Espaços vetoriais de dimensão infinita, tipos de convergências e aplicação em integração numérica

Abstract

In this paper, we will deal with some topics related to the study of functional analysis, highlighting the properties and structures of vector spaces of infinite dimension in relation to spaces of finite dimension. We will also show, as a result of the constructed theory, an application in numerical integration, in which, through the study of convergences and the theorems of numerical integration, it will be possible to obtain as corollaries the trapezoid and simpson rules. Finally, we will do some tests involving the corollaries, highlighting what was discussed during the work