Uma análise do Teorema Fundamental do Cálculo em alguns livros-texto

Abstract

This paper analyzes the Fundamental Theorum of Calculus as it is presented in the most quoted text books in bibliographic references and syllabuses of college calculus courses. We focus on teaching/learning methodology at work in these textbooks. In the analysis of the theorem and of its demonstration, we consider the following related aspects: pre-requisite requirements, logical links of the demonstration, the elected motivations, the presence of the geometric notion, applications, as well as proposed exercises. Such analysis is supported by the theory of Semantic Fields (Lins, 1993). We come to the conclusion that the Fundamental Calculus Theorem as a mathematical object is not exactly the same to different authors, not only exactly the same to different authors, not only in its formulation but also in the way it is treated. We also conclude that the authors, not only in its formulation but also in the way it is treated. We also conclude that the authors assume an ideal "complete interlocutor" that does not match the real interlocutor, i.e., the student who needs to learn.