Operation | Cartesian coordinates (x, y, z) | Cylindrical coordinates (ρ, φ, z) | Spherical coordinates (r, θ, φ), where θ is the polar angle and φ is the azimuthal angleα |
Vector field A | | | |
Gradient ∇f[1] | | | |
Divergence ∇ ⋅ A[1] | | | |
Curl ∇ × A[1] | | | |
Laplace operator ∇2f ≡ ∆f[1] | | | |
Vector gradient ∇Aβ | | | |
Vector Laplacian ∇2A ≡ ∆A[2] | | | |
Directional derivative (A ⋅ ∇)B[3] | | | |
Tensor divergence ∇ ⋅ Tγ | | | |
Differential displacement dℓ[1] | | | |
Differential normal area dS | | | |
Differential volume dV[1] | | | |