01.1 - Graduação (Sede)
URI permanente desta comunidadehttps://arandu.ufrpe.br/handle/123456789/2
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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.Item Processo de Renovação Generalizado baseado na distribuição Gumbel como modelo de estimativas de ocorrências de ondas de calor para auxiliar no processo de tomada de decisão do cultivo de manga no Sertão de Pernambuco(2023-05-08) Ferraz, Kimbelly Emanuelle Avelino; Cristino, Cláudio Tadeu; http://lattes.cnpq.br/0295290151219369; http://lattes.cnpq.br/2320958356149704Several types of events can harm the planting, harvesting or handling of plants and fruits in agricultural areas, one of them including the event called heat waves, which is characterized as a prolonged and relatively uncommon meteorological phenomenon with extremely high temperatures for the region and persistent for several days or even weeks. Given the importance of agriculture, this work seeks, through the analysis of the maximum temperature data in the Petrolina region, the study of the mango plantation, the Heat Wave event through the 90th percentile, optimization algorithms and the processes of generalized renewal and Gumbel, estimating this event contributing to the farmer’s decision making and optimization of Mango production. The proposed model uses the generalized renewal process based on the Gumbel distribution (GuGRP) to model the time intervals between heat waves, considering that consecutive events are conditionally independent. This model proved to be adherent to model events with a significance level of 0.05 and a P −V alue of 0.28 through the Kolmogorov-Smirnov adherence test on the adequacy data adapted to the GuGRP. The model parameters were estimated by Log-Likelihood using optimization algorithms, also specifically testing the Particle Swarm algorithm.