Degree theory from a geometric point of view and numerical experiments for systems of ODEs

Abstract: In this lecture we discuss an intuitive and geometric approach to the Brower degree and its basic properties. Focusing on geometric ideas in two dimensions, we explore the proof of several of the well-known results. We also discuss numerical experiments for finding solutions of a BVP for system of ODEs. These experiments are based on geometric aspects of the Poincare-Miranda Theorem.