Um estudo formal sobre sequências e séries de funções

Abstract

This work was developed in the area of Mathematics with an emphasis on Analysis, aiming at the development of the formal study of Sequences and Series of Functions, including the properties of uniform convergence, power series and the application in classical functions. In this context, this work investigates and clarifies concepts of uniform convergence, derivation and integration from the perspective of Sequences and Series of Functions, specifically addressing the concepts involving Sequences of functions, Series of Functions and limits, working examples on the referred theme, detailing and developing demonstrations and results present in the book Real Analysis, v1 by Elon Lages Lima to formally understand the definitions of Sine function , Cosine, Exponential and Logarithm from the formal point of view of Analysis.