Definition:Differential of Mapping/Functional

Definition
Let $ J \left [ { y } \right ] $ 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 \left [ { y; h } \right ] $.

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