Mathematical analysis, differentiation, Lebesgue integral and functional analysis

• Grant number: 17/26380-5
• Support Opportunities: Scholarships in Brazil - Scientific Initiation
• Start date: April 01, 2018
• End date: March 31, 2019
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Analysis
• Principal Investigator: Hildebrando Munhoz Rodrigues
• Grantee: Arthur Dantas Pacheco dos Santos Lima
• 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 the study of mathematical analysis with the intention of giving the students a more profound knowledge of the field and help them develop their academic and professional careers. It will be presented lectures in English, alternating between the students. The subjects to be studied are numerical sets (and its properties), basic notions of topology in metric spaces, continuous and differentiable functions, sequences and series of complex numbers and complex functions as well as the measure theory and integration, more specifically the Lebesgue's integral and its applications. The basis for the whole study will be the books "Principles of Mathematical Analysis" of Walter Rudin and "A Integral de Lebesgue e suas Aplicações" of C. S. Hönig. These books will also help a future study of the theory of linear operators in vector spaces of finite dimensions, which includes from the basic notions of vector spaces until positive matrices. In this case, the main source will be the book "A Short Introduction to Perturbation Theory for Linear Operators" of T. Kato. (AU)