Conceitos básicos para a introdução ao cálculo diferencial e integral

Abstract

This book is intended for students in the first semester of the Introduction to Calculus course, as well as for teachers. It aims to contribute to the study and, thus, to the learning of these students, preparing them for the disciplines of Calculus I and Calculus II. We will give the fundamental definitions and properties for the Introduction to Calculus course. We seek to deepen some important properties for Differential and Integral Calculus, with a text that would contribute to the better development of the discipline that begins the study of Calculus I. We organize this material as follows: In chapter 1 we bring a brief introduction to the language of numerical sets needed to express ourselves formally and correctly in mathematics. Chapters 2 and 3 study the set of Real Numbers and their properties. In Chapters 4 and 5 we present the Cartesian plane and the concept of a function, with its properties. In Chapters 6 through 11 we detail the functions: Affine, quadratic, polynomial, rational, exponential, and logarithmic. In the last chapters, 12 to 14, basic concepts of trigonometry are resumed, seeking to study elementary trigonometric functions.