dc.contributor Boza Rocho, Santiago dc.contributor.author Satorres Almenara, Àngel dc.contributor.other Universitat Politècnica de Catalunya. Departament de Matemàtica Aplicada IV dc.date.accessioned 2016-09-08T11:17:29Z dc.date.available 2016-09-08T11:17:29Z dc.date.issued 2016-07 dc.identifier.uri http://hdl.handle.net/2117/89743 dc.description.abstract The objective of this thesis is to make a theoretical and formal study of the Fourier Transform and to introduce some of its many applications. We start studying the Fourier Transform in L^1 and L^2, its behavior respect to the convolution and the multidimensional generalization. This study will allow us to solve, analyze and understand more two of the most well-known and important Partial Differential Equations: the Heat equation and the Wave equation. Finally, we will introduce and study the most relevant properties of filters. In order to give the most general results and exploit the full potential of the Fourier Transform, we will introduce the distributions, their basic properties and the theory of the Fourier Transform for distributions. dc.language.iso eng dc.publisher Universitat Politècnica de Catalunya dc.rights.uri http://creativecommons.org/licenses/by-nc-nd/3.0/es/ dc.subject Àrees temàtiques de la UPC::Matemàtiques i estadística::Anàlisi matemàtica dc.subject.lcsh Fourier analysis dc.subject.other Fourier Transform dc.subject.other Partial Differential Equation dc.subject.other Wave equation dc.subject.other Heat equation dc.subject.other Distribution dc.subject.other Convolution dc.subject.other Filter dc.subject.other Schwartz Space dc.title Transformada de Fourier: aplicacions a la resolució d'equacions en derivades parcials dc.type Bachelor thesis dc.subject.lemac Fourier, Anàlisi de dc.subject.ams Classificació AMS::42 Fourier analysis::42B Fourier analysis in several variables dc.identifier.slug FME-1094 dc.rights.access Open Access dc.date.updated 2016-07-23T05:42:46Z dc.audience.educationlevel Grau dc.audience.mediator Universitat Politècnica de Catalunya. Facultat de Matemàtiques i Estadística
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