In applied mathematics and the calculus of variations, the first variation of a functional J(y) is defined as the linear functional mapping the function h to
where y and h are functions, and ε is a scalar.[1] This is recognizable as the Gateaux derivative of the functional.[1]
Example
Compute the first variation of
From the definition above:
See also
References
- 1 2 "1.3.2 First variation and first-order necessary condition". liberzon.csl.illinois.edu. Retrieved 3 March 2026.