Differentiation, Lebesgue Integral and Functional Analysis

• Grant number: 12/19660-8
• Support Opportunities: Scholarships in Brazil - Scientific Initiation
• Start date: December 01, 2012
• End date: December 31, 2014
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Analysis
• Principal Investigator: Marcio Fuzeto Gameiro
• Grantee: José Inácio da Costa Filho
• 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, in order to deepen the knowledge mathematics of students and give them a solid foundation for better development 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.