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Help with partial derivatives

  1. Aug 20, 2011 #1
    1. The problem statement, all variables and given/known data

    Let [itex]f = f(u,v)[/itex] where [itex] u = x+y , v = x-y[/itex]
    Find [itex] f_{xx} [/itex] and [itex] f_{yy} [/itex] in terms of [itex] f_u, f_v, f_{uu}, f_{vv}, f_{uv}[/itex]

    Then express the wave equation [itex]\frac{\partial^2f}{\partial x^2} - \frac{\partial^2f}{\partial y^2} = 0[/itex]

    2. Relevant equations

    Chain rule, product rule

    3. The attempt at a solution

    I've solved the partial derivatives [itex]f_{xx} = f_{uu) + 2f_{uv} + f_{vv}[/itex] and [itex]f_{yy} = f_{uu) - 2f_{uv} + f_{vv}[/itex]

    So then [itex]\frac{\partial^2f}{\partial x^2} - \frac{\partial^2f}{\partial y^2} = 0[/itex] is not true unless [itex]f_{uv} = 0[/itex], how am I meant to express it?
     
  2. jcsd
  3. Aug 20, 2011 #2

    Ray Vickson

    User Avatar
    Science Advisor
    Homework Helper

    You have just expressed it! f_{uv} = 0.

    RGV
     
  4. Aug 20, 2011 #3
    I was thinking it couldn't be that simple, apparently it is lol, thanks
     
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