A <coordinate transformation> is a continuously differentiable bijection from the <open set> $U$ onto an open image, with continuously differentiable inverse. Equivalently one may specify a one-to-one continuously differentiable map whose <Jacobian determinant> is everywhere nonzero; the <inverse function theorem> gives the corresponding smooth inverse on its image.

Solution

Past exam of the options II course of the University of Oxford / 2007 / D / D3 / i / Solution

 Solution (source code)