Numerical Methods for Chemical Engineers Using Excel, VBA, and MATLAB

4 Numerical Differentiation and Integration

4.1 NUMERICAL DIFFERENTIATION

4.1.1 APPROXIMATION OF A DERIVATIVE IN ONE VARIABLE

Recall the definition of the derivative from calculus:

For a finite Δx, this is an approximation of the derivative:

This is the simplest form of “finite difference derivative” and is called the “forward” difference approximation to the derivative. E(x) represents the “error” in the approximation. In order to estimate the ...