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Functional derivation

  1. Jun 24, 2007 #1
    I have a problem with this simple (?) derivation

    [tex] u(f(t),t) = \frac{\partial }{\partial f(t)}
    \int_0^T \ g(f(t),f(t'),t,t') \ dt'
  2. jcsd
  3. Jun 29, 2007 #2
    Hi 'etzzzz' the derivative you have put has some bit different notation.

    The expression you gave is just a 'Frechet' derivative on an infinite dimensional space if we note

    [tex] g( f(t) , f(t') ,t,t')=F [/tex]

    considering that we are varying the function f(t') but not the function f(t) the Euler-Lagrange equations are.

    [tex] \frac{ \partial g}{\partial f(t)} [/tex]

    in case the derivative respect to t' of f(t') do not appear
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