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Second variation

In the calculus of variations, the second variation extends the idea of the second derivative test to functionals. Much like for functions, at a stationary point where the first derivative is zero, the second derivative determines the nature of the stationary point; it may be negative (if the point is a maximum point), positive (if a minimum) or zero (if…

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Derivation

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The Jacobi necessary condition

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The Jacobi necessary condition

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Second variation

Nodes30
Edges29
Triples0
Avg. degree1.93
Density0.066667
Components1

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Important terminology

displaystyle jacobi problem functional variational second point first equation condition minimum variation derivative conjugate points necessary y' solution y'y' stationary

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