curl

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1: 1.6 Vectors and Vector-Valued Functions

… ►The curl of $𝐅$ is ►

1.6.22

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Defines:

$\mathrm{curl}$: of vector-valued function

Symbols:

$det$: determinant, $\frac{\partial f}{\partial x}$: partial derivative of $f$ with respect to $x$ , $\partial x$: partial differential of $x$ , $z$: variable, $𝐢$: unit vector, $𝐣$: unit vector, $𝐤$: unit vector and $F_j$: vector function components

Permalink:

http://dlmf.nist.gov/1.6.E22

Encodings:

pMML, png, TeX

See also:

Annotations for §1.6(iii), §1.6(iii), §1.6 and Ch.1

… ►

1.6.27 $$\nabla \cdot (\nabla \times 𝐅)=\mathrm{div}\mathrm{curl}𝐅=0,$$

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Symbols:

$\mathrm{curl}$: of vector-valued function and $\mathrm{div}$: divergence of vector-valued function

Permalink:

http://dlmf.nist.gov/1.6.E27

Encodings:

pMML, png, TeX

See also:

Annotations for §1.6(iii), §1.6(iii), §1.6 and Ch.1

… ►

1.6.29 $$\nabla \times (\nabla f)=\mathrm{curl}\mathrm{grad}f=0,$$

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Symbols:

$\mathrm{curl}$: of vector-valued function and $\mathrm{grad}$: gradient of differentiable scalar function

Permalink:

http://dlmf.nist.gov/1.6.E29

Encodings:

pMML, png, TeX

See also:

Annotations for §1.6(iii), §1.6(iii), §1.6 and Ch.1

… ►

1.6.34 $$\nabla \times (\nabla \times 𝐅)=\mathrm{curl}\mathrm{curl}𝐅=\nabla (\nabla \cdot 𝐅)-{\nabla }^2𝐅.$$

ⓘ

Symbols:

$\mathrm{curl}$: of vector-valued function

Permalink:

http://dlmf.nist.gov/1.6.E34

Encodings:

pMML, png, TeX

See also:

Annotations for §1.6(iii), §1.6(iii), §1.6 and Ch.1

…