Deprecated : $wgMWOAuthSharedUserIDs=false is deprecated, set $wgMWOAuthSharedUserIDs=true, $wgMWOAuthSharedUserSource='local' instead [Called from MediaWiki\HookContainer\HookContainer::run in /var/www/html/w/includes/HookContainer/HookContainer.php at line 135] in /var/www/html/w/includes/Debug/MWDebug.php on line 372 DLMF:1.6.E22 - MaRDI portal
Statements
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
.
𝐅
∇
𝐅
𝐢
𝐣
𝐤
partial-derivative
𝑥
partial-derivative
𝑦
partial-derivative
𝑧
subscript
𝐹
1
subscript
𝐹
2
subscript
𝐹
3
partial-derivative
subscript
𝐹
3
𝑦
partial-derivative
subscript
𝐹
2
𝑧
𝐢
partial-derivative
subscript
𝐹
1
𝑧
partial-derivative
subscript
𝐹
3
𝑥
𝐣
partial-derivative
subscript
𝐹
2
𝑥
partial-derivative
subscript
𝐹
1
𝑦
𝐤
{\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}.}}
det
{\displaystyle{\displaystyle\det}}
∂
f
∂
x
partial-derivative
𝑓
𝑥
{\displaystyle{\displaystyle\frac{\partial\NVar{f}}{\partial\NVar{x}}}}
∂
x
𝑥
{\displaystyle{\displaystyle\partial\NVar{x}}}
z
𝑧
{\displaystyle{\displaystyle z}}
𝐢
𝐢
{\displaystyle{\displaystyle\mathbf{i}}}
𝐣
𝐣
{\displaystyle{\displaystyle\mathbf{j}}}
𝐤
𝐤
{\displaystyle{\displaystyle\mathbf{k}}}
F
j
subscript
𝐹
𝑗
{\displaystyle{\displaystyle F_{j}}}
Identifiers
