Teoria da medida, análise matemática, álgebra linear e análise funcional

• Grant number: 11/19532-7
• Support Opportunities: Scholarships in Brazil - Scientific Initiation
• Start date: November 01, 2011
• End date: October 31, 2012
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Analysis
• Principal Investigator: Hildebrando Munhoz Rodrigues
• Grantee: Guilherme Rodrigues Borges
• Host Institution: Instituto de Ciências Matemáticas e de Computação (ICMC). Universidade de São Paulo (USP). São Carlos , SP, Brazil

Abstract

The goal of this project is the study of analysis, metric spaces, and Lebesgue Integral, with the purpose of deepening the knowledge in mathematics of the engineering student. The project is divided into four parts. The first is for the study of metric spaces and some basic properties such as compactness and connectedness. The second part is for the study of numerical sequences and series, continuity of functions, and differentiability of real-valued functions. The third part of the project is dedicated to the study of sequences and series of real-valued functions, with the main results of the theorems of Arzel-Ascoli and Stone-Weierstrass. The fourth and final part is devoted to the study of metric theory, specifically the Lebesgue integral and its applications, such as integrals of functions dependent on parameters and derivation under the integral sign.(AU)