Finite Difference in Several Variables
Finite differences can be considered in more than one variable. They are analogous to partial derivatives in several variables.
Some partial derivative approximations are:
Alternatively, for applications in which the computation of is the most costly step and both first and second derivatives must be computed, a more efficient formula for the last case is:
since the only values to be computed which are not already needed for the previous four equations are and .
Read more about this topic: Finite Difference
Famous quotes containing the words finite, difference and/or variables:
“Sisters define their rivalry in terms of competition for the gold cup of parental love. It is never perceived as a cup which runneth over, rather a finite vessel from which the more one sister drinks, the less is left for the others.”
—Elizabeth Fishel (20th century)
“Take away an accident of pigmentation of a thin layer of our outer skin and there is no difference between me and anyone else. All we want is for that trivial difference to make no difference.”
—Shirley Chisholm (b. 1924)
“Science is feasible when the variables are few and can be enumerated; when their combinations are distinct and clear. We are tending toward the condition of science and aspiring to do it. The artist works out his own formulas; the interest of science lies in the art of making science.”
—Paul Valéry (1871–1945)