TCC Matemática

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https://repositorio.ifal.edu.br/handle/123456789/50

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Navegando TCC Matemática por Assunto "Cálculo diferencial"

Agora exibindo 1 - 2 de 2
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    Da geometria ao movimento: a motivação para o conceito de derivada
    (2025-07-07) Silva, Jonas Alexandre dos Santos; Nascimento, Arlysson Alves do; http://lattes.cnpq.br/9395417554768580; Siqueira, Anderson Rangel Batista; http://lattes.cnpq.br/8130778140721340; Santos, Vívia Dayana Gomes dos; http://lattes.cnpq.br/2740547167333947
    Differential calculus represents one of the most significant discoveries in mathematics and science. Its development occurred gradually, with contributions from several thinkers throughout history, being largely attributed to the works of Gottfried Leibniz and Isaac Newton. Although both were polymaths, they had different perspectives: Leibniz approached the topic from a purely mathematical standpoint, seeking methods to determine the slope of tangent lines, while Newton focused on calculating the instantaneous velocity of a moving object. This work aims to present the development of differential calculus from both perspectives, ranging from its applications in analytic geometry to its relevance in kinematics. Furthermore, the formal concept of the derivative, its main rules, and applications are discussed, highlighting its importance as a tool for analyzing the motion of bodies.
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    Propriedades geométricas e analíticas da família das cicloides: um estudo comparativo
    (2025-07-11) Queiroz, Yasmin Laryssa Lima de Omena; Vasconcelos, Cleverton da Silva; http://lattes.cnpq.br/8600809859832837; Silva, Vanessa Lúcia da; https://orcid.org/0009-0001-9067-8936; http://lattes.cnpq.br/4017185539776065; Souza, Ana Paula Dantas de; http://lattes.cnpq.br/0855037244655705; Costa, Valdir Soares; http://lattes.cnpq.br/0249295123723616
    This work aims to investigate the geometric and analytical properties of the cycloid family, including variations such as the common cycloid, curtate cycloid, and prolate cycloid. The research is conducted through a comparative study that covers both theoretical and practical aspects of these curves, analyzing their parametric equations, derivatives, integrals, and geometric characteristics. Additionally, the study explores historical and contemporary applications of cycloids in contexts such as physics, engineering, and applied mathematics, highlighting classical problems such as the brachistochrone and the tautochrone. The work seeks to contribute to a deeper understanding of these curves from both mathematical and educational perspectives, serving as a resource for teaching differential and integral calculus.