The Inverse Function Theorem

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What conditions guarantee invertibility of functions that map n dimensional Euclidean spaces to n dimensional Euclidean spaces? And what's the derivative of the inverse if it exists? In this lecture, we'll prove the inverse function theorem that answers these questions as well as work out an example with implications for expanding the logarithm in the complex plane.
  1. Josef Sifuentes
  2. Real Analysis
  3. Inverse Function Theorem
  4. Derivatives
  5. Euclidean Space
  6. Multidimensional Functions
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Комментарии
Автор

Hello! Good video! Sorry, In what book is this based on?

ricardoguerrerobarraza
Автор

There's a typo at 19:51. Both x_1 and x_2 should be in the closed ball of radius \delta_1.

jmich
Автор

Thanks for the video. I still don't see what the open set U is in the statement of the theorem, maybe it's obvious and I'm missing something but it's not mentioned in the proof?

Take care and thanks again for your analysis videos they are great :)

cmdcs