Gfind the jacobian of the transformation. x = 6e−3r sin 2θ, y = e3r cos 2θ

Definition:

The Jacobian of the transformation x = f(r, θ) and y = g(r ,θ)  is:

=             ......[1]

Given: and  

then,  

and      

Substitute these value in [1] ;  

=

 =

On simplify:

 =  

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therefore, the jacobian transformation of and   is;