Equações diferenciais ordinárias : aplicações e uma proposta de intervenção no ensino básico

• Ano de defesa: 2019
• Autor(a) principal: Sá, Marcos Santos de
• Orientador(a): Araujo, Gerson Cruz
• Tipo de documento: Dissertação
• Tipo de acesso: Acesso aberto
• Idioma: por
• Programa de Pós-Graduação: Mestrado Profissional em Matemática
• Palavras-chave em Português: Matemática; Equações diferenciais ordinárias; Modelos matemáticos; Ensino médio; Modelagem matemática; Teoria quantitativa de equações diferenciais ordinárias; Proposta de intervenção; Ordinary differential equations; Mathematical modeling; Quantitative theory of ordinary differential equations; Proposed intervention; High school
• Área do conhecimento CNPq: CIENCIAS EXATAS E DA TERRA::MATEMATICA
• Link de acesso: http://ri.ufs.br/jspui/handle/riufs/11593

The Ordinary Di erential Equations are extremely important to mold the several physical, chemical and biological phenomena and problems towards engeneering. However, they are not part of the Elementary School curriculum because they demand previous concepts of the subject Calculus. Taking that into consideration, this paper work aims the study of these equations, specially the quantitative part. In order to do so, we studied the models of Malthus and Verhust applied to the population of Aracaju, through o cial data. Furthermore, we approached Newton's Law of Cooling, used by the forensic expertise, and the modeling of Radioactive Decay. After the construction of this theory, we applied the the knowledge on the Spring-Mole system, with and without damping, in the electric circuit in series R-L-C and on the simple pendulum of Galileo. Finally, we present a proposal of intervention to students of Elementary School, in which, through inherents concepts of the modality, they will be able not only to understand, but also to solve speci c problems related to the modeling of some natural phenomena. We hope to contribute to the improvement and the enrichment of the curriculum of the Elementary School students and, consequently, to the enlargement of their knowledge.