Comment #19 on issue 1816 by Vinzent.Steinberg: Adding partial derivatives
and taking derivatives with respect to functions
http://code.google.com/p/sympy/issues/detail?id=1816
In variational calculus, the first derivative of a functional is not that
complicated. Acutally, it's definition is pretty much the same as for the
directional derivative in finitedimensional real space. (Looking at the
wikipedia article, it seems this is the Gateaux derivative). Suppose we
have a functional J. Then the first variation of J in the function y
in "direction" of the test function h is:
d/(d eps) J(y + eps*h) at eps=0
(If J is an integral with y as the integrand, this vanishes if y solves the
Euler-Lagrange equations.)
How is this related to our case?
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