Numerical differentiation deals with the calculation of derivatives of a smooth function:
defined on a discrete
set of grid points (x0, x1, x2... xN).
The construction of numerical approximations of the derivatives is based on finite difference formalisms.
One approach we use is
the use of Taylor series approximations. The Taylor series expansion method has the advantage of providing information about
the error involved in the approximation. The McLaurin series expansion techniques will also yield similar approximations.