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Homework Help: Jacobian Question

  1. May 2, 2010 #1
    1. The problem statement, all variables and given/known data
    Let D be the image of R = [1; 3] x [1; 4]. under the map
    T(u; v) = (u^2/v , v^2/u)

    (a) Compute the Jacobian of T.
    (b) Compute the area of D.



    3. The attempt at a solution
    I'm pretty sure I found the Jacobian (I got -2v/u + 2u/v), but I am confused on the next part. How exactly do I find the ranges of u and v since I am not given functions for y and x. Or can I solve the u^2/v and v^2/u for the values in the ranges of x and y to find the ranges for u and v. Thanks for the help.
     
  2. jcsd
  3. May 2, 2010 #2

    lanedance

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    Homework Helper

    hmm... i would read this as
    [tex] (u,v) \in R = [1, 3] \cross [1, 4] [/tex]

    T then maps from R into D
    [tex] D = T(R) [/tex]
    or more explicity
    [tex] (s,t) \in D | (s,t) = T(u,v) [/tex]

    note i didn't use x & y as i thought they might be confusing the issue
     
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