2016年10月26日 · $\begingroup$ The previous link does not lead to the inverse function theorem, but to a nice geometric explanation of the formula for the derivative of the inverse function. The inverse function theorem is something else. $\endgroup$ –

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2018年7月5日 · I want to prove that the implicit function theorem implies the inverse function theorem. I saw in another post what's written below as the proof for this but I don't understand what they've done. $$ \text{ For } f : \mathbb{R}^n \to \mathbb{R}^n \text{, consider } F:\mathbb{R}^n\times\mathbb{R}^n \to \mathbb{R}^n \text{ given by } F({\bf x ...

2020年5月6日 · Since this definition is fairly abstract, Rudin introduces a more practical criterion to test whether a given function is of class $\mathscr{C}'$, in terms of the continuity of the partial derivatives (Theorem 9.21).

In Proving the Inverse function theorem in Mathematical Analysis Book of Rudin, when he want to show that V is open, Why he simply does not use that under continuous function (Mapping), the open set U ...

2017年12月17日 · Conditions for Inverse Function Theorem. Ask Question Asked 7 years, 1 month ago.

2013年7月1日 · I first studied the proof of the inverse function theorem over 20 years ago, and it seemed opaque. But now I finally understand the proof well enough that it seems clear and almost straightforward. I like the presentation of Spivak's proof that is given in Jerry Shurman's excellent book "Calculus and Analysis in Euclidean Space".

2011年4月24日 · The inverse/implicit function theorem tell you when you can (locally) solve a system of equations. This is incredibly important whenever you want to study a nonlinear problem -- e.g. differential geometry, PDE, etc. In the following I will call both of them "implicit function theorem", since they are the same thing, really.

2021年11月25日 · Inverse function theorem on smooth manifolds. Ask Question Asked 3 years, 1 month ago. Modified 3 years, 1 ...

2019年10月13日 · Inverse function theorem for manifolds. Ask Question Asked 5 years, 3 months ago. Modified 5 years, 3 ...