Cálculo Diferencial e Integral

Abstract

Differential and Integral Calculus are among the fundamental pillars of Pure and Applied Mathematics. However, in the Brazilian context, this subject is usually only presented in higher education, which contributes to a large part of the population being unaware of its essential concepts. The National Common Curricular Base (BNCC) and high school textbooks prioritize an approach based on technical language and the memorization of formulas, leaving aside fundamental content such as Geometry and almost completely neglecting Calculus. Added to this is the recurring practice among teachers of aligning their content with the requirements of college entrance exams and ENEM, which results in the omission of relevant topics, such as matrices. This paper argues that, once legal obstacles are overcome and a change in educational paradigm is promoted, it is possible to include the study of Calculus in high school. To this end, we propose an approach that relates graphs and functions, using the concept of derivative, in order to make learning more accessible and intuitive, avoiding, whenever possible, formal and abstract definitions of the concept of limit. This work is aimed at high school teachers and aims to present methodologies for approaching the Differential Calculus of one variable in the first year of this stage of education. It is understood that mastering this content will provide students with a greater ability to interpret the behavior of functions, both algebraic and transcendental, recurring themes in Mathematics and other disciplines throughout this educational cycle. In addition, it seeks to offer a more consistent preparation for facing the initial disciplines of higher education courses, especially in the exact sciences areas, in which unsatisfactory student performance rates have been observed in components such as Differential and Integral Calculus I and Physics I