Here we will discuss a few basic ideas in the construction of a representation of
a function at a point nearby a given point. For the present we focus on a function
of a single variable f(x). The generalization to functions of several variables
is straightforward and will be given when needed. We focus on using the so-called
Taylor series expansion, since we shall see later that
with it one can reduce the problem of generating approximations to derivatives to
algebraic manipulations. Further, with the Taylor series method one automatically gets
an indication of the order of accuracy of the particular approximation.