Transformada de Fourier: aplicacions a la resolució d'equacions en derivades parcials
Tutor / director / evaluadorBoza Rocho, Santiago
Tipo de documentoTrabajo final de grado
Condiciones de accesoAcceso abierto
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.