Partial differential equations and applications to physics

• Grant number: 17/03686-1
• Support type: Scholarships in Brazil - Scientific Initiation
• Effective date (Start): August 01, 2017
• Effective date (End): December 06, 2019
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Analysis
• Principal researcher: Marta Cilene Gadotti
• Grantee: Daniel Borin
• Home Institution: Instituto de Geociências e Ciências Exatas (IGCE). Universidade Estadual Paulista (UNESP). Campus de Rio Claro. Rio Claro , SP, Brazil
• Associated scholarship(s): 17/16441-7 - Laplace equation and applications to physics, BE.EP.IC

Abstract

This project aims to introduce the basic theory of Partial Differential Equations (PDE) and to perform a study about Fourier Series, definition of Fourier Series, to build results that guarantee the point and uniform convergence and to define the Fourier Transform and its properties. Next, we define the Variable Separation Method to solve certain PDE. In particular, it is intended to work with certain physical phenomena described by this type of equation, such as Maxwell's equations, Poissom's and Laplace's and wave equation. (AU)