Finite differences

Finite differences are a way to approximate how a quantity changes over small intervals. Instead of calculating exact derivatives, which can be complex, finite differences use the difference between function values at two points to estimate the rate of change. For example, if you know the values of a function at two points close together, the difference between these values divided by the distance gives an approximate slope. This concept is fundamental in numerical analysis, helping us analyze data, model systems, and solve equations when exact calculations are difficult or impossible.