prikaz prve stranice dokumenta Obične diferencijalne jednadžbe i primjene
  Download
PDF 748.67 KB
master's thesis
Obične diferencijalne jednadžbe i primjene
Zagreb: University of Zagreb, Faculty of Science, 2023. urn:nbn:hr:217:356238
Janjatović, Irena
University of Zagreb
Faculty of Science
Department of Mathematics

Institutional repository: Repository of the Faculty of Science

Cite this document

Janjatović, I. (2023). Obične diferencijalne jednadžbe i primjene (Master's thesis). Zagreb: University of Zagreb, Faculty of Science. Retrieved from https://urn.nsk.hr/urn:nbn:hr:217:356238

Janjatović, Irena. "Obične diferencijalne jednadžbe i primjene." Master's thesis, University of Zagreb, Faculty of Science, 2023. https://urn.nsk.hr/urn:nbn:hr:217:356238

Janjatović, Irena. "Obične diferencijalne jednadžbe i primjene." Master's thesis, University of Zagreb, Faculty of Science, 2023. https://urn.nsk.hr/urn:nbn:hr:217:356238

Janjatović, I. (2023). 'Obične diferencijalne jednadžbe i primjene', Master's thesis, University of Zagreb, Faculty of Science, accessed 26 November 2024, https://urn.nsk.hr/urn:nbn:hr:217:356238

Janjatović I. Obične diferencijalne jednadžbe i primjene [Master's thesis]. Zagreb: University of Zagreb, Faculty of Science; 2023 [cited 2024 November 26] Available at: https://urn.nsk.hr/urn:nbn:hr:217:356238

I. Janjatović, "Obične diferencijalne jednadžbe i primjene", Master's thesis, University of Zagreb, Faculty of Science, Zagreb, 2023. Available at: https://urn.nsk.hr/urn:nbn:hr:217:356238

Metadata
TitleObične diferencijalne jednadžbe i primjene
Title (english)Ordinary differential equations and applications
AuthorIrena Janjatović
MentorMarko Radulović (mentor)
Committee memberMarko Radulović (predsjednik povjerenstva)
Committee memberGoran Radunović (član povjerenstva)
Committee memberIgor Pažanin (član povjerenstva)
Committee memberTomislav Pejković (član povjerenstva)
GranterUniversity of Zagreb
Faculty of Science
(Department of Mathematics)
Zagreb
Defense date and country2023-09-27, Croatia
Scientific / art field,
discipline and subdiscipline		NATURAL SCIENCES
Mathematics
Abstract
U ovom diplomskom radu promatrali smo kako diferencijalnim jednadžama i sustavima možemo modelirati razne probleme. Izveli smo nekoliko modela, pronašli njihova rješenja i analizirali stabilnost rješenja. U prvom poglavlju smo definirali obične diferencijalne jednadžbe i sustave te naveli teoreme o egzistenciji, jedinstvenosti i stabilnosti rješenja. U drugom poglavlju smo modelirali i analizirali nekoliko modela korištenjem običnih diferencijalnih jednadžbi, dok smo u trećem poglavlju isto napravili korištenjem sustava diferencijalnih jednadžbi. Modelirali smo probleme društvene, biološke i financijske prirode. Promatrali smo kako eutanazijom i sterilizacijom kontrolirati pse lutalice, kako kapital i radna snaga utječu na proizvodnju, vremensko zadržavanje lijeka u krvotoku te promjenu broja zaraženih i osjetljivih pojedinaca za gripu i koleru. Vidjeli smo kako diferencijalne jednadžbe imaju široku primjenu u stvarnom svijetu i da su jako koristan alat za modeliranje promjena varijabli koje su nam od interesa u određenom problemu.
Abstract (english)
In this thesis, we looked at how we can model various problems with differential equations and systems. We performed several models, found their solutions and analyzed the stability of the solutions. In the first chapter, we defined ordinary differential equations and systems, and stated theorems on the existence, uniqueness and stability of solutions. In the second chapter we modeled and analyzed several models using ordinary differential equations, while in the third chapter we did the same using a system of differential equations. We modeled problems of a social, biological and financial nature. We observed how to control stray dogs by euthanasia and sterilization, how capital and labor affect production, the time retention of the drug in the bloodstream, and the change in the number of infected and susceptible individuals for influenza and cholera. We have seen that differential equations have wide application in the real world and that they are a very useful tool for modeling the changes of variables that are of interest to us in a particular problem.
Keywords
Keywords (english)
Languagecroatian
URN:NBNurn:nbn:hr:217:356238
Study programmeTitle: Financial and Business Mathematics
Study programme type: university
Study level: graduate
Academic / professional title: sveučilišni magistar matematike (sveučilišni magistar matematike)
Type of resourceText
File originBorn digital
Access conditionsOpen access
Terms of useLicence In copyright icon
Created on2024-02-01 13:35:04