Polynomials
Do you like calculus? Well I love it! One of the ideas in calculus is Taylor expansion, that is, representing a differentiable function as an infinite series (see https://www.khanacademy.org/math/integral-calculus/sequences_series_approx_calc/taylor-series/v/generalized-taylor-series-approximation and http://en.wikipedia.org/wiki/Taylor_series.).
Note
The Taylor series is defined as the following sum:
in this definition is the nth derivative of the function f computed at the point a.
In practice, this means that we can estimate any differentiable, and therefore continuous, function with a polynomial of a high degree. We would then assume that the terms of the higher degrees are negligibly small.
