Study about Fourier series and applications

• Grant number: 15/00534-0
• Support Opportunities: Scholarships in Brazil - Scientific Initiation
• Start date: June 01, 2015
• End date: December 31, 2016
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Analysis
• Principal Investigator: Marta Cilene Gadotti
• Grantee: Felipe Felix Souto
• Host Institution: Instituto de Geociências e Ciências Exatas (IGCE). Universidade Estadual Paulista (UNESP). Campus de Rio Claro. Rio Claro , SP, Brazil

Abstract

This project aims to establish the basic theory of Fourier analysis, to define the series, fabricate results to ensure the timely and uniform convergence and define the Fourier transform. Then, using this theory to describe certain physical phenomena that are modeled by partial differential equations, including the problem of heat conduction in a bar, transverse vibrations of a string and a balance membrane under the action of certain forces. For these problems, is intended to seek solutions also satisfying certain initial or boundary conditions, logo basics of the theory of partial differential equations must be developed.