https://repositorio.ufms.br/handle/123456789/7221 2026-05-06T11:39:40Z https://repositorio.ufms.br/handle/123456789/10775 Título: Padrões em Integrais Abstract: In this paper, we will explore the subject of patterns in integrals of certain functions. To introduce the concept, we will present examples which we will solve in two ways: using computer algebraic systems, such as SYMBOLAB and WOLFRAM, and using conventional integration methods, which we will develop step by step algebraically. After solving each example, we will identify the patterns presented in the solutions in order to establish logical and consistent reasoning. Based on this, we will show that the observed patterns are in fact valid for the corresponding general cases, allowing for a more detailed analysis of the standard behavior of the integrals of these functions. Tipo: Trabalho de Conclusão de Curso 2024-01-01T00:00:00Z https://repositorio.ufms.br/handle/123456789/10568 Título: Equações Diferenciais Ordinárias de Primeira Ordem e Algumas Aplicações. Abstract: Ordinary differential equations are useful tools for modeling applications ranging from natural to laboratory phenomena. In view of this, the aim of this work is to relate first-order ordinary differential equations classified as linear or non-linear to some applications, bearing in mind that the analytical solutions of these equations are simplistic. The methodology used in this work is a bibliographical survey of differential equations, using university textbooks. The definitions and theorems are related to the books by Boyce, Yartey, Chasnov and Doering, and the applications are taken from the university textbooks by Braun, Zill, Bassanezi and Tygel. In view of these bibliographical surveys, some of the results obtained by the analytical solutions of the differential equations presented is the interdisciplinarity between theory and application. Thus, from these surveys, it is possible to establish a relationship between the applicability of these differential equations and applied mathematics. Tipo: Trabalho de Conclusão de Curso 2024-01-01T00:00:00Z