Conceitos e ideias do cálculo diferencial e integral

Abstract

The concepts of integral and derivatives are fundamental to the understanding of several concepts of modern sciences. This is one of many reasons by which the subject Diferential Calculus is presented on the curriculum of many courses. Despite of being acknoledged as essential, it is also the subject of higher degree of fail and several students atribute to it their worse learning's difficulties. On the other hand, this subject's teachers face difficulties to fullfill menus and programs, mostly with students laking any motivation. Besides this unfavorable scenario, it is observed that there's a big leap between Mathematics learnt on high-school and Mathematics taught on college. Based on these assuptions, many questions are raised, such as: How to stimulate the learning of Integral and Diferential Mathematics? How to diminish the leap between high-school Mathematics and college one? In the present paper, central ideas of Diferential and Integral Calculus are introduced, approaching concepts of Integral and Derivative in a intuitive mode, regardless technical aspects and rigor. The dissertation is divided into two chapters, in which in the first is discussed the concept of derivative as a crucial need to problem solving envolving applied variations's rate and the problem of defining a tangent to a curve in a point. In the second chapter, is introduced the concept of integral as a fundamental tool to the solutions of problems regarding how to define the area of a non regular plane region, solids volumes and curves lenghts, among others. Finally, is presented Calculus's Fundamental Theorem