Geometrijska interpretacija kompleksnih funkcija

master's thesis

• Author: Antonia Bilaver
• Mentor: Ljiljana Arambašić (mentor)
• Committee member: Ljiljana Arambašić (predsjednik povjerenstva)
• Committee member: Ilja Gogić (član povjerenstva)
• Committee member: Ana Prlić (član povjerenstva)
• Committee member: Franka Miriam Brückler (član povjerenstva)
• Granter: University of Zagreb; Faculty of Science; (Department of Mathematics); Zagreb
• Defense date and country: 2020-09-30, Croatia
• Scientific / art field, discipline and subdiscipline: NATURAL SCIENCES; Mathematics

Abstract

U ovom diplomskom radu proučavali smo kompleksne funkcije kompleksne varijable i njihovu geometrijsku interpretaciju. Na početku smo rekli nešto o tome kako je došlo do razvoja kompleksne analize. Zatim smo definirali kompleksne funkcije kompleksne varijable i objasnili problem koji se javlja kod prikazivanja slika tih funkcija. Obično za prikaz slike kompleksnih funkcija koristimo dva dvodimenzionalna koordinatna sustava - jedan za domenu, drugi za kodomenu. Na taj način prikazali smo kako elementarne kompleksne funkcije preslikavaju različite podskupove domene. Na kraju smo opisali način prikazivanja kompleksnih funkcija pomoću boja koji nam omogućava uočavanje svojstava kompleksnih funkcija poput periodičnosti, ograničenosti, postojanje nultočaka, singulariteta, te kako se funkcija ponaša u beskonačnosti.

Abstract (english)

In this thesis we study complex functions of complex variable and their geometric interpretation. We begin with a very short historical development of complex analysis. Then, we give deffinition of complex functions of complex variable and explain the problem of presenting their images. Usually we use two two-dimensional coordinate systems - one for domain, the other for codomain, for presenting images of complex functions. In this manner, we show how elementary complex functions map different subsets of domain. Finally, we describe another way of representing complex functions using colors which can be helpful since it can show properties like periodicity, boundedness, zero points of a function, singularities of a function, and also behavior of a function at inffinity.

• Keywords: kompleksne funkcije kompleksne varijable; kompleksna analiza
• Keywords (english): complex functions of complex variable; complex analysis
• Language: croatian
• URN:NBN: urn:nbn:hr:217:168622
• 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: 2020-12-01 13:49:46