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An epistemological analysis of Colin Maclaurin's A Treatise of Fluxions and its contributions to the teaching of differential and integral calculus

Fluxional method; derivative; integral; and history of mathematics

This work develops a historical and epistemological analysis about differential and integral calculus in the conceptual and approach related to the study of derivatives and integrals in two volumes that make up the work A Treatise of Fluxions, by Colin MacLaurin on the treatise on fluxions, published in 1742 For the development of this investigation, I rescued aspects related to the construction of the history of mathematics concerning the understanding of the study of differential and integral calculus from the logical foundations of the fluxional method idealized by Issac Newton and, later, improving and amplified by Colin Maclaurin. The systematization of the study involving fluxion consolidated the idea about derivatives, properties, rules and proofs, which became known as the straight fluxion method. From this approach to the study of derivatives through the fluxional method emerged the formalization of the study of the notion of integral as well as its methods, rules and properties derived from the fluxion known as the inverse method. The potentialization and conceptual identity of calculus from the study of the fluxional method will serve as subsidies for future teachers in understanding this content in the teaching and learning process of mathematics in order to re-signify and complement the conceptual approach present in calculus books. in order to strengthen the construction of knowledge and analysis of the study of differential and integral calculus in undergraduate mathematics courses.