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master's thesis
Modeliranje običnim diferencijalnim jednadžbama
Zagreb: University of Zagreb, Faculty of Science, 2018. urn:nbn:hr:217:548373
Karačić, Paula
University of Zagreb
Faculty of Science
Department of Mathematics

Institutional repository: Repository of the Faculty of Science

Cite this document

Karačić, P. (2018). Modeliranje običnim diferencijalnim jednadžbama (Master's thesis). Zagreb: University of Zagreb, Faculty of Science. Retrieved from https://urn.nsk.hr/urn:nbn:hr:217:548373

Karačić, Paula. "Modeliranje običnim diferencijalnim jednadžbama." Master's thesis, University of Zagreb, Faculty of Science, 2018. https://urn.nsk.hr/urn:nbn:hr:217:548373

Karačić, Paula. "Modeliranje običnim diferencijalnim jednadžbama." Master's thesis, University of Zagreb, Faculty of Science, 2018. https://urn.nsk.hr/urn:nbn:hr:217:548373

Karačić, P. (2018). 'Modeliranje običnim diferencijalnim jednadžbama', Master's thesis, University of Zagreb, Faculty of Science, accessed 23 December 2024, https://urn.nsk.hr/urn:nbn:hr:217:548373

Karačić P. Modeliranje običnim diferencijalnim jednadžbama [Master's thesis]. Zagreb: University of Zagreb, Faculty of Science; 2018 [cited 2024 December 23] Available at: https://urn.nsk.hr/urn:nbn:hr:217:548373

P. Karačić, "Modeliranje običnim diferencijalnim jednadžbama", Master's thesis, University of Zagreb, Faculty of Science, Zagreb, 2018. Available at: https://urn.nsk.hr/urn:nbn:hr:217:548373

Metadata
TitleModeliranje običnim diferencijalnim jednadžbama
AuthorPaula Karačić
MentorIgor Pažanin (mentor)
Committee memberIgor Pažanin (predsjednik povjerenstva)
Committee memberNikola Sandrić (član povjerenstva)
Committee memberMarko Tadić (član povjerenstva)
Committee memberDijana Ilišević (član povjerenstva)
GranterUniversity of Zagreb
Faculty of Science
(Department of Mathematics)
Zagreb
Defense date and country2018-07-16, Croatia
Scientific / art field,
discipline and subdiscipline		NATURAL SCIENCES
Mathematics
Abstract
Cilj ovog rada je prezentirati različite matematičke modele iz područja kemije, fizike i biologije opisane običnim diferencijalnim jednadžbama. U prvom, uvodnom, poglavlju, upoznali smo se s osnovnim konceptima matematičkog modeliranja te svojstvima običnih diferencijalnih jednadžbi koje ćemo koristiti u nastavku. U drugom poglavlju, izvodom niza matematičkih modela promatrali smo mijenjanje veličine populacije. U trećem poglavlju smo koristeći zakon o djelovanju masa promatrali kinetiku enzima kroz tri različite reakcije: kompetitivna inhibicija, alosterička inhibicija i kooperativnost. U četvrtom poglavlju izveli smo razne modele bolesti populacije te iznijeli zaključke o uvjetima širenja zaraze.
Abstract (english)
The purpose of this work is to present various mathematical models in the field of chemistry, physics and biology, all of them described by ordinary differential equations. In the first, introductory, chapter, we recalled the basic concepts of mathematical modeling and the properties of ordinary differential equations that we used in the sequel. In the second chapter, we have studied the population dynamics by formally deriving several mathematical models. In the third chapter, we have addressed the enzyme kinetics by employing the law of mass action via three different reactions: competitive inhibition, allosteric inhibition and cooperativity. In the fourth chapter, we have derived various models of population diseases and made conclusions regarding the conditions of spreading the disease.
Keywords
Keywords (english)
Languagecroatian
URN:NBNurn:nbn:hr:217:548373
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 conditionsAccess restricted to students and staff of home institution
Terms of useLicence In copyright icon
Created on2018-11-29 13:07:51