Introduction to the qualitative theory of differential equations

• Grant number: 13/14601-6
• Support Opportunities: Scholarships in Brazil - Scientific Initiation
• Start date: August 01, 2013
• End date: July 31, 2014
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Geometry and Topology
• Principal Investigator: Ana Cristina de Oliveira Mereu
• Grantee: Daniel Medeiros da Silva
• Host Institution: Centro de Ciências e Tecnologias para a Sustentabilidade (CCTS). Universidade Federal de São Carlos (UFSCAR). Sorocaba , SP, Brazil
• Associated research grant: 12/18780-0 - Geometry of control systems, dynamical and stochastics systems, AP.TEM

Abstract

The main goal of this project is the qualitative study of differential equations. We will study systems of linear differential equations with their planar phase portraits. Next, we will dedicate our study the qualitative theory or geometrical systems of differential equations nonlinear. Focusing on local theory of such systems, we will study the Existence and Uniqueness Theorem Solutions, Theorem of Hartman-Grobman and Theorem Stable Variety. Global aspects of the theory will be studied including limit sets of trajectories and Poincaré-Bendixson. The study will include Averaging Method to study the existence of limit cycles. Other goals of this project are: to instill in student interest in mathematics and to enable him not only to fill the gaps in their training but also enhance their critical thinking.