For Class Functions, Transformation has Jacobian Determinant
\frac{\partial x}{\partial u} & \frac{\partial x}{\partial v}\\ \frac{\partial y}{\partial u} & \frac{\partial y}{\partial v}\\ \end{array}\right]$$For C1 Class Functions, Transformation T(u,v)=(x(u,v),y(u,v)) has Jacobian Determinant
\frac{\partial x}{\partial u} & \frac{\partial x}{\partial v}\\ \frac{\partial y}{\partial u} & \frac{\partial y}{\partial v}\\ \end{array}\right]$$