Metric Theory, Mathematical Analysis, Linear Algebra and Functional Analysis

• Grant number: 11/19533-3
• Support Opportunities: Scholarships in Brazil - Scientific Initiation
• Start date: November 01, 2011
• End date: October 31, 2013
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Analysis
• Principal Investigator: Hildebrando Munhoz Rodrigues
• Grantee: Gabrielle Migliato Marega
• Host Institution: Instituto de Ciências Matemáticas e de Computação (ICMC). Universidade de São Paulo (USP). São Carlos , SP, Brazil

Abstract

The objective of this project is the study of Analysis, metric spaces and Lebesgue integral, in order to deepen knowledge in mathematics for Engineering studing.This project is divided in four parts. The first is for the study of metric spaces and some basic properties such as compactness and connectedness.The second part is intended for studies of numerical sequences and series, the continuity of functions and differentiability of real valued functions.The third part of this project is focused on studies of sequences and series of real valued functions, with the main results of Theorems Arzel-Ascoli and the Stone-Weiertrass.The fourth and final part is devoted to the study of measure theory, more specifically the Lebesgue integral and its applications, such as integral dependent functions and parameter derivation under the integral sign.The study books will be: "Principles of Mathematical Analysis" de Walter Rudin and "A Integral de Lebesgue e suas Aplicações"de C. S. Honig.The student will used the AMS-LATEX for typing reports.