Difference between revisions of "1617-257/TUT-R-6"

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(Created page with "On 10/20/16, we discussed how one can calculate the derivative of the inverse of a map <math>f: (0,1/2) \times (0, \pi/4) \to U \subset \mathbb R^2</math> where <math>f(r, \th...")
 
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On 10/20/16, we discussed how one can calculate the derivative of the inverse of a map <math>f: (0,1/2) \times (0, \pi/4) \to U \subset \mathbb R^2</math> where <math>f(r, \theta) := (r \cos \theta, r \sin \theta)</math>:
 
On 10/20/16, we discussed how one can calculate the derivative of the inverse of a map <math>f: (0,1/2) \times (0, \pi/4) \to U \subset \mathbb R^2</math> where <math>f(r, \theta) := (r \cos \theta, r \sin \theta)</math>:
  
Method 1. Find <math>f^{-1}</math> explicitly and differentiate it.
+
<b>Method 1</b>. Find <math>f^{-1}</math> explicitly and differentiate it.
  
Method 2. Use the inverse function theorem.
+
<b>Method 2</b>. Use the inverse function theorem.

Revision as of 13:23, 21 October 2016

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

Method 1. Find f^{-1} explicitly and differentiate it.

Method 2. Use the inverse function theorem.