Activity 12.9.3

In this activity, we will look at a few familiar Jacobians and their interpretations.

1. Find the Jacobian for the transformation given by $x=3s-1$ and $y=\frac{t}{3}+2$. Write a couple of sentences about why the area of a region will not change with respect to this change of coordinates.

2. Find the Jacobian when changing from rectangular to polar coordinates. Write a couple of sentences to connect to our work on double integrals in polar coordinates.