Finite Difference - Rules For Calculus of Finite Difference Operators

Rules For Calculus of Finite Difference Operators

Analogous to rules for finding the derivative, we have:

  • Constant rule: If c is a constant, then
  • Linearity: if a and b are constants,

All of the above rules apply equally well to any difference operator, including as to .

  • Product rule:
  • Quotient rule:
\nabla \left( \frac{f}{g} \right) = \frac{1}{g} \det \begin{bmatrix} \nabla f & \nabla g \\ f & g \end{bmatrix} \left( \det {\begin{bmatrix} g & \nabla g \\ 1 & 1 \end{bmatrix}}\right)^{-1}
or
  • Summation rules:


Read more about this topic:  Finite Difference

Famous quotes containing the words rules, calculus, finite and/or difference:

    “... a large portion of success is derived from flexibility. It is all very well to have principles, rules of behavior concerning right and wrong. But it is quite as essential to know when to forget as when to use them.”
    —Alice Foote MacDougall (1867–1945)

    “I try to make a rough music, a dance of the mind, a calculus of the emotions, a driving beat of praise out of the pain and mystery that surround me and become me. My poems are meant to make your mind get up and shout.”
    —Judith Johnson Sherwin (b. 1936)

    “Put shortly, these are the two views, then. One, that man is intrinsically good, spoilt by circumstance; and the other that he is intrinsically limited, but disciplined by order and tradition to something fairly decent. To the one party man’s nature is like a well, to the other like a bucket. The view which regards him like a well, a reservoir full of possibilities, I call the romantic; the one which regards him as a very finite and fixed creature, I call the classical.”
    —Thomas Ernest Hulme (1883–1917)

    “There is no difference between the client and the prostitute. If a man goes to a prostitute, he is also a prostitute.”
    —Sister Michele, Indian nun. As quoted in the New York Times Magazine, p. 35 (January 16, 1994)