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Differentiation, Lebesgue integral and functional analysis

Grant number: 12/21136-5
Support type:Scholarships in Brazil - Scientific Initiation
Effective date (Start): November 01, 2012
Effective date (End): October 31, 2014
Field of knowledge:Physical Sciences and Mathematics - Mathematics - Analysis
Principal researcher:Hildebrando Munhoz Rodrigues
Grantee:Tomás Lopes de Oliveira
Home 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, in order to deepen the knowledge mathematics of students and give them a solid foundation for better development of their academic and professional lives. This project is divided into two parts. The first is for the study of the differentiability of real valued functions and for the study of measure theory, specifically the Lebesgue integral and its applications, such as integrals of functions dependent on parameters and derivation under the integral sign. The second part is for the study of operator theory in finite dimensional vector spaces, with topics ranging from basic notions of normed vector spaces up to positive definite matrices. (AU)

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