Elementarne nejednakosti i primjene

master's thesis

• Title (english): Elementary inequalities and applications
• Author: Eva Razum
• Mentor: Ana Prlić (mentor)
• Mentor: Vedran Kojić (sumentor)
• Committee member: Ana Prlić (predsjednik povjerenstva)
• Committee member: Vedran Kojić (član povjerenstva)
• Committee member: Vanja Wagner (član povjerenstva)
• Committee member: Matko Ljulj (član povjerenstva)
• Granter: University of Zagreb; Faculty of Science; (Department of Mathematics); Zagreb
• Defense date and country: 2023-09-25, 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: problem optimizacije u matematici i ekonomiji; diferencijalni račun; aritmetičko-geometrijska nejednakost; Cauchy-Schwarz- Buniakowskyjeva nejednakost; Bernoullijeva nejednakost; EOQ model
• Keywords (english): optimization problem in mathematics and economics; differential calculus; arithmetic-geometric inequality; Cauchy-Schwarz-Buniakowsky inequality; Bernoulli’s inequality; EOQ model
• Language: croatian
• URN:NBN: urn:nbn:hr:217:272015
• Study programme: Title: 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 resource: Text
• File origin: Born digital
• Access conditions: Open access
• Created on: 2023-10-24 09:13:39