Introduction

Numerical differentiation/ integration is the process of computing the value of the derivative of a function, whose analytical expression is not available, but is specified through a set of values at certain tabular points ${x_0, x_1, \cdots, x_n}$ In such cases, we first determine an interpolating polynomial approximating the function (either on the whole interval or in sub-intervals) and then differentiate/integrate this polynomial to approximately compute the value of the derivative at the given point.