Ideally, every function would be easy to deal with in all mathematical situations, abstract and applied. Unfortunately, this is not always the case. It sometimes becomes convenient to have an approximation to the function, usually a polynomial or some other "well-behaved" series of functional terms. There are several ways to formulate an approximation when this is desirable.

The simplest method of approximation is the least accurate one: estimation. With a certain amount of mathematical intuition, sometimes it is possible to guess a curve (or some related quantity of interest) that is fairly close to the actual desired curve. However, this method is only recommended as a starting point for more exact approximations, since it is an educated guess in the most literal sense of that phrase.

A Taylor series approximation relies upon the derivatives of the function being approximated, and it requires a central...