Measure Theory, Mathematical Analysis, Linear Algebra and Functional Analysis

• Grant number: 11/19233-0
• Support Opportunities: Scholarships in Brazil - Scientific Initiation
• Effective date (Start): November 01, 2011
• Effective date (End): October 31, 2012
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Analysis
• Principal Investigator: Hildebrando Munhoz Rodrigues
• Grantee: Vágner Egídio Velho Júnior
• Host Institution: Instituto de Ciências Matemáticas e de Computação (ICMC). Universidade de São Paulo (USP). São Carlos , SP, Brazil

Abstract

The general objective of this project is the study of the analysis, metric spaces, and the integral of Lebesgue, with the purpose of increase the mathematical knowlegde of the student of engineering. This project is divided in four parts. The first one is destinated to the study of metric spaces and some basic properties like compacity and connectivity. The second part is destinated to the study of the sequences and numerical series, continuity of functions and the diferenciability of the functions with real values. The third part of this project is focused in the study of the sequences and series of functions with real values, having how principal results the Theorems of Arzelá-Ascoli and the Stone-Weierstrass. The fourth and last part is turned to the study of the measure theory, more especifically the integral of Lebesgue and yours aplications, like how integrals of functions dependents of parameters and derivation over the integration signal. For these ways, the books that will be studied are "Principles of Mathematical Analysis" of Walter Rudin and "A Integral de Lebesgue e suas Aplicações" of C S. Honig. The student will use the tool AMS-LATEX for the typing of the reports.