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undergraduate thesis
Eulerova diferencijalna jednadžba
2021. urn:nbn:hr:126:091037
Ledenčan, Robert
Josip Juraj Strossmayer University of Osijek
Department of Mathematics

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Ledenčan, R. (2021). Eulerova diferencijalna jednadžba (Undergraduate thesis). Osijek: Josip Juraj Strossmayer University of Osijek, Department of Mathematics. Retrieved from https://urn.nsk.hr/urn:nbn:hr:126:091037

Ledenčan, Robert. "Eulerova diferencijalna jednadžba." Undergraduate thesis, Josip Juraj Strossmayer University of Osijek, Department of Mathematics, 2021. https://urn.nsk.hr/urn:nbn:hr:126:091037

Ledenčan, Robert. "Eulerova diferencijalna jednadžba." Undergraduate thesis, Josip Juraj Strossmayer University of Osijek, Department of Mathematics, 2021. https://urn.nsk.hr/urn:nbn:hr:126:091037

Ledenčan, R. (2021). 'Eulerova diferencijalna jednadžba', Undergraduate thesis, Josip Juraj Strossmayer University of Osijek, Department of Mathematics, accessed 19 October 2024, https://urn.nsk.hr/urn:nbn:hr:126:091037

Ledenčan R. Eulerova diferencijalna jednadžba [Undergraduate thesis]. Osijek: Josip Juraj Strossmayer University of Osijek, Department of Mathematics; 2021 [cited 2024 October 19] Available at: https://urn.nsk.hr/urn:nbn:hr:126:091037

R. Ledenčan, "Eulerova diferencijalna jednadžba", Undergraduate thesis, Josip Juraj Strossmayer University of Osijek, Department of Mathematics, Osijek, 2021. Available at: https://urn.nsk.hr/urn:nbn:hr:126:091037

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Metadata
TitleEulerova diferencijalna jednadžba
Title (english)Euler Differential Equation
AuthorRobert Ledenčan
MentorKrešimir Burazin (mentor)
GranterJosip Juraj Strossmayer University of Osijek
Department of Mathematics
Osijek
Defense date and country2021-09-06, Croatia
Scientific / art field,
discipline and subdiscipline		NATURAL SCIENCES
Mathematics
Mathematical Analysis
Abstract
U ovom radu upoznat ćemo se sa Eulerovom diferencijalnom jednadžbom. Ova se jednadžba često pojavljuje u raznim granama znanosti poput fizike, inženjerstva i računalne znanosti. Primjerice, pojavljuje se u analizi quicksort i stabla pretraživanja te u rješavanju Laplaceove jednadžbe u polarnim koordinatama. S obzirom da Eulerova jednadžba pripada linearnim diferencijalnim jednadžbama n-tog reda, u radućemo definirati osnovne pojmove i iskazati teoreme vezane za sustave običnih diferencijalnih jednadžbi 1. reda i linearne obične diferencijalne jednadžbe n-tog reda. Nakon toga, denirat ćemo Eulerovu diferencijalnu jednadžbu i pokazati na koji način određujemo njezina rješenja. U nastavku ćemo klasificirati vrste singularnih točaka diferencijalnih jednadžbi i pokazati metodu za pronalazak rješenja u okolini regularnih singularnih točaka. Na kraju ćemo navesti neke od primjena Eulerove diferencijalne jednadžbe u fizici.
Abstract (english)
In this paper, we shall introduce the Euler's dierential equation. This equation often appears in various branches of science such as physics, engineering, and computer science. For example, it appears in analysis of quicksort and search trees and when solving the Laplace equation in polar coordinates. Given that the Euler's equation belongs to the linear dierential equations of nth order, in this paper we will dene basic concepts and express theorems related to systems of ordinary dierential equations of the 1st order and linear ordinary dierential equations of nth order. After that, we will dene Euler's dierential equation and show how to determine its solutions. In the following, we will classify the types of singular points of dierential equations and show a method for nding solutions in the neighborhood of regular singular points. Finally, we shall list some of the applications of Euler's dierential equation in physics.
Keywords
Keywords (english)
Languagecroatian
URN:NBNurn:nbn:hr:126:091037
Study programmeTitle: University undergraduate study programme in mathematics
Study programme type: university
Study level: undergraduate
Academic / professional title: sveučilišni/a prvostupnik/prvostupnica (baccalaureus/baccalaurea) matematike (sveučilišni/a prvostupnik/prvostupnica (baccalaureus/baccalaurea) matematike)
Type of resourceText
File originBorn digital
Access conditionsOpen access
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Created on2021-10-05 10:01:10