8. Midterm 1 and Change of Variables

Jacobians In Two Variables — Quiz

Test your understanding of jacobians in two variables with 5 practice questions.

Practice Questions

Question 1

For the transformation $x=u+v$ and $y=u-v$, what is $\frac{\partial(x,y)}{\partial(u,v)}$?

Question 2

In a change of variables, which quantity tells how area is scaled locally?

Question 3

For polar coordinates $x=r\cos\theta$ and $y=r\sin\theta$, what is $\frac{\partial(x,y)}{\partial(r,\theta)}$?

Question 4

If $x=2u$ and $y=3v$, what is $\frac{\partial(x,y)}{\partial(u,v)}$?

Question 5

What does a Jacobian determinant of $0$ at a point usually indicate?