Da propagação do calor à construção de desenhos: uma aplicação das séries de Fourier com Python

Abstract

This work aims to present an application of Fourier series in generating figures. To do so, we first study the problem of heat conduction in a finite rod, as well as the equation that models it and its solution, both proposed by Joseph Fourier in the early 19th century. Initially, a historical note is presented, exhibiting some facts that lead to the motivation for studying heat propagation. Then, we derive the Heat Equation from two physical laws and study how Fourier series emerge in an attempt to solve this equation. Subsequently, through convergence theorems, we study necessary conditions for a function to be represented by its Fourier series. Finally, we explore an application of Fourier series in figure generation using epicycles and develop a Python algorithm to visualize this application.