In different coordinate systems of the form x = x ( u 1 , u 2 , u 3 ) {\displaystyle x=x(u_{1},u_{2},u_{3})} , y = y ( u 1 , u 2 , u 3 ) {\displaystyle y=y(u_{1},u_{2},u_{3})} , z = z ( u 1 , u 2 , u 3 ) {\displaystyle z=z(u_{1},u_{2},u_{3})} , the volume element changes by the Jacobian (determinant) of the coordinate change: