1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

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

    User Avatar
    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
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Jacobian Question
  1. Jacobian question (Replies: 5)

  2. Jacobian matrices (Replies: 5)

  3. Inverse Jacobian (Replies: 2)

Loading...