Question

Confusions on functions on open intervals

score 24 · Answer 1 · 2020-02-12 06:40:42

24

Views

Confusions on functions on open intervals

Published on 12 Feb 2020 - 6:40

score 172 · Answer 2 · 2020-02-24 07:24:29

172

Views

Is a bijective smooth map of the closed disk with invertible differential a diffeomorphism?

Published on 24 Feb 2020 - 7:24

score 124 · Answer 3 · 2020-03-05 02:34:10

124

Views

Find the differential of an inverse function of $G(u,v) = (u^4 - u + uv + v^2,\cos u + \sin v)$

Published on 05 Mar 2020 - 2:34

score 22 · Answer 4 · 2020-03-05 06:38:21

22

Views

Invertible $ T \in L(R^n, R^n) $ such that there is no $S \in L(R^n,R^n)$ with $e^S = T.$

Published on 05 Mar 2020 - 6:38

score 62 · Answer 5 · 2020-03-06 03:45:28

62

Views

Show that non-singular is necessary for the Inverse Function Theorem

Published on 06 Mar 2020 - 3:45

score 104 · Answer 6 · 2020-03-14 05:26:58

104

Views

Assuming $A = Df(x_0)$ is invertible, prove that there exists $\mu > 0$ such that for all $x \in R^n$ $ ||Ax|| \geq \mu||x||$

Published on 14 Mar 2020 - 5:26

score 66 · Answer 7 · 2026-03-25 14:03:19

66

Views

Showing that a function in $\Bbb{R}^{2}$ is a diffeomorphism.

Published on 25 Mar 2026 - 14:03

score 281 · Answer 8 · 2020-03-27 04:41:17

281

Views

Set of points such that derivative is injective is an open set

Published on 27 Mar 2020 - 4:41

score 4.5k · Answer 9 · 2020-04-05 16:38:39

4.5k

Views

proving bi-Lipschitz function has an inverse that is lipschitz

Published on 05 Apr 2020 - 16:38

score 137 · Answer 10 · 2026-03-25 15:39:47

137

Views

Application of Implicit Function Theorem to a function $\psi:U\subset\Bbb{R}^{2}\rightarrow \Bbb{R}^{4}$

Published on 25 Mar 2026 - 15:39

score 30 · Answer 11 · 2020-04-11 16:24:02

30

Views

Determine the inverse g(x) of the function f(x)=1+1/x , stating its domain and range. Verify that f(g(x)) = g(f(x)) = x and that g’(f(x))= 1/(f’(x))

Published on 11 Apr 2020 - 16:24

score 22 · Answer 12 · 2020-04-26 19:45:55

22

Views

What is solution of $f'(f(x))=\exp(f'^{-1}(x))$ with $ f'^{-1}$ is a compositional inverse of $f'$?

Published on 26 Apr 2020 - 19:45

score 413 · Answer 13 · 2020-05-17 02:28:00

413

Views

Inverse Function Theorem for functions $f(x,y)$ and $\int\limits_0^1\frac{\partial f}{\partial x}(tx,y)dt$

Published on 17 May 2020 - 2:28

score 163 · Answer 14 · 2020-05-27 23:47:56

163

Views

Unique Solution for Square-root function on Matrices

Published on 27 May 2020 - 23:47

score 644 · Answer 15 · 2020-05-28 05:38:03

644

Views

Unique Solution to 1st Order Autonomous ODE

Published on 28 May 2020 - 5:38

List Question

Confusions on functions on open intervals

Is a bijective smooth map of the closed disk with invertible differential a diffeomorphism?

Find the differential of an inverse function of $G(u,v) = (u^4 - u + uv + v^2,\cos u + \sin v)$

Invertible $ T \in L(R^n, R^n) $ such that there is no $S \in L(R^n,R^n)$ with $e^S = T.$

Show that non-singular is necessary for the Inverse Function Theorem

Assuming $A = Df(x_0)$ is invertible, prove that there exists $\mu > 0$ such that for all $x \in R^n$ $ ||Ax|| \geq \mu||x||$

Showing that a function in $\Bbb{R}^{2}$ is a diffeomorphism.

Set of points such that derivative is injective is an open set

proving bi-Lipschitz function has an inverse that is lipschitz

Application of Implicit Function Theorem to a function $\psi:U\subset\Bbb{R}^{2}\rightarrow \Bbb{R}^{4}$

Determine the inverse g(x) of the function f(x)=1+1/x , stating its domain and range. Verify that f(g(x)) = g(f(x)) = x and that g’(f(x))= 1/(f’(x))

What is solution of $f'(f(x))=\exp(f'^{-1}(x))$ with $ f'^{-1}$ is a compositional inverse of $f'$?

Inverse Function Theorem for functions $f(x,y)$ and $\int\limits_0^1\frac{\partial f}{\partial x}(tx,y)dt$

Unique Solution for Square-root function on Matrices

Unique Solution to 1st Order Autonomous ODE

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