# Numerical Methods/Numerical Differentiation

Often in Physics or Engineering it is necessary to use a calculus operation known as differentiation. Unlike textbook mathematics, the differentiated functions are data generated by an experiment or a computer code.

Begin with the Taylor series as seen in Equation 1.

Next by cutting off the Taylor series after the fourth term and evaluating it at h and -h yields Equations (2) and (3).

Then by subtracting Equation (2) by Equation (3) yields.

### Central DifferenceEdit

### Forward DifferenceEdit

### Backward DifferenceEdit

## Second DerivativeEdit

The second order derivatives can be obtained by adding equations (2) and (3) (if properly expanded to include the fourth-derivative-term):