Multivariable Calculus | Transformations of the plane.

Working towards a formula for change of variables in multiple integrals, we introduce the notion of a one to one transformation of the plane.
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Hi Michael
Is the map from the polar rectangle with open boundary at the top to the ellipse 1-1?
Shouldn't the left boundary also be open (excepting the origin point, which sounds messy) as (0,ϴ)→(0,0) for all angles ϴ?

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