# 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 Difference

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### Forward Difference

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### Backward Difference

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## Second Derivative

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