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Homework Help: Change of Variables: Jacobians (Answer check)

  1. Nov 12, 2008 #1
    1. The problem statement, all variables and given/known data

    Sketch the image S in the uv-plane of the region R in the xy-plane using the given transformations: x=(1/3)(4u-v) y=(1/3)(u-v)


    r0bmrn.jpg

    2. Relevant equations



    3. The attempt at a solution

    3y=u-v
    3y+v=u place this into the x equation

    3x=4(3y+v)-v
    3x-12y=3v

    x-4y=v
    place this back into equation above, simplify, and we have

    x-y=u

    (x,y) (u,v)
    (0,0) (0,0)
    (2,2) (0,-6)
    (4,1) (3,0)
    (6,3) (3,-6)


    2hd1pq8.jpg


    Seems to come out correct, but just want to double check. Any help is appreciated :smile:
     
  2. jcsd
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