A <coordinate transformation> is a continuously differentiable <bijection> from the <open set> $U$ onto an open subset $T(U)\subset\mathbb R^2$, with continuously differentiable inverse. Equivalently, it is a $C^1$ <diffeomorphism>; its <Jacobian determinant> never vanishes. The <inverse function theorem> supplies the local inverse, while global <injectivity> is an additional requirement.

Solution

Past exam of the Probability, statistics and options II course of the University of Oxford / 2007 / D / 3 / i / Solution

 Solution (source code)