List questions from vector-fields

73

Views

The curl operator: Why does it map $C^k$ functions in $\mathbb{R}^3$ to $C^{k-1}$ functioins in $\mathbb{R}^3$?

Published on 30 Mar 2026 - 5:15

30

Views

How does this differential equation's solutions embedded in an exponential-exponential coordinate plane change the form of the differential equation?

Published on 18 Jun 2020 - 12:45

181

Views

How to show $\Delta f(r) = f''(r) + \frac{2}{r} f'(r)$?

Published on 27 Mar 2026 - 1:47

406

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Every smooth function on a manifold defines a hamiltonian vector field.

Published on 27 Mar 2026 - 19:31

61

Views

Flux through the positive part of a sphere centered at $(0,0,1)$

Published on 20 Jun 2020 - 16:13

412

Views

Flux of a vector field through the boundary of a closed surface

Published on 28 Mar 2026 - 10:41

1.5k

Views

Pushforward of a Vector Field by a Diffeomorphism

Published on 25 Mar 2026 - 11:11

82

Views

Pushforward and pull back of the vector fields $x^n \partial _x + y^n \partial_y$

Published on 23 Jun 2020 - 2:33

97

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Normal vector field of $I \times_f S^n$

Published on 23 Jun 2020 - 18:04

104

Views

Proving stability where conservative vector field is given

Published on 26 Mar 2026 - 8:14

459

Views

Conservation of energy in three dimension

Published on 25 Jun 2020 - 2:37

139

Views

Orthonormal bases and orthonormal frames

Published on 26 Mar 2026 - 3:19

809

Views

Lie derivatives of tensor product

Published on 26 Mar 2026 - 4:31

301

Views

Hypersurface-orthogonal vector field and helicity

Published on 25 Mar 2026 - 20:17

169

Views

Geometric interpretation of Isotropic vector

Published on 28 Jun 2020 - 16:54

List Question

The curl operator: Why does it map $C^k$ functions in $\mathbb{R}^3$ to $C^{k-1}$ functioins in $\mathbb{R}^3$?

How does this differential equation's solutions embedded in an exponential-exponential coordinate plane change the form of the differential equation?

How to show $\Delta f(r) = f''(r) + \frac{2}{r} f'(r)$?

Every smooth function on a manifold defines a hamiltonian vector field.

Flux through the positive part of a sphere centered at $(0,0,1)$

Flux of a vector field through the boundary of a closed surface

Pushforward of a Vector Field by a Diffeomorphism

Pushforward and pull back of the vector fields $x^n \partial _x + y^n \partial_y$

Normal vector field of $I \times_f S^n$

Proving stability where conservative vector field is given

Conservation of energy in three dimension

Orthonormal bases and orthonormal frames

Lie derivatives of tensor product

Hypersurface-orthogonal vector field and helicity

Geometric interpretation of Isotropic vector

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