Question

Does $\operatorname{curl}(\mathbf{a})=\mathbf0$ always imply $\mathbf{a}=\boldsymbol{\nabla}b$? Is it always conservative?

score 166 · Answer 1 · 2019-11-27 21:39:33

166

Views

Does $\operatorname{curl}(\mathbf{a})=\mathbf0$ always imply $\mathbf{a}=\boldsymbol{\nabla}b$? Is it always conservative?

Published on 27 Nov 2019 - 21:39

score 94 · Answer 2 · 2019-11-28 12:00:42

94

Views

If vector fields commute at each point of a manifold then they are tangent to manifold

Published on 28 Nov 2019 - 12:00

score 196 · Answer 3 · 2019-11-29 09:02:38

196

Views

Difficulty understanding proof regarding conservative vector fields

Published on 29 Nov 2019 - 9:02

score 73 · Answer 4 · 2026-03-26 11:16:13

73

Views

Stokes' Theorem equaling $0$.

Published on 26 Mar 2026 - 11:16

score 22 · Answer 5 · 2019-11-30 16:18:04

22

Views

Express the field $X(x,y) =(-y,x)$ of $\mathbb{S}^1$ in terms of a known atlas.

Published on 30 Nov 2019 - 16:18

score 242 · Answer 6 · 2026-03-27 15:35:42

242

Views

Explanation of Surface Integral problem

Published on 27 Mar 2026 - 15:35

score 146 · Answer 7 · 2019-12-01 08:57:34

146

Views

Gradient Vector Plot: Determine Function From A Plot

Published on 01 Dec 2019 - 8:57

score 86 · Answer 8 · 2026-03-26 09:49:44

86

Views

Does Stokes' Theorem give the same answer for all shadows with the same area?

Published on 26 Mar 2026 - 9:49

score 83 · Answer 9 · 2019-12-02 04:31:36

83

Views

How can I understand this vector-field?

Published on 02 Dec 2019 - 4:31

score 113 · Answer 10 · 2019-12-03 15:48:17

113

Views

Why is the formula for gradient different in different co-ordinate systems?

Published on 03 Dec 2019 - 15:48

score 21 · Answer 11 · 2026-03-25 23:35:27

21

Views

Vector fields such that their Lie derivatives differ

Published on 25 Mar 2026 - 23:35

score 173 · Answer 12 · 2026-03-26 22:15:07

173

Views

Can divergence of a vector field be different at different points?

Published on 26 Mar 2026 - 22:15

score 3.3k · Answer 13 · 2026-03-26 18:57:50

3.3k

Views

Vector calculus - Evaluate this line integral

Published on 26 Mar 2026 - 18:57

score 75 · Answer 14 · 2019-12-06 08:52:38

75

Views

Constructing piecewise smooth integral curve of $\ker(x \,dy - y \,dx + \,dz)$ connecting the origin to $(a, b, c) $

Published on 06 Dec 2019 - 8:52

score 415 · Answer 15 · 2019-12-07 15:29:06

415

Views

Index of vector field

Published on 07 Dec 2019 - 15:29

List Question

Does $\operatorname{curl}(\mathbf{a})=\mathbf0$ always imply $\mathbf{a}=\boldsymbol{\nabla}b$? Is it always conservative?

If vector fields commute at each point of a manifold then they are tangent to manifold

Difficulty understanding proof regarding conservative vector fields

Stokes' Theorem equaling $0$.

Express the field $X(x,y) =(-y,x)$ of $\mathbb{S}^1$ in terms of a known atlas.

Explanation of Surface Integral problem

Gradient Vector Plot: Determine Function From A Plot

Does Stokes' Theorem give the same answer for all shadows with the same area?

How can I understand this vector-field?

Why is the formula for gradient different in different co-ordinate systems?

Vector fields such that their Lie derivatives differ

Can divergence of a vector field be different at different points?

Vector calculus - Evaluate this line integral

Constructing piecewise smooth integral curve of $\ker(x \,dy - y \,dx + \,dz)$ connecting the origin to $(a, b, c) $

Index of vector field

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