Cálculo diferencial e integral no ensino médio: conceitos e aplicações

Abstract

Differential and Integral Calculus is one of the most important areas of Pure and Applied Mathematics, however, the Brazilian student only comes across this discipline when he arrives at higher education, which makes most of the Brazilian population not even know what it comes. High school textbooks and the BNCC (Common National Curriculum Base) in Brazil emphasize a sophisticated language and decorated formulas, giving little space to Geometry and sacrificing Calculus, its content to what is charged in entrance exams or ENEM (National High School Exam), not teaching subjects such as matrices. This work shows how, once these legislative barriers are overcome through a paradigm shift in the teaching of Mathematics in Brazil, teaching this discipline in high school through the association between graphs and functions, using the properties of derivative and integral, in a way to escape the complex and tedious formal definitions of limit. Some of the prerequisites for the study of Calculus are also addressed, such as reason and proportion, algebraic expressions, equations and functions, as well as the geometry of problems and series limit applications without formal definition. Finally, we talk about the applications of Calculus in the various areas of the exact sciences, with problem solving and examples of physical quantities that can be expressed as derivatives