List questions from vector-fields

Published on 19 May 2020 - 15:42

37

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Information/references/examples on fields $\mathbb R^3 \to \mathbb C^3$ with divergence and curl free real and imaginary parts

Published on 20 May 2020 - 8:58

1.7k

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Conditions for a vector field to be a gradient

Published on 20 May 2020 - 12:41

68

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Surface integral on close surface

Published on 28 Mar 2026 - 8:47

240

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Why do we use tangent bundles to define vector fields on manifolds?

Published on 25 Mar 2026 - 12:15

208

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Why does this "gradient field test" not work on the spin field $S / r^2$? (from Strang's Calculus)

Published on 24 May 2020 - 16:52

127

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$\nabla(\vec{A}\cdot\vec{r})=\vec{A}.$ Using index notation for vector calculus. Practicing for exam

Published on 26 May 2020 - 14:24

39

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Column space of matrix

Published on 26 May 2020 - 16:20

281

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Hairy ball theorem for $S^2$

Published on 28 Mar 2026 - 1:46

538

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Show that there is a $\pi_i$-related smooth vector field for each smooth vector field $X_i \in \Gamma(M_i,TM_i)$

Published on 25 Mar 2026 - 12:21

63

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An $L_1$-bounded, divergent sequence of divergence-free vector fields

Published on 02 Jun 2020 - 12:05

925

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Integral Curves of Vector Fields with Zero Divergence or Zero Curl

Published on 02 Jun 2020 - 20:48

350

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Divergence of vector-valued function

Published on 27 Mar 2026 - 1:42

670

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Can a discontinuous vector field be conservative?

Published on 25 Mar 2026 - 11:00

41

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Flux through cone revisited

Published on 26 Mar 2026 - 23:21

List Question

Proving $d\omega(X,Y) = X\omega(Y)-Y\omega(X) - \omega([X,Y])$ without choosing local coordinates.

Information/references/examples on fields $\mathbb R^3 \to \mathbb C^3$ with divergence and curl free real and imaginary parts

Conditions for a vector field to be a gradient

Surface integral on close surface

Why do we use tangent bundles to define vector fields on manifolds?

Why does this "gradient field test" not work on the spin field $S / r^2$? (from Strang's Calculus)

$\nabla(\vec{A}\cdot\vec{r})=\vec{A}.$ Using index notation for vector calculus. Practicing for exam

Column space of matrix

Hairy ball theorem for $S^2$

Show that there is a $\pi_i$-related smooth vector field for each smooth vector field $X_i \in \Gamma(M_i,TM_i)$

An $L_1$-bounded, divergent sequence of divergence-free vector fields

Integral Curves of Vector Fields with Zero Divergence or Zero Curl

Divergence of vector-valued function

Can a discontinuous vector field be conservative?

Flux through cone revisited

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