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This is a list of some vector calculus formulae of general use in working with standard coordinate systems.
Table with the del operator in cylindrical and spherical coordinates
Operation Cartesian coordinates (x,y,z) Cylindrical coordinates (ρ,φ,z) Spherical coordinates (r,θ,φ)
Definition of coordinates
Gradient
Divergence
Curl
Laplace operator or
Differential displacement
Differential normal area
Differential volume Non-trivial calculation rules:
1. (Laplacian) 2. 3. 4. (using Lagrange's formula for the cross product) 5.
Remarks
1 of 2 10/20/2007 7:08 PM Del in cylindrical and spherical coordinates - Wikipedia, the free encycl... http://en.wikipedia.org/wiki/Nabla_in_cylindrical_and_spherical_coordi...
This page uses standard physics notation; some (American mathematics) sources define φ as the angle from the z-axis instead of θ. The function atan2(y, x) is used instead of the mathematical function arctan(y/x) due to its domain and image. The classical arctan(y/x) has an image of (-π/2, +π/2), whereas atan2(y, x) is defined to have an image of (-π, π].
See also
Orthogonal coordinates Curvilinear coordinates Vector fields in cylindrical and spherical coordinates
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Categories: Vector calculus | Coordinate systems
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