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Gelfand "Calculus of Variation" 1.7 question on definition and purpose of variational deriva...

In Gelfand Calculus of Variation, chapter 1.7, the variational derivative is defined as: $$\left.\frac{\partial J}{\partial y}\right|_{x = x_0} = \lim_{\Delta\sigma \rightarrow 0}\frac{J[y+h]-J[y]}{\ …
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