This is second post in the blog series, and it is meant to give a broad narrative of the content for next two blog posts. Like the previous post, it will be more of an overview, but the two posts that will follow it will unpack and discuss deeply whatever appears in this one and slightly more.
Humble Beginnings: Ordinary Differential Equations
The story begins with differential equations. Consider such that is a continuous function. We can construct a rather simple differential equation given this in the following way. We let
A solution to this system is a continuous map that is defined in the neighbourhood of such that this map satisfies the differential equation.
Ordinary differential equations are well-studied, and we know that, for example, a solution to the given differential equation will exist whenever the function satisfies the following:
This property is known as Lipschitz continuity. A function that satisfies this condition is said to be Lipschitz.…