1617-257/TUT-R-6

On 10/20/16, we discussed how one can calculate the derivative of the inverse of the map [math]\displaystyle{ f: (0,1/2) \times (0, \pi/4) \to U \subset \mathbb R^2 }[/math] where [math]\displaystyle{ f(r, \theta) := (r \cos \theta, r \sin \theta) }[/math]:

Method 1. Find [math]\displaystyle{ f^{-1} }[/math] explicitly and differentiate it.

Method 2. Use the inverse function theorem.

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Students who did both calculations noted that Method 2 was simpler than Method 1.