magistrsko delo
Polona Šenkinc (Author), Marko Slapar (Mentor)

Abstract

V magistrskem delu se bomo osredotočili na Laplaceovo transformacijo in si pogledali njeno uporabo. Na začetku bo na kratko predstavljeno življenje in delo Pierra Simona Laplacea, po katerem so Laplaceove transformacije dobile ime. V nadaljevanju bo predstavljen nepravi integral, ki ga pozneje tudi uporabimo pri definiciji Laplaceove transformacije. Prikazani bodo primeri izračunov transformacij za nekaj elementarnih funkcij, ki jih uporabljamo pri reševanju konkretnih nalog. Pri reševanju zapletenejših primerov so nam v pomoč lepe lastnosti Laplaceove transformacije, ki nam omogočijo lažje reševanje. Nekaj lastnosti bo predstavljenih v magistrskem delu. V nadaljevanju bo predstavljena stopničasta funkcija, ki jo pogosto srečamo tudi pri fiziki. Prav tako se pri fiziki velikokrat srečamo z impulzno funkcijo, predvsem pri električnem krogu in nihanju. Na koncu bo predvsem na primerih predstavljena uporaba Laplaceove transformacije pri reševanju linearnih diferencialnih enačb s konstantnimi koeficienti, pri diferencialni enačbi nihanja z nezvezno silo in uporaba Laplaceove transformacije v fiziki, in sicer v električnih vezjih in pri mehaniki.

Keywords

Laplaceova transformacija;nepravi integral;stopničasta funkcija;impulzna funkcija;diferencialna enačba nihanja z nezvezno silo;

Data

Language: Slovenian
Year of publishing:
Typology: 2.09 - Master's Thesis
Organization: UL PEF - Faculty of Education
Publisher: [P. Šenkinc]
UDC: 517.382(043.2)
COBISS: 12086345 Link will open in a new window
Views: 583
Downloads: 110
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Other data

Secondary language: English
Secondary title: Laplace transform and linear differential equations
Secondary abstract: In the master's thesis, we discuss the use of Laplace transforms. Before we start with the mathematical aspect we briefly look at Laplace’s history, that is his work and life in general. We continue by presenting improper integral, which we later use in the definition of the Laplace transforms. For some elementary functions we present examples of transformation calculations, frequently needed when solving some specific problems. It turns out that Laplace transforms have some nice properties which are useful when solving some difficult problems presented in the thesis. Furthermore, we take a look at the step function, often used in physics, and examine the impulse function used in physics when discussing the electric circuit or oscillation. In the end we, mostly through examples, look at the use of the Laplace transforms when solving linear differential equations with constant coefficients. We also consider its use in differential equation with discontinuous force function and in physics when discussing electric circuit or mechanics.
Secondary keywords: mathematics;matematika;
File type: application/pdf
Type (COBISS): Master's thesis/paper
Thesis comment: Univ. v Ljubljani, Pedagoška fak., Poučevanje, Predmetno poučevanje, Fizika in matematika
Pages: 50 str.
ID: 10954187