Licenciatura em Matemática (Sede)
URI permanente desta comunidadehttps://arandu.ufrpe.br/handle/123456789/24
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APP - Artigo Publicado em Periódico
TAE - Trabalho Apresentado em Evento
TCC - Trabalho de Conclusão de Curso
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Resultados da Pesquisa
Item A Transformada de Fourier: da motivação à equação do calor numa barra infinita(2024-10-02) Basilio, Evellyn Karoline Alves Freitas; Freitas, Lorena Brizza Soares; http://lattes.cnpq.br/2302580820419163; http://lattes.cnpq.br/8020476628705052This paper presents an overview of the Fourier Transform, its properties and applications, with a particular emphasis on the space of rapidly decreasing functions, which is known as the Schwartz space. The Fourier transform is a fundamental tool in mathematical analysis, employed for the resolution of partial differential equations. This enables differential equations to be converted into more readily manageable algebraic equations. The methodology adopted is based on an analysis of the Schwartz space and its properties, which are essential to ensure the proper behavior of functions in the context of the Fourier transform. Subsequently, the principal properties of the Fourier Transform are examined, including its linearity, differentiability and applicability within the context of Schwartz space, as well as its inverse transform. This work was developed based on an investigation of bibliographical references and theoretical materials listed at the end of this paper. The results obtained demonstrate the significance of the Fourier Transform in determining the solution to the heat equation in an infinite bar, thereby facilitating the identification of a potential solution for the associated partial differential equation. It is our intention that this work provides a clear and comprehensive overview of the Fourier Transform, its properties and its theoretical applications, thus establishing it as an essential tool in analysis.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.