- Consider the change of coordinates $x=2u-v$, $y=u+2v$.
- In the $uv$ plane draw the curve $u^2+v^2=4$ and give the area inside the region.
- Compute $dx$ and $dy$, and then write them in the matrix form $$ \begin{bmatrix} dx\\dy \end{bmatrix}= \begin{bmatrix} ?&?\\?&? \end{bmatrix} \begin{bmatrix} du\\dv \end{bmatrix}.$$
- Draw the region in the $xy$ plane given by this change of coordinates. What do you think the area is?
- A region in the plane lies above the line $y=x$, below the line $y=4$, and to the right of the $x$-axis (think of it as a triangular axe head).
|
Sun |
Mon |
Tue |
Wed |
Thu |
Fri |
Sat |