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Jacobian transformation, find new limits

  1. Apr 13, 2014 #1
    1. The problem statement, all variables and given/known data
    jacobian.png


    2. Relevant equations



    3. The attempt at a solution
    What I don't understand is how I'm supposed to find those limits for U and V. That's not at all what I'm getting. I've tried solving for the max and min x,y coordinates from the given graphs but that doesn't yield the correct answer.
     
  2. jcsd
  3. Apr 13, 2014 #2

    Zondrina

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    Look at the original equations you are given:

    ##x - 2y = 0##
    ##x - 2y = 4##
    ##3x - y = 1##
    ##3x - y = 8##

    Applying your transformation yields:

    ##u = 0##
    ##u = 4##
    ##v = 1##
    ##v = 8##

    These yield your limits.
     
  4. Apr 13, 2014 #3

    vela

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    It quite often helps to make a sketch of the region. What do the u=constant and v=constant lines look like in the xy-plane?
     
  5. Apr 13, 2014 #4

    HallsofIvy

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    It unfortunate that you did not tell us how you tried "solving for the max and min x, y coordinates" since if you had we might be able to point out your mistake. All I can say is that if you have "u= x- 2y", one of the boundaries is x- 2y= 0 and the other is x- 2y= 4, u= 0 and 4 pretty much leaps out at you- u= x- 2y= 0 and u= x- 2y= 4!
     
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