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Anyone have time to check my Jacobian for this transformation?

  1. Apr 19, 2004 #1
    Anyone have time to check my Jacobian for this transformation!?

    [tex]x = e^{u-v}[/tex] [tex]y = e^{u+v}[/tex] [tex]z = e^{u+v+w}[/tex]

    I ended up getting the Jacobian as ZERO.

    This is why Im doubting myself--- it seems wrong! What do you guys get?

    Thanks for you help. :redface:
  2. jcsd
  3. Apr 19, 2004 #2
    the jacobian isnt zero, check your calculations, you might have a bad sign...
  4. Apr 19, 2004 #3
    Yeah i screwed up --- i got something like 2^(u-v) * (e^2u+2v+w)

    does that look oK?
  5. Apr 19, 2004 #4
    whoops i mean [2*e^(u-v)] * [(e^2u+2v+w)]
  6. Apr 19, 2004 #5


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    You still may be off: I get 2eu+v+we2u= 2e3u+v+w.

    (Edited after jdavel pointed out an error.)
    Last edited by a moderator: Apr 19, 2004
  7. Apr 19, 2004 #6
    Halls of Ivy,

    You have a typo in your final answer. That should be 3u, not 2u.

    Theelectricchild, to keep from confusing the signs, it helps (at least in this case, since exp(x) is its own derivative) to find all nine derivates and then write the determinant in terms of x, y and z. Then, with those two beautiful zeros, the Jacobian = 2xyz is almost staring you in the face.
    Last edited: Apr 19, 2004
  8. Apr 20, 2004 #7
    Thx for your help guys--- I find this class a big leap in difficulty from where we left off in our calculus III course which was on tangent planes--- I am glad I am getting help. Ugh now to get ready for Friday's midterm.
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