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Generalizations of the derivative
An important case is the variational derivative in the calculus of variations. Repeated application of differentiation leads to derivatives of higher order and ...
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May 3, 2006 ... Consider that one of the node, (xk,yk) moves vertically by δyk, the variational derivative. δI/δy at x = xk is the change of I divided by the change ...
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Variational Derivatives. Without giving strict justification, we shall explain here several simple rules of calculating variational derivatives. They follow from the fact ...
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Allow me to start with a definition. Given a function $u = u(x)$, a function $L$ of $ x, u$, and all derivatives of $u$;
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The extremal functions are solutions of the Euler(-Lagrange) equations that are obtained by setting the first variational derivatives of the functional F with respect ...
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Jan 14, 1998 ... next up previous contents. Next: Parameter Adaptation Up: Information Maximization in Single Neurons Previous: Model Description ...
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This approach starts directly with a general expression for the first variational derivative. (Setting this to zero is called “first order optimality condition” in the ...
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The authors introduce a new class of structure preserving numerical methods which improve the qualitative behavior of solutions of partial differential equations ...
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A collection of Mathematica v.2 routines by Peter Olver.
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Dec 9, 2010 ... The methods put forward in Discrete Variational Derivative Method concentrate on a new class of "structure-preserving numerical equations" ...
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