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Landau and Lifschitz derivation question

  1. Oct 27, 2013 #1
    Greetings,

    On page 7 of Landau and Lifschitz Vol. 1 3rd. Ed, it says

    [itex]L(v'^2)=L(v^2+2\bf{v}\cdot\bf{ε}+\bf{ε}^2)[/itex].

    They then Taylor expand in powers of ε, getting (ignoring second order terms and higher)

    [itex]L(v'^2)=L(v^2)+\frac{\partial L}{\partial v^2}2\bf{v}\cdot\bf{ε}[/itex].

    The [itex]\frac{\partial L}{\partial v^2}[/itex] confuses me. We effectively have a function of the form

    [itex]f(g(x))=f(a+bx+cx^2)[/itex], which, Taylor expanding around [itex]x=0[/itex], would give

    [itex]f(a+bx+cx^2)=f(x=0)+\frac{df}{dg}(x=0)\frac{dg}{dx}(x=0)x=\frac{df}{dg}(x=0)bx[/itex].

    So, where I have [itex]\frac{df}{dg}(x=0)[/itex], Landau has [itex]\frac{\partial f}{\partial a}[/itex].

    How do I go from what I have to what Laundau has?

    Thanks.

    -HJ Farnsworth
     
  2. jcsd
  3. Oct 27, 2013 #2
    Landau's notation is just a short hand for your notation so there isn't any math to explain here.
     
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