## Jacobian (Change of Variables in Multiple Integrals)

Jacobians If $x=x(u,v)$ and $y=y(u,v)$ then the Jacobian of $x$ and $y$ with respect to $u$ and $v$ is \begin{equation} \frac{\partial (x,y)}{\partial (u,v)} =J(u,v)=\left| \begin{array}{cc} \frac{\partial x}{\partial u} & \frac{\partial x}{\partial v} \\ \frac{\partial y}{\partial u} & \frac{\partial y}{\partial v} \end{array} \right|=\frac{\partial x}{\partial u}\frac{\partial y}{\partial v}-\frac{\partial y}{\partial u}\frac{\partial x}{\partial v}. \end{equation} Example. Determine the Jacobian …

Jacobian (Change of Variables in Multiple Integrals) Read More