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Partial Derivative Matrix Proof

  1. Sep 24, 2010 #1
    x=rcos(θ), y=rsin(θ) Do these formulas look familiar? They give the relationship between two coordinate systems in the plane. Evaluate:
    |x'r x'θ|

    |y'r y'θ|

    I know that the x primes are cos(θ) and -rsin(θ), and the y primes are sin(θ) and rcos(θ), respectively. I am not sure what to do with the matrix. The original functions do look familiar, but I do not remember what they mean.
  2. jcsd
  3. Sep 24, 2010 #2


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    The notation stands for the determinant.

    \left|\begin{matrix} a& b \\ c & d \end{matrix} \right|= ad - bc
  4. Sep 25, 2010 #3
    As for the meaning: these are polar coordinates.
  5. Sep 25, 2010 #4
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