Nabla in verschillende assenstelsels: verschil tussen versies
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Geen bewerkingssamenvatting |
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Regel 172:
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! style="background: white" | Operatie
! style="background: white" | Cartesische coördinaten {{math|(''x'', ''y'', ''z'')|x}}
! style="background: white" | Cilindercoördinaten {{math|(''ρ'', ''φ'', ''z'')|x}}
! style="background: white" | Bolcoördinaten {{math|(''r'', ''θ'', ''φ'')|x}}, waar ''φ'' de azimutale en {{math|
<!-- Definition of A -->
|- align="center"
! style="background: white" | [[Vectorveld]] <span style="font-weight: normal">{{math|'''A'''|x}}</span>
| <math>A_x \hat{\mathbf x} + A_y \hat{\mathbf y} + A_z \hat{\mathbf z}</math>
| <math>A_\rho \hat{\boldsymbol \rho} + A_\varphi \hat{\boldsymbol \varphi} + A_z \hat{\mathbf z}</math>
Regel 185:
<!-- grad f -->
|- align="center"
! style="background: white" | [[Gradiënt (wiskunde)|Gradiënt]] <span style="font-weight: normal">{{math|∇''f''|x}}</span>
| <math>{\partial f \over \partial x}\hat{\mathbf x} + {\partial f \over \partial y}\hat{\mathbf y}
+ {\partial f \over \partial z}\hat{\mathbf z}</math>
Regel 197:
<!-- div A -->
|- align="center"
! style="background: white" | [[Divergentie (vectorveld)|Divergentie]] <span style="font-weight: normal">{{math|∇ ⋅ '''A'''|x}}</span><ref name="griffiths" />
| <math>{\partial A_x \over \partial x} + {\partial A_y \over \partial y} + {\partial A_z \over \partial z}</math>
| <math>{1 \over \rho}{\partial \left( \rho A_\rho \right) \over \partial \rho}
Regel 208:
<!-- curl A -->
|- align="center"
! style="background: white" | [[Rotatie (vectorveld)|Rotatie]] <span style="font-weight: normal">{{math|∇ × '''A'''|x}}</span><ref name="griffiths" />
| <math>\begin{align}
\left(\frac{\partial A_z}{\partial y} - \frac{\partial A_y}{\partial z}\right) &\hat{\mathbf x} \\
Regel 245:
<!-- Laplacian f -->
|- align="center"
! style="background: white" | [[Laplace-operator]] <span style="font-weight: normal">{{math|∇<sup>2</sup>''f'' ≡ ∆''f''|x}}</span>
| <math>{\partial^2 f \over \partial x^2} + {\partial^2 f \over \partial y^2} + {\partial^2 f \over \partial z^2}</math>
| <math>{1 \over \rho}{\partial \over \partial \rho}\left(\rho {\partial f \over \partial \rho}\right)
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