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master's thesis
Konformna preslikavanja u kompleksnoj ravnini
2021. urn:nbn:hr:126:006538
Katić, Marija
Josip Juraj Strossmayer University of Osijek
Department of Mathematics

Cite this document

Katić, M. (2021). Konformna preslikavanja u kompleksnoj ravnini (Master's thesis). Osijek: Josip Juraj Strossmayer University of Osijek, Department of Mathematics. Retrieved from https://urn.nsk.hr/urn:nbn:hr:126:006538

Katić, Marija. "Konformna preslikavanja u kompleksnoj ravnini." Master's thesis, Josip Juraj Strossmayer University of Osijek, Department of Mathematics, 2021. https://urn.nsk.hr/urn:nbn:hr:126:006538

Katić, Marija. "Konformna preslikavanja u kompleksnoj ravnini." Master's thesis, Josip Juraj Strossmayer University of Osijek, Department of Mathematics, 2021. https://urn.nsk.hr/urn:nbn:hr:126:006538

Katić, M. (2021). 'Konformna preslikavanja u kompleksnoj ravnini', Master's thesis, Josip Juraj Strossmayer University of Osijek, Department of Mathematics, accessed 23 December 2024, https://urn.nsk.hr/urn:nbn:hr:126:006538

Katić M. Konformna preslikavanja u kompleksnoj ravnini [Master's thesis]. Osijek: Josip Juraj Strossmayer University of Osijek, Department of Mathematics; 2021 [cited 2024 December 23] Available at: https://urn.nsk.hr/urn:nbn:hr:126:006538

M. Katić, "Konformna preslikavanja u kompleksnoj ravnini", Master's thesis, Josip Juraj Strossmayer University of Osijek, Department of Mathematics, Osijek, 2021. Available at: https://urn.nsk.hr/urn:nbn:hr:126:006538

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Metadata
TitleKonformna preslikavanja u kompleksnoj ravnini
Title (english)Conformal Mappings in Complex Plain
AuthorMarija Katić
MentorTomislav Marošević (mentor)
Committee memberSuzana Miodragović (predsjednik povjerenstva)
Committee memberDarija Marković (član povjerenstva)
Committee memberIvan Soldo (član povjerenstva)
GranterJosip Juraj Strossmayer University of Osijek
Department of Mathematics
Osijek
Defense date and country2021-10-29, Croatia
Scientific / art field,
discipline and subdiscipline		NATURAL SCIENCES
Mathematics
Mathematical Analysis
Abstract
U radu se razmatraju kompleksne funkcije koja su konformna preslikavanja. Posebno se promatra Möbiusova transformacija, koja kao kompleksna funkcija jeste konformno preslikavanje, a znamo da ono čuva orijentaciju i kuteve što smo prikazali na primjerima. Neki od osnovnih primjera Möbiusove transformacije su translacija, afina (linearna) funkcija i rotacija. Möbiusova transformacija je bijekcija te je prikazujemo kao kompoziciju homotetije, translacije, inverzije te rotacije. Dokazali smo i da je kompozicija Möbiusovih transformacija Möbiusova transformacija. Tvrdnje smo ilustrirali na primjerima. Naveli smo i neka druga svojstva Möbiusove transformacije, kao primjerice svojstvo da je Möbiusova transformacija jednoznačno određena sa svojim vrijednostima u tri točke. Primjena Möbiusove transformacije važna je i u mnogim područjima znanosti, jer se temelji na preslikavanju sfere na kompleksnu ravninu. U radu smo opisali neka područja u kojima je koristimo.
Abstract (english)
In this work complex functions that are conformal mappings are considered. The Mobius transformation is conformal mapping such that preserves the orientation and angles which is shown by the examples. Some of examples explained in this work are translation, linear function and rotation. The Mobius transformation is bijection and we can present it as a composition of homothety, translation, inversion and rotation. It is proved that the composition of Mobius transformation is also a Mobius transformation through examples. Some other properties of the Mobius transformation are also mentioned. For example, the Mobius transformation is uniquely determined with its values at 3 points. The application of the Mobius transformation is also important in many fields of science since it is based on the mapping of a sphere to a complex plane. Applications in some fields of science are described in this work.
Keywords
Keywords (english)
Languagecroatian
URN:NBNurn:nbn:hr:126:006538
Study programmeTitle: Mathematics; specializations in: Financial and Statistical Mathematics, Mathematics and Computer Science, Industrial and Applied Mathematics
Course: Financial and Statistical Mathematics
Study programme type: university
Study level: graduate
Academic / professional title: magistar/magistra matematike (magistar/magistra matematike)
Type of resourceText
File originBorn digital
Access conditionsOpen access
Terms of useLicence In copyright icon
Created on2021-11-02 11:24:34