Qualitative theory and applications of ordinary differential equations with MAPLE software

• Grant number: 19/08303-9
• Support Opportunities: Scholarships in Brazil - Scientific Initiation
• Start date: July 01, 2019
• End date: June 30, 2020
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Applied Mathematics
• Principal Investigator: Marcelo Messias
• Grantee: Guilherme dos Santos Oliveira Miguel
• Host Institution: Faculdade de Ciências e Tecnologia (FCT). Universidade Estadual Paulista (UNESP). Campus de Presidente Prudente. Presidente Prudente , SP, Brazil
• Associated research grant: 13/24541-0 - Ergodic and qualitative theory of dynamical systems, AP.TEM

Abstract

We propose the study of qualitative theory of ordinary differential equations and its applications in the analysis of mathematical models arising in Physics, Biology and Engineering. Beyond the analytical study of the main definitions and theorems, we intend to study mathematical models in R2 and R3 using the Software MAPLE to drawn the phase portraits and study the bifurcations which can occur under the variation of parameters. One of the goals of this project is to prepare the student to enter in a master degree course, where he can continue studying this important and interesting area of mathematical research.