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:
“Are not all finite beings better pleased with motions relative than absolute?”
—Henry David Thoreau (1817–1862)
“That was always the difference between Muhammad Ali and the rest of us. He came, he saw, and if he didn’t entirely conquer—he came as close as anybody we are likely to see in the lifetime of this doomed generation.”
—Hunter S. Thompson (b. 1939)
“The variables of quantification, ‘something,’ ‘nothing,’ ‘everything,’ range over our whole ontology, whatever it may be; and we are convicted of a particular ontological presupposition if, and only if, the alleged presuppositum has to be reckoned among the entities over which our variables range in order to render one of our affirmations true.”
—Willard Van Orman Quine (b. 1908)