In this section we will discuss a few basic ideas in the construction of numerical approximations for derivatives. We focus on using the Taylor series method, since 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.
In no sense do we intend on presenting a complete treatment. What we hope the reader comes away with is an appreciation of the origin of some commmon approximations and an ability to generate such approximations for him/herself in the future, as well as being able to invent other approximations which are needed by some future particular context.