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Del in cylindrical and spherical coordinates - Wikipedia, the free encycl... http://en.wikipedia.org/wiki/Nabla_in_cylindrical_and_spherical_coordi... Make a donation to Wikipedia and give the gift of knowledge! Del in cylindrical and spherical coordinates From Wikipedia, the free encyclopedia (Redirected from Nabla in cylindrical and spherical coordinates) 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 A vector field 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 Retrieved from "http://en.wikipedia.org/wiki/Del_in_cylindrical_and_spherical_coordinates" Categories: Vector calculus | Coordinate systems This page was last modified 11:17, 11 October 2007. All text is available under the terms of the GNU Free Documentation License. (See Copyrights for details.) Wikipedia® is a registered trademark of the Wikimedia Foundation, Inc., a U.S. registered 501(c)(3) tax-deductible nonprofit charity. 2 of 2 10/20/2007 7:08 PM.

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