[Solved] Find the Jacobian of the transformation, x = u2 -v2 and y = u2+ v2

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Find the Jacobian of the transformation, x = u^2 -v^2 and y = u^2+ v^2

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To find the Jacobian of the transformation given by the equations π‘₯=𝑒2βˆ’π‘£2x=u2βˆ’v2 and 𝑦=𝑒2+𝑣2y=u2+v2, we need to compute the determinant of the Jacobian matrix. The Jacobian matrix for the transformation from (𝑒,𝑣)(u,v) to (π‘₯,𝑦)(x,y) is given by

Β 
Β 
Β 
Β 
Thus, the Jacobian determinant of the transformation is: 8 𝑒 𝑣
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