Uporaba diferencialnih enačb pri mešanju tekočin

magistrsko delo

Tina Špringer (Author), Marko Slapar (Mentor)

Abstract

V magistrskem delu bo najprej predstavljena osnovna teorija sistema linearnih diferencialnih enačbe prvega reda. Bistveni del bo reševanje ustreznega homogenega sistema, kjer bomo vpeljali pojem fundamentalne matrike, predstavili način reševanja v primeru diagonalizabilnih sistemov in način reševanja s pomočjo eksponentne funkcije matrike v primeru splošnih sistemov. Vse to pa bomo v nadaljevanju uporabili pri primerih modeliranja količine topljenca, ko se raztopina pretaka v sistemih posod, povezanih s cevmi. Obravnavali bomo zvezdno, dvosmerno linearno, krožno ter odprto stopničasto razporeditev posod.

Keywords

linearna diferencialna enačba;homogeni sistem;fundamentalna matrika;krožne matrike;problem mešanja;

Data

Language:	Slovenian
Year of publishing:	2020
Typology:	2.09 - Master's Thesis
Organization:	UL PEF - Faculty of Education
Publisher:	[T. Špringer]
UDC:	51(043.2)
COBISS:	15062019
Views:	351
Downloads:	61
Average score:	0 (0 votes)
Metadata:

Other data

Secondary language:	English
Secondary title:	Use of differential equations at mixing liquids
Secondary abstract:	In this masters thesis, we first present the basic theory of systems of linear differential equations of first order. We mostly focus on solving the appropriate homogeneous system, introduce the fundamental matrix and show how to solve a diagonalizable system and how to solve a general system using the exponential function on matrices. We apply the theory on the problem of modeling the concentration of a solvent in a solution that flows inside a system of tanks connected by pipes. We will look at star arrangements, linear arrangements and circular arrangements of tanks.
Secondary keywords:	mathematics;matematika;
File type:	application/pdf
Type (COBISS):	Master's thesis/paper
Thesis comment:	Univ. v Ljubljani, Pedagoška fak., Poučevanje, Predmetno poučevanje
Pages:	43 str.
ID:	11670539