Existência de solução da equação diferencial ordinária escalar x0 = f(t; x) via método da poligonal - MOTA, Rosinildo Nunes (2019)
In this work we will take a basic approach on the qualitative theory of the ordinary differential equations In what concerns the existence of the solution of a scalar equation of first order. To do so, we present the main de nitions and examples of metric spaces and approach sequences in metric spaces, especially those of Cauchy, then we did a basic study on compact sets and their main theorems and introduced the concept of continuous functions in metric spaces. We show the theorem of Arzelà Ascolí and we demonstrate the theorem of Cauchy-Peano called the method of the polygonal and nally we made an application of the main theorem to the ecology.