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\begin{center}
{Mathematical Physics --- PHZ 3113}\\\vspace {2mm} 
Homework 9 (March 25, 2013) \\ 
Jacobi Determinant
\end{center}
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\noindent 1. Calculate
\begin{eqnarray} \nonumber
  I\ =\ \int_{-\infty}^{+\infty} \int_{-\infty}^{+\infty}
  dx\,dy\,e^{-(x-y)^2-(x+y)^2}\,.
\end{eqnarray} 
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\noindent 2. Calculate
\begin{eqnarray} \nonumber
  I &=& \int_{-\infty}^{+\infty} \int_{-\infty}^{+\infty}
  \int_{-\infty}^{+\infty} dx_1\,dx_2\,dx_3\,\\ \nonumber
  &~& \\ \nonumber
  &~& e^{-(x_1+x_2+x_3)^2-(x_1+x_2-x_3)^2-(x_1-x_2-x_3)^2}\,.
\end{eqnarray} 
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