Question

If $T_t$ is a diffeomorphism and $t\mapsto T_t(x)$ is differentiable, can we find a map $v$ with $v(t,T_t(x))=\frac{\partial T}{\partial t}(t,x)$?

score 115 · Answer 1 · 2026-03-25 19:07:14

115

Views

If $T_t$ is a diffeomorphism and $t\mapsto T_t(x)$ is differentiable, can we find a map $v$ with $v(t,T_t(x))=\frac{\partial T}{\partial t}(t,x)$?

Published on 25 Mar 2026 - 19:07

score 61 · Answer 2 · 2026-03-20 17:13:33

61

Views

$F(x,t)=a_n(t)x^n+ \ldots +a_1(t)x+a_0(t)$. Show that $F(\cdot , t_0)$ has exactly one zero using the Implicit Function Theorem

Published on 20 Mar 2026 - 17:13

score 165 · Answer 3 · 2026-03-20 00:48:37

165

Views

how to find the the maximum of an implicit function

Published on 20 Mar 2026 - 0:48

score 932 · Answer 4 · 2026-03-26 04:28:38

932

Views

Implicit function theorem for Banach spaces

Published on 26 Mar 2026 - 4:28

score 116 · Answer 5 · 2026-03-26 01:04:49

116

Views

Find conditions on $x$ and $y$ which guarantee that one can locally solve the following for $u(x, y)$ and $v(x, y)$

Published on 26 Mar 2026 - 1:04

score 124 · Answer 6 · 2026-03-21 15:14:31

124

Views

Usage of implicit function theorem for $f(x,y)=x^2+2xy-y^2-a^2$

Published on 21 Mar 2026 - 15:14

score 388 · Answer 7 · 2026-03-21 01:50:06

388

Views

Multivariable implicit function - Jacobi Matrix

Published on 21 Mar 2026 - 1:50

score 60 · Answer 8 · 2026-03-21 02:16:14

60

Views

Taylor formula exercice

Published on 21 Mar 2026 - 2:16

score 509 · Answer 9 · 2026-03-20 18:52:38

509

Views

How to linearlize level curves at a saddle point

Published on 20 Mar 2026 - 18:52

score 55 · Answer 10 · 2026-03-21 04:10:31

55

Views

Implicit theorem exercies

Published on 21 Mar 2026 - 4:10

score 92 · Answer 11 · 2026-03-21 09:11:04

92

Views

Implicit Function Theorem and linear dependence

Published on 21 Mar 2026 - 9:11

score 1.3k · Answer 12 · 2026-03-21 12:34:04

1.3k

Views

Why does the shape operator (Weingarten map) exist?

Published on 21 Mar 2026 - 12:34

score 154 · Answer 13 · 2026-03-21 07:31:40

154

Views

Dini's theorem and strictly convex function

Published on 21 Mar 2026 - 7:31

score 125 · Answer 14 · 2026-03-20 19:17:15

125

Views

Show there exists a differentiable function y=g(x) given an equation in x and y.

Published on 20 Mar 2026 - 19:17

score 409 · Answer 15 · 2026-03-21 02:37:10

409

Views

Example when the hypothesis of the implicit function theorem is false, but the conclusion is true.

Published on 21 Mar 2026 - 2:37

List Question

If $T_t$ is a diffeomorphism and $t\mapsto T_t(x)$ is differentiable, can we find a map $v$ with $v(t,T_t(x))=\frac{\partial T}{\partial t}(t,x)$?

$F(x,t)=a_n(t)x^n+ \ldots +a_1(t)x+a_0(t)$. Show that $F(\cdot , t_0)$ has exactly one zero using the Implicit Function Theorem

how to find the the maximum of an implicit function

Implicit function theorem for Banach spaces

Find conditions on $x$ and $y$ which guarantee that one can locally solve the following for $u(x, y)$ and $v(x, y)$

Usage of implicit function theorem for $f(x,y)=x^2+2xy-y^2-a^2$

Multivariable implicit function - Jacobi Matrix

Taylor formula exercice

How to linearlize level curves at a saddle point

Implicit theorem exercies

Implicit Function Theorem and linear dependence

Why does the shape operator (Weingarten map) exist?

Dini's theorem and strictly convex function

Show there exists a differentiable function y=g(x) given an equation in x and y.

Example when the hypothesis of the implicit function theorem is false, but the conclusion is true.

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