Mathematical analysis, differentiation, Lebesgue integral and functional analysis

• Grant number: 17/26514-1
• Support Opportunities: Scholarships in Brazil - Scientific Initiation
• Start date: April 01, 2018
• End date: January 31, 2019
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Analysis
• Principal Investigator: Hildebrando Munhoz Rodrigues
• Grantee: Samuel Marinheiro de Souza Melo
• Host Institution: Instituto de Ciências Matemáticas e de Computação (ICMC). Universidade de São Paulo (USP). São Carlos , SP, Brazil

Abstract

The main purpose of this project is to enable the students to have a steady mathematical knowledge, specifically in Mathematical Analysis, in order to complement and improve their academic development. Through the books "Principles of Mathematical Analysis", by Walter Rudin, and "A Integral de Lebesgue e Suas Aplicações"(The Lebesgue Integral and its Applications), by C.S. Hönig, we will study basic notions of Topology, Numerical Series, Series of Functions, Continuous Functions, Differentiable Functions and the Lebesgue Integral and its applications. The entire programme will be developed in one year through seminar lectures and will serve as a basis to carry out a future study on the theory of operators for finite dimensional vector spaces, through the book "A Short Introduction to Perturbation Theory for Linear Operators", by Tosio Kato. (AU)