The first variation of a functional at in the direction is
(1)
If a continuous function satisfies
(1)
for every smooth compactly supported test function , then on .

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  1. Variation
  2. Functional
  3. Calculus of variations
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First variation by Wikipedia Bot 1
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The term "first variation" is often used in the context of calculus of variations, which is a mathematical field that deals with optimizing functionals, usually integrals that depend on functions and their derivatives. The first variation is a concept that measures how a functional changes when the function is varied or perturbed slightly.
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