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:

    “Retaliation is related to nature and instinct, not to law. Law, by definition, cannot obey the same rules as nature.”
    —Albert Camus (1913–1960)

    “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)

    “We know then the existence and nature of the finite, because we also are finite and have extension. We know the existence of the infinite and are ignorant of its nature, because it has extension like us, but not limits like us. But we know neither the existence nor the nature of God, because he has neither extension nor limits.”
    —Blaise Pascal (1623–1662)

    “There is singularly nothing that makes a difference a difference in beginning and in the middle and in ending except that each generation has something different at which they are all looking. By this I mean so simply that anybody knows it that composition is the difference which makes each and all of them then different from other generations and this is what makes everything different otherwise they are all alike and everybody knows it because everybody says it.”
    —Gertrude Stein (1874–1946)