Jacobian Matrix: It is a matrix which is used to relate the derivatives in two different co-ordinates. It is generally represented by

$$ \begin{bmatrix} J \end{bmatrix} = \begin{bmatrix} \frac{\partial x}{\partial \xi} & \frac{\partial y}{\partial \xi} \\ \frac{\partial x}{\partial \eta} & \frac{\partial y}{\partial \eta} \end{bmatrix} $$

It relates the derivatives of cartesian and natural system where the term x-y represents cartesian co-ordinate system and $\xi$-$\eta$ represents natural co-ordinate system.