First variation

In applied mathematics and the calculus of variations, the first variation of a functional J(y) is defined as the linear functional δ J ( y ) {displaystyle delta J(y)} mapping the function h to In applied mathematics and the calculus of variations, the first variation of a functional J(y) is defined as the linear functional δ J ( y ) {displaystyle delta J(y)} mapping the function h to where y and h are functions, and ε is a scalar. This is recognizable as the Gateaux derivative of the functional.