Cartilha de análise: seminários de análise na reta

Abstract

This is not a book, this text was written from the notes and doodles of seminars and presentations by students of the course and mathematics of UEA Tefé and Eirunepé, during the execution of the productivity project entitled "Topics of Analysis: Real numbers and topology on the line "that occurred between the months of March 2018 and February 2020 under the coordination of Professor Josimauro Borges and participation the students Jhonny Oliveira, Érison Cardoso, both academics from the mathematics by Eirunepé, by academics Alisson Athos, Alison Taylo, Rodrigo Meza, Ismael Quirino and Elcimar Arante, these are students of the Mathematics course at the Centro of Higher Studies of Tefé- CEST. The project had a total workload of 144 hours distributed over 6 hours per month. There are some questions to be clarified: i) Which sets are considered as bodies ii) Are there two ordered bodies complete, or is the set of real numbers unique with these properties? And, iii) Worth reciprocal of the Borel-Lebesgue theorem? In the part we barely spoke briefly about some important spaces in the mathematical environment. The text has an elementary character because it that, at first, the results have been written for academics beginning the mathematics, although, it also extended to those who intend to enter the courses of post-graduation, since this theme is charged in the entrance exams in such courses. The objective is to facilitate the understanding of some topics covered in the discipline of Mathematical Analysis for undergraduate and Linear Algebra. The material is available at library of Tefé and Eirunepé.