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Calculate the jacobian

  1. Jan 7, 2009 #1
    calculate the jacobian d(x,y)/d(u,v) of the transformation u=x2+y2
    v=x+y

    for this do i first have to calculate the jacobian d(u,v)/d(x,y) then do 1over the answer? because i would assume the matrix to be det|{(dudx,dudy)(dvdx,dvdy)} but with (u,v) on top i cannot get this
     
  2. jcsd
  3. Jan 8, 2009 #2

    HallsofIvy

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    You can do any of three things:
    1) Solve for x and y as functions of u and v.
    2) Use implicit differentiation to find [itex]\partial x/\partial u[/itex], [itex]\partial y/\partial u[/itex], [itex]\partial x/\partial v[/itex], and [itex]\partial y/\partial v[/itex].
    3) Take the reciprocal of d(u,v)/d(x,y).
     
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