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master's thesis
Stabilnost diferencijalnih jednadžbi
Zagreb: University of Zagreb, Faculty of Science, 2016. urn:nbn:hr:217:572206
Vopel, Ramona Mihaela
University of Zagreb
Faculty of Science
Department of Mathematics

Institutional repository: Repository of the Faculty of Science

Cite this document

Vopel, R. M. (2016). Stabilnost diferencijalnih jednadžbi (Master's thesis). Zagreb: University of Zagreb, Faculty of Science. Retrieved from https://urn.nsk.hr/urn:nbn:hr:217:572206

Vopel, Ramona Mihaela. "Stabilnost diferencijalnih jednadžbi." Master's thesis, University of Zagreb, Faculty of Science, 2016. https://urn.nsk.hr/urn:nbn:hr:217:572206

Vopel, Ramona Mihaela. "Stabilnost diferencijalnih jednadžbi." Master's thesis, University of Zagreb, Faculty of Science, 2016. https://urn.nsk.hr/urn:nbn:hr:217:572206

Vopel, R. M. (2016). 'Stabilnost diferencijalnih jednadžbi', Master's thesis, University of Zagreb, Faculty of Science, accessed 23 November 2024, https://urn.nsk.hr/urn:nbn:hr:217:572206

Vopel RM. Stabilnost diferencijalnih jednadžbi [Master's thesis]. Zagreb: University of Zagreb, Faculty of Science; 2016 [cited 2024 November 23] Available at: https://urn.nsk.hr/urn:nbn:hr:217:572206

R. M. Vopel, "Stabilnost diferencijalnih jednadžbi", Master's thesis, University of Zagreb, Faculty of Science, Zagreb, 2016. Available at: https://urn.nsk.hr/urn:nbn:hr:217:572206

Metadata
TitleStabilnost diferencijalnih jednadžbi
AuthorRamona Mihaela Vopel
MentorLavoslav Čaklović (mentor)
Committee memberLavoslav Čaklović (predsjednik povjerenstva)
Committee memberDražen Adamović (član povjerenstva)
Committee memberPavle Pandžić (član povjerenstva)
Committee memberMirko Primc (član povjerenstva)
GranterUniversity of Zagreb
Faculty of Science
(Department of Mathematics)
Zagreb
Defense date and country2016-09-27, Croatia
Scientific / art field,
discipline and subdiscipline		NATURAL SCIENCES
Mathematics
Abstract
Diferencijalne jednadžbe imaju važnu ulogu u mnogim granama znanosti i industrije. Predmet proučavanja teorije stabilnosti je asimptotsko ponašanje funkcija u okviru familije rješenja, tj. da li se one približavaju ili razilaze jedna od druge na beskonačnom intervalu. U ovom radu smo se usredotočili na obične diferencijalne jednadžbe, njihovu podjelu, te osnovne teoreme o postojanju i jedinstvenosti rješenja. Dana je kratka povijest razvoja teorije stabilnosti , kao i različite definicije stabilnosti. Pod određenim uvjetima, pitanje koje teorija stabilnosti postavlja se može svesti na problem koji razmatra svojstvene vrijednosti matrica. U analizi stabilnosti rješenja običnih diferencijalnih jednadžbi smo koristili dvije metode, direktnu metodu te metodu linearizacije. Također smo pokazali neke od metoda određivanja Lyapunovih funkcija.
Abstract (english)
Differential equations have come to play an important role in many branches of science and industry. Stability theory addresses the following questions: Will a nearby orbit indefinitely stay close to a given orbit? Will it converge to the given orbit? We describe the ordinary differential equations, their classification, as well as the basic theorems of existence and uniqueness of solutions. A brief history of stability theory development is given, as well as stability definitions. Various criteria have been developed to prove stability or instability of an orbit. Under favorable circumstances, above question may be reduced to a well-studied problem involving eigenvalues of matrices. In stability analysis of solutions of ODE, two methods are used: direct method and method of linearisation. Some techniques are shown to determine the Lyapunov function.
Keywords
Keywords (english)
Languagecroatian
URN:NBNurn:nbn:hr:217:572206
Study programmeTitle: Finance and Business 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 on2019-02-19 15:19:11