Laplaceova transformacija

master's thesis

• Title (english): Laplace transform
• Author: Lara Ćuća
• Mentor: Ljiljana Arambašić (mentor)
• Committee member: Ljiljana Arambašić (predsjednik povjerenstva)
• Committee member: Matija Bašić (član povjerenstva)
• Committee member: Goran Radunović (član povjerenstva)
• Committee member: Goran Igaly (član povjerenstva)
• Granter: University of Zagreb; Faculty of Science; (Department of Mathematics); Zagreb
• Defense date and country: 2023-09-27, Croatia
• Scientific / art field, discipline and subdiscipline: NATURAL SCIENCES; Mathematics

Abstract

Budući da je Laplaceova transformacija jedna od najvažnijih integralnih transformacija, cilj rada je upoznati se s Laplaceovom transformacijom i njezinim osnovnim svojstvima. Analiziramo na koje funkcije ju možemo primijeniti i na koji način efikasno odrediti Laplaceovu transformaciju nekih funkcija, te kako nam neka njezina svojstva mogu u tome pomoći. Također, bavimo se i pitanjem postojanja i metodama određivanja inverza Laplaceove transformacije. Na samom kraju rada, detaljnije proučavamo jednu primjenu Laplaceove transformacije u matematici, a odnosi se na rješavanje linearnih diferencijalnih jednadžbi.

Abstract (english)

Since the Laplace transform is one of the most important integral transforms, the aim of this paper is to introduce ourselves with Laplace transform and its basic properties. We analyze which functions we can apply it on and how to efficiently determine the Laplace transform of some functions, and how some of its properties can help us. Also, we deal with the question of existence and methods of determining the inverse of the Laplace transform. At the end of the paper, we study in more detail one application of the Laplace transform in mathematics, related to solving linear differential equations.

• Keywords: integralne transformacije; inverz Laplaceove transformacije; linearne diferencijalne jednadžbe
• Keywords (english): integral transforms; inverse of the Laplace transform; linear differential equations
• Language: croatian
• URN:NBN: urn:nbn:hr:217:200517
• Study programme: Title: Mathematics Education; specializations in: Mathematics Education; Course: Mathematics Education; Study programme type: university; Study level: graduate; Academic / professional title: sveučilišni magistar edukacije matematike (sveučilišni magistar edukacije matematike)
• Type of resource: Text
• File origin: Born digital
• Access conditions: Open access
• Created on: 2024-01-30 13:36:06