Modeliranje običnim diferencijalnim jednadžbama

master's thesis

• Author: Paula Karačić
• Mentor: Igor Pažanin (mentor)
• Committee member: Igor Pažanin (predsjednik povjerenstva)
• Committee member: Nikola Sandrić (član povjerenstva)
• Committee member: Marko Tadić (član povjerenstva)
• Committee member: Dijana Ilišević (član povjerenstva)
• Granter: University of Zagreb; Faculty of Science; (Department of Mathematics); Zagreb
• Defense date and country: 2018-07-16, 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... More 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. Less

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... More 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. Less

• Keywords: matematičko modeliranje; kinetika enzima; modeli bolesti populacije; uvjeti širenja zaraze
• Keywords (english): mathematical modeling; enzyme kinetics; models of population diseases; conditions of spreading the disease
• Language: croatian
• URN:NBN: urn:nbn:hr:217:548373
• Study programme: Title: Finance and Business Mathematics; Study programme type: university; Study level: graduate; Academic / professional title: magistar/magistra matematike (magistar/magistra matematike)
• Type of resource: Text
• File origin: Born digital
• Access conditions: Access restricted to students and staff of home institution
• Created on: 2018-11-29 13:07:51