Transformada de Fourier: definições, propriedades e aplicações em equações diferenciais parciais

Abstract

The main objective of this work is to present the Fourier Transform as a method to solve some applications of Partial Differential Equations. In this sense, it comprises some important definitions such as: Definition of the Fourier Series as well as its coefficients, definition of the Fourier Transform and some of its properties such as Linearity, Translation, Dilation, among others, and also the definition of Convolution of Functions that is an important tool when dealing with Partial Differential Equations. In particular, we studied two applications that were the Wave Equation and the Heat Equation. For a greater specificity of these solutions and in order to present the reader with more suggestions for solutions, we sought to resolve them using two techniques. Thus, we present the first solution via Fourier Series and its coefficients and then we present the solution using the Fourier Transform. For the development of this work we used exploratory research that aims to provide the student with greater familiarity with the content. greater familiarity with the content.