this document

Razum, E. (2023). Elementarne nejednakosti i primjene (Master's thesis). Zagreb: University of Zagreb, Faculty of Science. Retrieved from https://urn.nsk.hr/urn:nbn:hr:217:272015

Razum, Eva. "Elementarne nejednakosti i primjene." Master's thesis, University of Zagreb, Faculty of Science, 2023. https://urn.nsk.hr/urn:nbn:hr:217:272015

Razum, Eva. "Elementarne nejednakosti i primjene." Master's thesis, University of Zagreb, Faculty of Science, 2023. https://urn.nsk.hr/urn:nbn:hr:217:272015

Razum, E. (2023). 'Elementarne nejednakosti i primjene', Master's thesis, University of Zagreb, Faculty of Science, accessed 07 October 2024, https://urn.nsk.hr/urn:nbn:hr:217:272015

Razum E. Elementarne nejednakosti i primjene [Master's thesis]. Zagreb: University of Zagreb, Faculty of Science; 2023 [cited 2024 October 07] Available at: https://urn.nsk.hr/urn:nbn:hr:217:272015

E. Razum, "Elementarne nejednakosti i primjene", Master's thesis, University of Zagreb, Faculty of Science, Zagreb, 2023. Available at: https://urn.nsk.hr/urn:nbn:hr:217:272015

Metadata
TitleElementarne nejednakosti i primjene
Title (english)Elementary inequalities and applications
AuthorEva Razum
MentorAna Prlić (mentor)
MentorVedran Kojić (sumentor)
Committee memberAna Prlić (predsjednik povjerenstva)
Committee memberVedran Kojić (član povjerenstva)
Committee memberVanja Wagner (član povjerenstva)
Committee memberMatko Ljulj (član povjerenstva)
GranterUniversity of Zagreb
Faculty of Science
(Department of Mathematics)
Zagreb
Defense date and country2023-09-25, Croatia
Scientific / art field,
discipline and subdiscipline		NATURAL SCIENCES
Mathematics
Abstract
Diplomski rad istražuje upotrebu metode nejednakosti kao alternativnog pristupa rješavanju problema optimizacije u matematici i ekonomiji. Najčešće se za pronalaženje minimuma ili maksimuma funkcija koristi diferencijalni račun, ali ta metoda može biti zahtjevna zbog provjera nužnih i dovoljnih uvjeta za ekstrem računanjem derivacija. U radu promatramo neke elementarne nejednakosti (aritmetičko-geometrijska nejednakost, Cauchy-Schwarz- Buniakowskyjeva nejednakost i Bernoullijeva nejednakost) i njihovu primjenu u matematici i ekonomiji te na matematičkim natjecanjima. Posebno se analizira primjena nejednakosti u ekonomiji, kao što su model ekonomične količine nabave (EOQ model) i usporedba jednostavnih i složenih kamata. Ovaj rad doprinosi boljem razumijevanju metode nejednakosti u rješavanju problema optimizacije te ističe njezine prednosti u odnosu na metode temeljene na diferencijalnom računu.
Abstract (english)
The paper explores the use of inequalities as an alternative method to solving optimization problems in mathematics and economics. The common approach to finding the minimum or maximum of a function is to use calculus, but this method can be demanding due to the derivation of necessary and sufficient conditions for the extrema using derivatives. In the paper, some elementary inequalities (arithmetic-geometric inequality, Cauchy-Schwarz-Buniakowsky inequality and Bernoulli’s inequality) and their application in mathematics, economics and in mathematical competitions are observed. The application of inequalities in economics, such as the economic order quantity model (EOQ model) and the comparison of simple and compound interest, are especially analyzed. This paper contributes to a better understanding of the use of inequalities in solving optimization problems, and highlights its advantages over methods based on calculus.
Keywords
Keywords (english)
Languagecroatian
URN:NBNurn:nbn:hr:217:272015
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 on2023-10-24 09:13:39