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Laplace transform and linear differential equations

Polona Šenkinc (2018) Laplace transform and linear differential equations. MSc thesis.

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    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.

    Item Type: Thesis (MSc thesis)
    Keywords: Laplace transform, improper integral, step function, impulse function, differential equation with discontinuous forcing function
    Number of Pages: 50
    Language of Content: Slovenian
    Mentor / Comentors:
    Mentor / ComentorsIDFunction
    izr. prof. dr. Marko SlaparMentor
    Link to COBISS: http://www.cobiss.si/scripts/cobiss?command=search&base=50126&select=(ID=12086345)
    Institution: University of Ljubljana
    Department: Faculty of Education
    Item ID: 5224
    Date Deposited: 20 Aug 2018 14:14
    Last Modified: 20 Aug 2018 14:14
    URI: http://pefprints.pef.uni-lj.si/id/eprint/5224

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