  We demonstrate how to make the coordinate transformation or change of
variables from Cartesian coordinates to curvilinear coordinates by making use
of a convolution of a function with Dirac delta functions whose arguments are
determined by the transformation functions between the two coordinate systems.
By integrating out an original coordinate with a Dirac delta function, we
replace the original coordinate with a new coordinate in a systematic way. A
recursive use of Dirac delta functions allows the coordinate transformation
successively. After replacing every original coordinate into a new curvilinear
coordinate, we find that the resultant Jacobian of the corresponding coordinate
transformation is automatically obtained in a completely algebraic way. In
order to provide insights on this method, we present a few examples of
evaluating the Jacobian explicitly without resort to the known general formula.
