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Can u-substitution be described as a Jacobian?

  1. Feb 7, 2012 #1

    Char. Limit

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    So u-substitution is used to make an effective change of variables in one-dimensional calculus. Jacobian determinants are used to make a change of variables in two or higher-dimensional calculus. Can a u-substitution be thought of as a one-dimensional Jacobian determinant?

    And on an entirely unrelated note, does anyone know how to make vertical dots in matrix? I was going to draw out the Jacobian determinant, but I couldn't figure that out.
     
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  3. Feb 7, 2012 #2

    AlephZero

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    You can think of it as the determinant of a 1x1 Jacobian matrix if you want. But apart from telling you that single-variable calculus is consistent with multiple-variable calculus, I'm not sure what that buys you.

    \vdots.
     
  4. Feb 7, 2012 #3

    Char. Limit

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    It's always nice to know that things are consistent between the two areas, though. Thanks!
     
  5. Feb 7, 2012 #4

    micromass

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    What kind of "vertical dots"?? And did you type "matrix" instead of "LaTeX"??
     
  6. Feb 7, 2012 #5

    Char. Limit

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    Typo, and, well, ellipses, but vertical, not horizontal. Like this:

    [tex]\vdots[/tex]
     
  7. Feb 7, 2012 #6

    micromass

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    Did you just answer your own question?? :rofl: Yes, vdots is the way to type vertical ellipses. And ddots is the way to type diagonal ellipses.
     
  8. Feb 7, 2012 #7

    Char. Limit

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    I got vdots from AlephZero above, and ddots from you! Now I can type out n-size matrices!
     
  9. Feb 7, 2012 #8

    micromass

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    Oh, how did I miss that??

    Also, don't forget hdots which is a nice way to type ...
     
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