Licenciatura em Matemática (Sede)
URI permanente desta comunidadehttps://arandu.ufrpe.br/handle/123456789/24
Siglas das Coleções:
APP - Artigo Publicado em Periódico
TAE - Trabalho Apresentado em Evento
TCC - Trabalho de Conclusão de Curso
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2 resultados
Resultados da Pesquisa
Item Da propagação do calor à construção de desenhos: uma aplicação das séries de Fourier com Python(2024) Domingos, Cleianderson Paz; Freitas, Lorena Brizza Soares; http://lattes.cnpq.br/2302580820419163; http://lattes.cnpq.br/8909785797719318This 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.Item Equação da onda: soluções de problemas de valores iniciais e de fronteira a partir da análise de Fourier(2020-12-19) Lopes, Daniel César Pereira; Silva, Clessius; http://lattes.cnpq.br/2401078773322406; http://lattes.cnpq.br/0084883368794758In this work, we will study the Wave Equation, an important equation in the study of Partial Differential Equations. We will work on problems involving the finite-string wave equation with fixed ends, the infinite string, and the semi-infinite string. However, to get to such problems, we will need to do a study about the Fourier Series, studying the convergence of such series, so we will need some Real Analysis. In addition, we will study some important inequalities such as: Bessel Inequality, Cauchy-Schwarz Inequality and Minkowski Inequality. For that, we have a basis for solving the EDP’s in question.