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 March 17th, 2014, 06:16 PM #1 Newbie   Joined: Mar 2014 Posts: 8 Thanks: 0 Jacobian determinant We have $d\xi=\frac{1}{\Delta}\left{ -\left( u_{2}\frac{\partial U}{\partial y}+v_{2}\frac{\partial U}{\partial x} \right) dx+\left( u_{2}\frac{\partial U}{\partial x}-v_{2}\frac{\partial U}{\partial y} \right) dy \right}$ $d\eta=\frac{1}{\Delta}\left{ \left( u_{1}\frac{\partial U}{\partial y}+v_{1}\frac{\partial U}{\partial x} \right) dx-\left( u_{1}\frac{\partial U}{\partial x}-v_{1}\frac{\partial U}{\partial y} \right) dy \right}$ where $\Delta=u_{1}v_{2}-u_{2}v_{1}$ What is the Jacobian determinant of the above expressions, in this case $\frac{\partial (\xi,\eta)}{\partial (x,y)}$?
 March 17th, 2014, 06:20 PM #2 Newbie   Joined: Mar 2014 Posts: 8 Thanks: 0 Re: Jacobian determinant We know that $u_{1}(x,y)$ $u_{2}(x,y)$ $u_{3}(x,y)$ $v_{1}(x,y)$ $v_{2}(x,y)$ $v_{3}(x,y)$ They are dependent functions x and y.

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