Laplaceova transformacija

master's thesis

• Author: Valentina Zemlić
• Mentor: Maja Resman (mentor)
• Committee member: Maja Resman (predsjednik povjerenstva)
• Committee member: Sanja Varošanec (član povjerenstva)
• Committee member: Andrej Dujella (član povjerenstva)
• Committee member: Filip Najman (član povjerenstva)
• Granter: University of Zagreb; Faculty of Science; (Department of Mathematics); Zagreb
• Defense date and country: 2017-11-28, Croatia
• Scientific / art field, discipline and subdiscipline: NATURAL SCIENCES; Mathematics

Abstract

U diplomskom radu bavimo se Laplaceovom transformacijom. U prvom poglavlju proučavamo Stieltjesov integral, posebno uvjete postojanja i bitna svojstva. U drugom poglavlju bavimo se uvođenjem i definiranjem Laplaceove transformacije te analizom područja konvergencije i analitičnosti Laplaceovog transformata. Nakon toga, određujemo Laplaceove transformate elementarnih funkcija i pokazujemo osnovna svojstva Laplaceove transformacije. Treće poglavlje posvećeno je inverznoj Laplaceovoj transformaciji. Na samom kraju, u četvrtom poglavlju dajemo jednu primjenu Laplaceove transformacije u rješavanju linearnih diferencijalnih jednadžbi s konstanstnim koeficijentima.

Abstract (english)

In this thesis we study the Laplace transform. In the first chapter we analyze the Stieltjes integral, especially the conditions under which the Stieltjes integral exists and elementary properties of the Siteltjes integral. In the second chapter we introduce and define the Laplace transform, analyze the area of convergence and analytic properties of the Laplace transform. After that, we compute the Laplace transform of elementary functions and observe elementary properties of the Laplace transform. The third chapter is dedicated to the inverse Laplace transform. At the end, in the fourth chapter, we present one application of the Laplace transform in solving linear differential equations with constant coefficients.

• Keywords: Laplaceova transformacija; Stieltjesov integral
• Keywords (english): Laplace transform; Stieltjes integral
• Language: croatian
• URN:NBN: urn:nbn:hr:217:628980
• Study programme: Title: Mathematics Education; specializations in: Mathematics Education; Course: Mathematics Education; Study programme type: university; Study level: graduate; Academic / professional title: magistar/magistra edukacije matematike (magistar/magistra edukacije matematike)
• Type of resource: Text
• File origin: Born digital
• Access conditions: Open access
• Created on: 2018-07-04 13:13:48