gradient

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1: 1.6 Vectors and Vector-Valued Functions

… ►The gradient of a differentiable scalar function $f(x,y,z)$ is ►

1.6.20 $$\mathrm{grad}f=\nabla f=\frac{\partial f}{\partial x}𝐢+\frac{\partial f}{\partial y}𝐣+\frac{\partial f}{\partial z}𝐤.$$

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Defines:

$\mathrm{grad}$: gradient of differentiable scalar function

Symbols:

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

Permalink:

http://dlmf.nist.gov/1.6.E20

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

…

2: 21.7 Riemann Surfaces

… ►This compact curve may have singular points, that is, points at which the gradient of $\tilde{P}$ vanishes. …