UM ESTUDO DO LIVRO CÁLCULO DIFERENCIAL E INTEGRAL DE RICHARD COURANT: REFLEXÕES PARA O ENSINO DE CONTEÚDOS DE ANÁLISE REAL

Abstract

In this article, we present a comparative study between books commonly used in the discipline of real analysis, from some courses of the formation of mathematics teachers, specifically, with the book Differential and Integral Calculus I, published in the early 20th century, by the mathematician Richard Courant, with the objective of discussing possible variations in the presentation of the themes covered in this discipline and carry out a systematic study of the way concepts are presented. For this, through a bibliographical research, we searched in the history of real analysis the contents that best characterize it to be approached in our comparative study. Next, we detail important aspects of Courant's book to, finally, draw a parallel between the works. Through this investigation, it was possible to point out aspects of this discipline that can be worked in a different way, exploring other interpretative forms, with re-readings of some topics, in order to expand the look at issues that proved essential for the development, and current conception, of the mathematics, entailing to pedagogical implications regarding the teaching of these topics.