Operation
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Cartesian coordinates (x, y, z)
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Cylindrical coordinates (ρ, ϕ, z)
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Spherical coordinates (r, θ, ϕ)
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Parabolic cylindrical coordinates (σ, τ, z)
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Definition of coordinates
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Definition of unit vectors
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A vector field
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scalar field Gradient
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Divergence
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Curl
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Laplace operator
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Vector Laplacian
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Modèle:Collapsible section
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Modèle:Collapsible section
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Material derivative[1]
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Modèle:Collapsible section
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Modèle:Collapsible section
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Differential displacement
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Differential normal area
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Differential volume
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Non-trivial calculation rules:
![{\displaystyle \operatorname {div} \,\operatorname {grad} f\equiv \nabla \cdot \nabla f=\nabla ^{2}f\equiv \Delta f}](https://wikimedia.org/api/rest_v1/media/math/render/svg/383cbf9e48db1cdba20e65378449ad5fa335c4be)
![{\displaystyle \operatorname {curl} \,\operatorname {grad} f\equiv \nabla \times \nabla f=\mathbf {0} }](https://wikimedia.org/api/rest_v1/media/math/render/svg/2524528406d8b5cb4c25eb670693c0db6e602e69)
![{\displaystyle \operatorname {div} \,\operatorname {curl} \mathbf {A} \equiv \nabla \cdot (\nabla \times \mathbf {A} )=0}](https://wikimedia.org/api/rest_v1/media/math/render/svg/4f23b06333ab36f02c4dbd039dc10ac8f35c4bd1)
(Lagrange's formula for del)
![{\displaystyle \Delta (fg)=f\Delta g+2\nabla f\cdot \nabla g+g\Delta f}](https://wikimedia.org/api/rest_v1/media/math/render/svg/7219d380c5ca5546bb89e79f36b10399b510261f)
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