Introduction to the Qualitative Theory of Ordinary Differential Equations and some applications to the Newtonian Mechanics

• Grant number: 13/09624-7
• Support Opportunities: Scholarships in Brazil - Scientific Initiation
• Start date: September 01, 2013
• End date: December 31, 2014
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Geometry and Topology
• Principal Investigator: Tatiana Miguel Rodrigues
• Grantee: Otavio Henrique Perez
• Host Institution: Faculdade de Ciências (FC). Universidade Estadual Paulista (UNESP). Campus de Bauru. Bauru , SP, Brazil

Abstract

This project will begin with the study of several examples modeled by ordinary differential equations. These examples run from electrical, biological, chemical, and especially mechanical problems (mass-spring system or other). We will study these systems through their phase portraits, where we will be able to explore important qualitative/geometric informations about the dynamic behavior of such systems. Then we will address the formal results about the Qualitative Theory of Vector Fields, where we discussclassical results such as the Existence and Uniqueness Theorem, the Theorem Tubular Flow Theorem, the Hartman-Grobman Theorem and the Poincaré-Bendixson Theorem.