TCC Matemática
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Item Aplicações de variáveis aleatórias contínuas em problemas reais(2024-08-01) Gonçalves, Douglas Floering Brêda; Nunes, Hugo Santos; http://lattes.cnpq.br/4304337631466259; Nascimento, Arlyson Alves do; http://lattes.cnpq.br/9395417554768580; Nunes, Hugo Santos; http://lattes.cnpq.br/4304337631466259; Lopes, Rafael do Sacramento; http://lattes.cnpq.br/2775224211896509The present work aims to explore the applications of continuous random variables in real problems, addressing fundamental concepts of probability and their distributions. The study begins with an introduction to the concept of probability, events and sample space, moving on to the additive and multiplicative rules that govern the combination of events. During the work, random variables and their probability distributions are discussed, focusing on the differences between discrete and continuous distributions. Particular attention is paid to continuous random variables. In this context, concepts such as the probability density function, expectation, variance and standard deviation are presented, which are essential for the analysis of these variables. The Study explores three continuous probability distributions: the Uniform, the Normal and the Exponential distribution, detailing their characteristics and behavior in different scenarios. In the last part of the work, practical applications of these distributions in real contexts are presented, demonstrating the usefulness of continuous random variables in modeling phenomena in various areas such as finance, engineering, data science, among others.Item Equações diferenciais ordinárias de segunda ordem: uma abordagem analítica e com o software GeoGebra(Instituto Federal de Educação Ciência e Tecnologia de Alagoas, 2023-11-30) Lima, Jonathan Willams Lins de Ataide; Lima, Leon Cavalcante; http://lattes.cnpq.br/7616688310117461; Nascimento, Arlyson Alves do; http://lattes.cnpq.br/9395417554768580; Silva Júnior, Rinaldo Vieira da; http://lattes.cnpq.br/9156830519836354; Melo, Enaldo Vieira de; http://lattes.cnpq.br/1041528154664700Models involving Ordinary Second Order Differential Equations are present in several problems in various areas of Exact and Earth Sciences, through applications in fluid mechanics, heat conduction, electrical circuits and electromagnetic phenomena. In this sense, the present work presents a study on these equations, covering the fundamental concepts of first-order to second-order equations. Throughout the development of the work, with the exception of the analysis via GeoGebra, the independent variable was time, so that we could also cover Physics students, considering that in general all physical models are based on this parameter. For the application, we brought two problems involving mathematical modeling, the first being a model for detecting diabetes and the other involving a series circuit RLC. Initially, we carried out an analytical analysis of the two problems, detailing how all the calculations were made, and the other was carried out using a applet created in software GeoGebra during a technological initiation project developed at Instituto Federal de Alagoas - Campus Maceió, with the aim of students being able to combine the theoretical part with the practical part. Understanding the solution methods is an important step during the process of teaching and learning differential equations, considering that it was only possible to develop this interactive window by understanding how these methods work. We concluded, from the analysis of the problems, that the use of technology aimed at education provides students with a new learning environment through interactivity and experimentation with different scenarios.Item Programação linear: da engenharia de produção à sala de aula(2025-06-16) Gonçalves, Alisson de Melo; Nunes , Hugo Santos; http://lattes.cnpq.br/4304337631466259; Nascimento, Arlyson Alves do; http://lattes.cnpq.br/9395417554768580; Melo, Enaldo Vieira de; http://lattes.cnpq.br/1041528154664700This Final Undergraduate Paper aims to analyze Linear Programming (LP) from two perspectives: its application in Production Engineering and its integration into high school as a didactic tool. Initially, the theoretical foundations of Operational Research and Linear Programming are presented, highlighting their historical and practical relevance for resource optimization, profit maximization, and decision-making in productive environments. From this basis, the graphical method for solving LP problems with two variables and the mathematical modeling involved in this process are explored. In the second part of the study, a didactic sequence was developed and implemented for 3rd-year high school students at Colégio Inovar (Atalaia-AL), using active methodologies and technological tools such as GeoGebra and Excel Solver. The proposal included introductory lessons, group activities, and the resolution of contextualized problems, focusing on developing students’ logical reasoning and decision-making skills. The analysis of the results revealed a significant improvement in students’ performance and an increased interest in mathematics, especially when they recognized the applicability of Linear Programming in real-life situations. The data collected through practical activities and student feedback indicated that the use of digital technologies in teaching LP facilitates the visualization of concepts and contributes to a more meaningful and interactive learning experience. It is concluded that Linear Programming, in addition to being an essential tool in Production Engineering, can be successfully integrated into the school context, provided that appropriate pedagogical strategies are adopted to bring students closer to real-world applications and professional environments.