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 for, rules, calculus, finite and/or difference:

    Logic teaches rules for presentation, not thinking.
    Mason Cooley (b. 1927)

    For 350 years we have been taught that reading maketh a full man, conference a ready man and writing an exact man. Football’s place is to add a patina of character, a deference to the rules and a respect for authority.
    Walter Wellesley (Red)

    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)

    For it is only the finite that has wrought and suffered; the infinite lies stretched in smiling repose.
    Ralph Waldo Emerson (1803–1882)

    A young man is not a proper hearer of lectures on political science; for he is inexperienced in the actions that occur in life, but its discussions start from these and are about these; and, further, since he tends to follow his passions, his study will be vain and unprofitable, because the end that is aimed at is not knowledge but action. And it makes no difference whether he is young in years or youthful in character.
    Aristotle (384–323 B.C.)