DLMF:1.6.E22 (Q203): Difference between revisions

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Language	Label	Description	Also known as
English	DLMF:1.6.E22	No description defined

Statements

Defining formula

{\displaystyle{\displaystyle\operatorname{curl}\mathbf{F}=\nabla\times\mathbf{% F}=\begin{vmatrix}\mathbf{i}&\mathbf{j}&\mathbf{k}\\ \displaystyle{\frac{\partial}{\partial x}}&\displaystyle{\frac{\partial}{% \partial y}}&\displaystyle{\frac{\partial}{\partial z}}\\ F_{1}&F_{2}&F_{3}\end{vmatrix}\\ =\left(\frac{\partial F_{3}}{\partial y}-\frac{\partial F_{2}}{\partial z}% \right)\mathbf{i}+\left(\frac{\partial F_{1}}{\partial z}-\frac{\partial F_{3}% }{\partial x}\right)\mathbf{j}+\left(\frac{\partial F_{2}}{\partial x}-\frac{% \partial F_{1}}{\partial y}\right)\mathbf{k}.}}

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DLMF:1.6.E22

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Symbols defined

of vector-valued function

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Defining formula

{\displaystyle{\displaystyle\det}}

C1.S3.SS1.m1aadec

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partial derivative of $$f$$ with respect to $$x$$

Defining formula

{\displaystyle{\displaystyle\frac{\partial\NVar{f}}{\partial\NVar{x}}}}

C1.S5.E3.m4acdec

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partial differential of $$x$$

Defining formula

{\displaystyle{\displaystyle\partial\NVar{x}}}

C1.S5.E3.m2acdec

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Defining formula

{\displaystyle{\displaystyle z}}

C1.S1.XMD1.m1cdec

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Defining formula

{\displaystyle{\displaystyle\mathbf{i}}}

C1.S6.XMD2.m1gdec

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Defining formula

{\displaystyle{\displaystyle\mathbf{j}}}

C1.S6.XMD3.m1gdec

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Sitelinks

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