Sequências e séries de funções

Abstract

The main objective of this work is to carry out a bibliographical study on sequences and series of functions, focusing on the two main types of convergence: pointwise and uniform. As a background, we present a brief history on the development of Analysis and a compilation of elements needed to discuss the theme, such as sequences and series of real numbers, topology, limit and continuity, differentiability and integrability of real functions. Finally, we present our theme, sequences and series of functions, establishing the pointwise and uniform convergences, its convergence conditions and the term-by-term derivation and integration.