Definition:Finite Difference Operator/Forward Difference/First

Definition

Let $f: \R \to \R$ be a real function.

Let $y = \map f x$ have known values:

$y_k = \map f {x_k}$

for $x_k \in \set {x_0, x_1, \ldots, x_n}$ defined as:

$x_k = x_0 + k h$

for some $h \in \R_{>0}$.

The first forward difference operator on $f$ is defined as:

$\Delta \map f {x_i} := \map f {x_{i + 1} } - \map f {x_i}$

for $i = 0, 1, 2, \ldots, n - 1$

Also known as

The first forward difference operator is also known as just the forward difference operator.

Also see

• Definition:Backward Difference Operator
• Definition:Central Difference Operator

• Results about the forward difference operator can be found here.

Sources

• 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): finite differences
• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): finite differences
• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): forward difference