Consider a domain
in the *xy*-plane. Suppose now that there exists an invertible function
*g*=(*g*_{1},*g*_{2}), defined over a domain
in the *uv*-plane such that
(*x*,*y*)=( *g*_{1}(*u*,*v*), *g*_{2}(*u*,*v*)). Moreover suppose that *g* is differentiable over
(i.e. each *g*_{i} is differentiable over
).
Thus, we have:
*f*(*x*,*y*)=*f*(*g*_{1}(*u*,*v*), *g*_{2}(*u*,*v*)).

is called the