Change of variables

What the problems look like

A few statements from this skill. Answers, hints and worked solutions live in the practice session.

1. Warm-up

   A change of variables is defined by $x = -2u + 4v$ and $y = 3u - 3v$. Compute the Jacobian determinant $\dfrac{\partial(x,y)}{\partial(u,v)}$.

2. Warm-up

   A change of variables is defined by $x = 0u + 4v$ and $y = 2u + 5v$. Compute the Jacobian determinant $\dfrac{\partial(x,y)}{\partial(u,v)}$.

3. Warm-up

   A change of variables is defined by $x = 4u - 4v$ and $y = 4u - 5v$. Compute the Jacobian determinant $\dfrac{\partial(x,y)}{\partial(u,v)}$.

Problems shown under their original terms: Generated (template, solver-computed).