Apsolutna vrijednost broja

master's thesis

• Author: Danka Jelenčić
• Mentor: Maja Starčević (mentor)
• Committee member: Maja Starčević (predsjednik povjerenstva)
• Committee member: Eduard Marušić-Paloka (član povjerenstva)
• Committee member: Dijana Ilišević (član povjerenstva)
• Committee member: Mladen Jurak (član povjerenstva)
• Granter: University of Zagreb; Faculty of Science; (Department of Mathematics); Zagreb
• Defense date and country: 2015-09-24, Croatia
• Scientific / art field, discipline and subdiscipline: NATURAL SCIENCES; Mathematics

Abstract

U ovom diplomskom rada proučavana je apsolutna vrijednost broja. U prvom poglavlju opisano je uvođenje pojma apsolutne vrijednosti realnog broja u nastavi matematike kao i rješavanje jednadžbi, odnosno nejednadžbi s apsolutnom vrijednošću u srednjim školama. U drugom poglavlju proučavana su svojstva funkcije apsolutna vrijednost te njeno ponašanje pri raznim matematičkim operacijama. U trećem poglavlju proučavane su neke vrste jednadžbi s apsolutnom vrijednošću te krivulje koje ih predstavljaju. Apsolutna vrijednost kompleksnog broja obrađena je u četvrtom poglavlju. Počevši od samog uvođenja kompleksnih brojeva u srednjim školama, preko modula kompleksnog broja, poglavlje završava trigonometrijskim prikazom kompleksnog broja. Peto poglavlje čine odabrani riješeni zadaci s matematičkih natjecanja i državne mature. U posljednjem šestom poglavlju proučavana je veza između apsolutne vrijednosti i norme u nekim vektorskim prostorima.

Abstract (english)

In this master’s thesis absolute value of a number has been analysed. The first chapter describes an introduction of the term absolute value (modulus) in mathematics teaching and solving equations and inequalities with absolute value in high school. The second chapter studies the properties of the absolute value function and its behaviour by different mathematical operations. In the third chapter, some equations with absolute value and curves that represent them, have been analysed. The absolute value of a complex number has been analysed in the fourth chapter. Starting from introducing complex numbers in high school, going through modulus of complex numbers, the chapter ends with the trigonometric form of complex numbers. The fifth chapter contains solved problems from mathematical competitions and national leaving exams. In the last, sixth chapter, the connection between absolute value and norms in some vector spaces has been studied.

• Keywords: apsolutna vrijednost broja; nastava matematike; srednja škola; rješavanje jednadžbi; rješavanje nejednadžbi; kompleksni broj; trigonometrijski prikaz kompleksnog broja; matematička natjecanja; državna matura; vektorski prostori
• Keywords (english): absolute value of a number; teaching mathematics; high school; middle school; solving equations; solving inequalities; complex number; trigonometric form of complex number; mathematical competitions; national leaving exams; vector spaces
• Language: croatian
• URN:NBN: urn:nbn:hr:217:888973
• 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: Access restricted to students and staff of home institution
• Created on: 2019-01-31 13:13:51