- #1

#### fatpotato

- Homework Statement
- Choose the correct change of variables among the three possible choices to map ##\Sigma## to a rectangular region.

- Relevant Equations
- None for now

Hello,

This problem comes just prior to introducing change of variables with Jacobian.

Given the following region in the x-y plane, I have to choose (with justification) the correct change of variables associated, for ##u\in [0,2]## and ##v \in [0,1]##.

The correct choice here is a), but I do not understand why...Solution only mentions that a possible change of variable for x would be ##x = -(y+1) + u(y+1)##, so we get to solution a).

Here is my question: is there a systematic way of finding the appropriate change of variables? How did the instructor suddenly decide that choosing the previous substition would be a good idea to solve the problem? I have no idea where to begin.

Thank you very much for your help.

This problem comes just prior to introducing change of variables with Jacobian.

Given the following region in the x-y plane, I have to choose (with justification) the correct change of variables associated, for ##u\in [0,2]## and ##v \in [0,1]##.

The correct choice here is a), but I do not understand why...Solution only mentions that a possible change of variable for x would be ##x = -(y+1) + u(y+1)##, so we get to solution a).

Here is my question: is there a systematic way of finding the appropriate change of variables? How did the instructor suddenly decide that choosing the previous substition would be a good idea to solve the problem? I have no idea where to begin.

Thank you very much for your help.