Um estudo histórico acerca de métodos de resolução de equações diferenciais: método das separáveis e método das lineares

Abstract

This doctoral thesis aims to investigate the development of methods for solving Differential Equations proposed by Gottfried Wilhelm Von Leibniz (1646–1716), Christiaan Huygens (1629-1695), Jakob Bernoulli (1655-1705), and Johann Bernoulli (1667-1748), as found in their correspondences and/or publications in the Acta Eruditorum during the last decade of the 17th century. It seeks to answer the question: What were the methods for solving Differential Equations developed by Huygens, Leibniz, and the Bernoulli brothers to address problems that spurred the advancement of mathematical studies thereafter? In light of this inquiry, the objectives include analyzing problems that shaped the formation of models and solutions for Differential Equations as a mathematical knowledge within the field of Differential Calculus, aiming to identify and explain their conceptual and didactic potential for teaching this subject in contemporary Mathematics courses. For this purpose, a qualitative methodological approach is employed, utilizing content analysis as proposed by Bardin (2016) to investigate information from primary sources explored throughout the text, along with commentary on the historical context of the 17th century. Scholars responsible for such works during the examined historical period are identified along with their respective problematics. The thesis concludes with suggestions and directions that can be explored in the classroom during Differential Equations courses (or related topics) and/or in History of Mathematics. It argues that this historical and sociocultural analysis of Differential Equations and their solution methods can offer insights into the development of Mathematics and its practical applications. Furthermore, it suggests that the observation of patterns can be utilized in teaching Differential Equations, promoting historical understanding and the development of more effective teaching and learning strategies. In summary, it is concluded that this research can contribute to the teaching of ordinary Differential Equations through investigative work on the subject matter.