Definition:Differential of Mapping/Functional

Definition
Let $J\sqbrk y$ be a differentiable functional.

Let $h$ be an increment of the independent variable $y$.

Then the term linear $h$ is called the differential of the functional $J$, and is denoted by $\delta J \sqbrk {y; h}$.

Also known as
The differential $\delta J \sqbrk {y; h}$ is also known as the (first) variation.