Question

Let $x = u\cos(v)$, and $y = u\sin(v)$, and assume $f(u,v)$ is given. Determine $f_x$ and $f_y$ in terms of $u, v, f_u$, and $f_v$.

score 610 · Answer 1 · 2022-09-21 03:19:12

610

Views

Let $x = u\cos(v)$, and $y = u\sin(v)$, and assume $f(u,v)$ is given. Determine $f_x$ and $f_y$ in terms of $u, v, f_u$, and $f_v$.

Published on 21 Sep 2022 - 3:19

score 66 · Answer 2 · 2022-09-22 09:10:13

66

Views

In Step 2, the author uses the two balls $B(b,2\delta)$ and $B(b,\delta)$. Why? ("Analysis on Manifolds" by James R. Munkres)

Published on 22 Sep 2022 - 9:10

score 236 · Answer 3 · 2022-09-26 15:00:02

236

Views

Does the inverse function theorem require continuity as a hypothesis?

Published on 26 Sep 2022 - 15:00

score 171 · Answer 4 · 2022-09-27 11:19:29

171

Views

Example of a function $f$ which is differentiable at $a$, but $f^{-1}$ is discontinuous at $f(a)$

Published on 27 Sep 2022 - 11:19

score 63 · Answer 5 · 2022-09-28 09:05:55

63

Views

Can this powerful version of inverse function theorem be extended to $\mathbb C^n$?

Published on 28 Sep 2022 - 9:05

score 75 · Answer 6 · 2022-09-28 10:10:47

75

Views

Does this version of inverse function theorem hold for Banach space?

Published on 28 Sep 2022 - 10:10

score 85 · Answer 7 · 2022-09-28 22:40:11

85

Views

Is the inverse function theorem for manifolds applicable here?

Published on 28 Sep 2022 - 22:40

score 58 · Answer 8 · 2022-10-13 12:49:07

58

Views

A question related to the invertibility of derivative

Published on 13 Oct 2022 - 12:49

score 380 · Answer 9 · 2022-10-13 16:24:06

380

Views

How can (dy/dx) = (1/(dx/dy)) be true when isolating different variables and differentiating them indicates this isn't the case?

Published on 13 Oct 2022 - 16:24

score 231 · Answer 10 · 2022-10-14 15:44:38

231

Views

Does a Jacobian matrix with entries equal to zero satisfy the inverse map theorem?

Published on 14 Oct 2022 - 15:44

score 71 · Answer 11 · 2022-10-17 14:35:40

71

Views

Non-singular Jacobian at a point means there exists a region where Jacobian is non-singular

Published on 17 Oct 2022 - 14:35

score 732 · Answer 12 · 2022-11-16 01:40:00

732

Views

If $f$ is continuously differentiable, $f'(x)$ is invertible, and $V$ is open, then $f(V)$ is open

Published on 16 Nov 2022 - 1:40

score 97 · Answer 13 · 2022-11-16 17:24:13

97

Views

Using the Mean Value Inequality to prove the Inverse Function Theorem

Published on 16 Nov 2022 - 17:24

score 171 · Answer 14 · 2022-11-17 12:45:25

171

Views

Most interesting exercises about the implicit and inverse function theorems

Published on 17 Nov 2022 - 12:45

score 100 · Answer 15 · 2022-12-02 20:50:05

100

Views

Is the inverse of a smooth bi-Lipschitz map continuously differentiable?

Published on 02 Dec 2022 - 20:50

List Question

Let $x = u\cos(v)$, and $y = u\sin(v)$, and assume $f(u,v)$ is given. Determine $f_x$ and $f_y$ in terms of $u, v, f_u$, and $f_v$.

In Step 2, the author uses the two balls $B(b,2\delta)$ and $B(b,\delta)$. Why? ("Analysis on Manifolds" by James R. Munkres)

Does the inverse function theorem require continuity as a hypothesis?

Example of a function $f$ which is differentiable at $a$, but $f^{-1}$ is discontinuous at $f(a)$

Can this powerful version of inverse function theorem be extended to $\mathbb C^n$?

Does this version of inverse function theorem hold for Banach space?

Is the inverse function theorem for manifolds applicable here?

A question related to the invertibility of derivative

How can (dy/dx) = (1/(dx/dy)) be true when isolating different variables and differentiating them indicates this isn't the case?

Does a Jacobian matrix with entries equal to zero satisfy the inverse map theorem?

Non-singular Jacobian at a point means there exists a region where Jacobian is non-singular

If $f$ is continuously differentiable, $f'(x)$ is invertible, and $V$ is open, then $f(V)$ is open

Using the Mean Value Inequality to prove the Inverse Function Theorem

Most interesting exercises about the implicit and inverse function theorems

Is the inverse of a smooth bi-Lipschitz map continuously differentiable?

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