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:


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