Vizualizacija kompleksnih funkcija

master's thesis

• Author: Lucija Šömen
• Mentor: Ivica Nakić (mentor)
• Committee member: Ivica Nakić (predsjednik povjerenstva)
• Committee member: Mladen Vuković (član povjerenstva)
• Committee member: Igor Pažanin (član povjerenstva)
• Committee member: Nikola Sandrić (član povjerenstva)
• Granter: University of Zagreb; Faculty of Science; (Department of Mathematics); Zagreb
• Defense date and country: 2017-09-26, Croatia
• Scientific / art field, discipline and subdiscipline: NATURAL SCIENCES; Mathematics

Abstract

Kompleksne funkcije su srž kompleksne analize koja igra važnu ulogu u raznim granama matematike poput algebre, geometrije, teorije brojeva te u praktičnim primjenama matematike kao što su fizika i inženjerstvo. Realne funkcije možemo lako prikazati pomoću dvodimenzionalnih grafova te je stoga prirodno da isto želimo i za kompleksne funkcije. S obzirom da se mi nalazimo u trodimenzionalnom prostoru, a za prikaz kompleksnih funkcija su potrebne četiri dimenzije jasno je da moramo nekako zamijeniti tu četvrtu dimenziju za što nam je prirodan izbor boja. Ovim radom dan je pregled nekoliko vizualnih tehnika za prikaz kompleksnih funkcija kompleksne varijable poput analitičkih pejsaža, bojanja domene i faznih portreta te je prikazana implementacija tih tehnika na primjerima funkcija.

Abstract (english)

Complex functions are the core of complex analysis which plays an important role in various branches of mathematics such as algebra, geometry, number theory and in practical applications of mathematics such as physics and engineering. Real functions can be easily represented by two-dimensional plots so it's only natural that we wish to do the same with complex functions. Considering that we live in three spatial dimensions and to depict complex functions we need four dimensions, it is clear that we need to find a substitute for the fourth dimension for which the natural choice is color. With this graduate work we are given an overview of several visual techniques for depicting complex functions of complex variable like analytic landscapes, domain coloring and phase portraits. Furthermore we are shown their implementation on different examples of complex functions.

• Keywords: kompleksne funckije; kompleksna analiza; vizualne tehnike prikaza; analitički pejsaž; bojanje domene; fazni portret
• Keywords (english): complex function; complex analysis; visual techniques of depiction; analytic landscapes; domain coloring; phase portraits
• Language: croatian
• URN:NBN: urn:nbn:hr:217:119310
• Study programme: Title: Computer Science and Mathematics; Study programme type: university; Study level: graduate; Academic / professional title: magistar/magistra računarstva i matematike (magistar/magistra računarstva i matematike)
• Type of resource: Text
• File origin: Born digital
• Access conditions: Open access
• Created on: 2018-03-26 12:15:03