- #1
minderbinder
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Homework Statement
Find a one-to-one C1 mapping [tex]f[/tex] from the first quadrant of the xy-plane to the first quadrant of the uv-plane such that the region where [tex]x^2 \leq y \leq 2x^2[/tex] and [tex]1 \leq xy \leq 3[/tex] is mapped to a rectangle. Compute the Jacobian det Df and the inverse mapping [tex]f^{-1}[/tex].
The hint for the question states: Map all the regions where [tex]ax^2 \leq y \leq bx^2[/tex] and [tex]c \leq xy \leq d[/tex] to rectangles.
Homework Equations
I'm a little confused on what they mean by map to a rectangle.
The Attempt at a Solution
I'm at a loss of where to begin...