Os teoremas de existência e unicidade de solução de um PVI e do fluxo tubular

Abstract

The main objective of this course completion work is to present the foundations of the Qualitative Theory of Ordinary Differential Equations, a branch of Mathematics that is considered one of the most applied. The present work covers the elementary definitions and part of the main results of the Qualitative Theory of Ordinary Differential Equations, based on previous concepts referring to Metric Spaces, which are used throughout the text. We present and demonstrate in detail two of the main results of the theory: the Theorem of Existence and Uniqueness of Solution of an Initial Value Problem and the Flow Box Theorem.