Overview

A Taylor Series is a representation of function in the form of infinite sums of terms. The coefficients of the infinite sums is derived based on the derivative and higher derivatives of the function at a single point.

We will look at how to derive these infinite sums of functions and also at some of the interesting properties that we can derive from these sums. Although we will cover the more mundane functions that we are used to Taylor series can be used to get a polynomial function that approximates some more difficult functions out there (specially if we want to integrate them for example and we don't know how, but we can differentiate them).

With Taylor series we can approximate function in one variable or more, complex numbers and even matrices and fractional integrals and differentiations.