DLMF:1.6.E22
type: Item
DLMF defining formula: <math xmlns="http://www.w3.org/1998/Math/MathML" id="p1.1.m1.1" class="ltx_Math" alttext="{\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}.}}" display="inline"> curl 𝐅 = ∇ × 𝐅 = | 𝐢 𝐣 𝐤 ∂ ∂ ⁡ x ∂ ∂ ⁡ y ∂ ∂ ⁡ z F 1 F 2 F 3 | = ( ∂ ⁡ F 3 ∂ ⁡ y - ∂ ⁡ F 2 ∂ ⁡ z ) ⁢ 𝐢 + ( ∂ ⁡ F 1 ∂ ⁡ z - ∂ ⁡ F 3 ∂ ⁡ x ) ⁢ 𝐣 + ( ∂ ⁡ F 2 ∂ ⁡ x - ∂ ⁡ F 1 ∂ ⁡ y ) ⁢ 𝐤 . <annotation-xml encoding="MathML-Content" id="p1.1.m1.1b"> <apply id="p1.1.m1.1.32.2.cmml" xref="p1.1.m1.1.32"> <and id="p1.1.m1.1.32.2a.cmml" xref="p1.1.m1.1.32"/> <apply id="p1.1.m1.1.32.2b.cmml" xref="p1.1.m1.1.32"> <eq id="p1.1.m1.1.3.cmml" xref="p1.1.m1.1.3"/> <apply id="p1.1.m1.1.32.2.2.cmml" xref="p1.1.m1.1.32.2.2"> <curl id="p1.1.m1.1.1.1.cmml" xref="p1.1.m1.1.1.5"/> <ci id="p1.1.m1.1.2.cmml" xref="p1.1.m1.1.2">𝐅</ci> </apply> <apply id="p1.1.m1.1.32.2.3.cmml" xref="p1.1.m1.1.32.2.3"> <times id="p1.1.m1.1.5.cmml" xref="p1.1.m1.1.5"/> <ci id="p1.1.m1.1.4.cmml" xref="p1.1.m1.1.4">∇</ci> <ci id="p1.1.m1.1.6.cmml" xref="p1.1.m1.1.6">𝐅</ci> </apply> </apply> <apply id="p1.1.m1.1.32.2c.cmml" xref="p1.1.m1.1.32"> <eq id="p1.1.m1.1.7.cmml" xref="p1.1.m1.1.7"/> <share href="#p1.1.m1.1.32.2.3.cmml" id="p1.1.m1.1.32.2d.cmml" xref="p1.1.m1.1.32"/> <apply id="p1.1.m1.1.8.1.cmml" xref="p1.1.m1.1.8.5"> <determinant id="p1.1.m1.1.8.1.1.cmml" xref="p1.1.m1.1.8.2"/> <matrix id="p1.1.m1.1.8.3.cmml" xref="p1.1.m1.1.8.3"> <matrixrow id="p1.1.m1.1.8.3a.cmml" xref="p1.1.m1.1.8.3"> <ci id="p1.1.m1.1.8.3.1.1.1.1.cmml" xref=…
Digital Library of Mathematical Functions ID: 1.6.E22
Symbols defined: curl of vector-valued function
Symbols used: Q10739
Symbols used: partial derivative of $$f$$ with respect to $$x$$
Symbols used: partial differential of $$x$$
Symbols used: variable
Symbols used: unit vector
Symbols used: vector function components
instance of: Digital Library of Mathematical Functions Formula
MaRDI profile type: MaRDI formula profile