Matches in DBpedia 2015-10 for { <http://dbpedia.org/resource/Curl_(mathematics)> ?p ?o }
- Curl_(mathematics) abstract "In vector calculus, the curl is a vector operator that describes the infinitesimal rotation of a 3-dimensional vector field. At every point in the field, the curl of that point is represented by a vector. The attributes of this vector (length and direction) characterize the rotation at that point.The direction of the curl is the axis of rotation, as determined by the right-hand rule, and the magnitude of the curl is the magnitude of rotation. If the vector field represents the flow velocity of a moving fluid, then the curl is the circulation density of the fluid. A vector field whose curl is zero is called irrotational.The curl is a form of differentiation for vector fields. The corresponding form of the fundamental theorem of calculus is Stokes' theorem, which relates the surface integral of the curl of a vector field to the line integral of the vector field around the boundary curve.The alternative terminology rotor or rotational and alternative notations rot F and ∇ × F are often used (the former especially in many European countries, the latter, using the del operator and the cross product, is more used in other countries) for curl and curl F.Unlike the gradient and divergence, curl does not generalize as simply to other dimensions; some generalizations are possible, but only in three dimensions is the geometrically defined curl of a vector field again a vector field. This is a similar phenomenon as in the 3 dimensional cross product, and the connection is reflected in the notation ∇ × for the curl.The name "curl" was first suggested by James Clerk Maxwell in 1871 but the concept was apparently first used in the construction of an optical field theory by James MacCullagh in 1839.".
- Curl_(mathematics) thumbnail Curl.svg?width=300.
- Curl_(mathematics) wikiPageExternalLink vector-calculus-understanding-circulation-and-curl.
- Curl_(mathematics) wikiPageExternalLink curl_idea.
- Curl_(mathematics) wikiPageID "6123".
- Curl_(mathematics) wikiPageLength "25335".
- Curl_(mathematics) wikiPageOutDegree "119".
- Curl_(mathematics) wikiPageRevisionID "671493017".
- Curl_(mathematics) wikiPageWikiLink Algebra.
- Curl_(mathematics) wikiPageWikiLink Ampxc3xa8res_circuital_law.
- Curl_(mathematics) wikiPageWikiLink Antisymmetric_tensor.
- Curl_(mathematics) wikiPageWikiLink Area.
- Curl_(mathematics) wikiPageWikiLink Area_density.
- Curl_(mathematics) wikiPageWikiLink Binomial_coefficient.
- Curl_(mathematics) wikiPageWikiLink Bivector.
- Curl_(mathematics) wikiPageWikiLink Boundary_(topology).
- Curl_(mathematics) wikiPageWikiLink Cartesian_coordinate_system.
- Curl_(mathematics) wikiPageWikiLink Cartesian_coordinates.
- Curl_(mathematics) wikiPageWikiLink Category:Analytic_geometry.
- Curl_(mathematics) wikiPageWikiLink Category:Linear_operators_in_calculus.
- Curl_(mathematics) wikiPageWikiLink Category:Vector_calculus.
- Curl_(mathematics) wikiPageWikiLink Chirality_(mathematics).
- Curl_(mathematics) wikiPageWikiLink Circulation_(fluid_dynamics).
- Curl_(mathematics) wikiPageWikiLink Conservative_vector_field.
- Curl_(mathematics) wikiPageWikiLink Cross_product.
- Curl_(mathematics) wikiPageWikiLink Curvilinear_coordinates.
- Curl_(mathematics) wikiPageWikiLink Cyclic_permutation.
- Curl_(mathematics) wikiPageWikiLink Cylindrical_coordinate_system.
- Curl_(mathematics) wikiPageWikiLink Cylindrical_coordinates.
- Curl_(mathematics) wikiPageWikiLink Degenerate_bilinear_form.
- Curl_(mathematics) wikiPageWikiLink Del.
- Curl_(mathematics) wikiPageWikiLink Del_in_cylindrical_and_spherical_coordinates.
- Curl_(mathematics) wikiPageWikiLink Derivative.
- Curl_(mathematics) wikiPageWikiLink Differential_(infinitesimal).
- Curl_(mathematics) wikiPageWikiLink Differential_operator.
- Curl_(mathematics) wikiPageWikiLink Divergence.
- Curl_(mathematics) wikiPageWikiLink Einstein_notation.
- Curl_(mathematics) wikiPageWikiLink Einstein_summation_convention.
- Curl_(mathematics) wikiPageWikiLink Elliptic_coordinate_system.
- Curl_(mathematics) wikiPageWikiLink Euclidean_vector.
- Curl_(mathematics) wikiPageWikiLink Exterior_algebra.
- Curl_(mathematics) wikiPageWikiLink Exterior_derivative.
- Curl_(mathematics) wikiPageWikiLink Faradays_law_of_induction.
- Curl_(mathematics) wikiPageWikiLink Flow_velocity.
- Curl_(mathematics) wikiPageWikiLink Fluid.
- Curl_(mathematics) wikiPageWikiLink Fluid_dynamics.
- Curl_(mathematics) wikiPageWikiLink Fluid_flow.
- Curl_(mathematics) wikiPageWikiLink Fundamental_theorem_of_calculus.
- Curl_(mathematics) wikiPageWikiLink Gas.
- Curl_(mathematics) wikiPageWikiLink George_B._Arfken.
- Curl_(mathematics) wikiPageWikiLink Gradient.
- Curl_(mathematics) wikiPageWikiLink Helmholtz_decomposition.
- Curl_(mathematics) wikiPageWikiLink Hodge_dual.
- Curl_(mathematics) wikiPageWikiLink Hodge_duality.
- Curl_(mathematics) wikiPageWikiLink Index_notation.
- Curl_(mathematics) wikiPageWikiLink Irrotational.
- Curl_(mathematics) wikiPageWikiLink James_Clerk_Maxwell.
- Curl_(mathematics) wikiPageWikiLink James_MacCullagh.
- Curl_(mathematics) wikiPageWikiLink Kelvin-Stokes_theorem.
- Curl_(mathematics) wikiPageWikiLink Kelvin–Stokes_theorem.
- Curl_(mathematics) wikiPageWikiLink Levi-Civita_symbol.
- Curl_(mathematics) wikiPageWikiLink Line_integral.
- Curl_(mathematics) wikiPageWikiLink Liquid.
- Curl_(mathematics) wikiPageWikiLink Maxwells_equations.
- Curl_(mathematics) wikiPageWikiLink Metric_tensor.
- Curl_(mathematics) wikiPageWikiLink Mnemonic.
- Curl_(mathematics) wikiPageWikiLink Multivector.
- Curl_(mathematics) wikiPageWikiLink Musical_isomorphism.
- Curl_(mathematics) wikiPageWikiLink Nabla_in_cylindrical_and_spherical_coordinates.
- Curl_(mathematics) wikiPageWikiLink Nondegenerate_form.
- Curl_(mathematics) wikiPageWikiLink Operator_(mathematics).
- Curl_(mathematics) wikiPageWikiLink Operator_(physics).
- Curl_(mathematics) wikiPageWikiLink Orientability.
- Curl_(mathematics) wikiPageWikiLink Orientation_(mathematics).
- Curl_(mathematics) wikiPageWikiLink Orientation_(vector_space).
- Curl_(mathematics) wikiPageWikiLink Orthogonal_coordinates.
- Curl_(mathematics) wikiPageWikiLink Orthogonal_group.
- Curl_(mathematics) wikiPageWikiLink P-vector.
- Curl_(mathematics) wikiPageWikiLink Paddle_wheel.
- Curl_(mathematics) wikiPageWikiLink Parabolic_coordinates.
- Curl_(mathematics) wikiPageWikiLink Pascals_triangle.
- Curl_(mathematics) wikiPageWikiLink Physics.
- Curl_(mathematics) wikiPageWikiLink Pseudo-Riemannian_manifold.
- Curl_(mathematics) wikiPageWikiLink Raising_and_lowering_indices.
- Curl_(mathematics) wikiPageWikiLink Riemannian_manifold.
- Curl_(mathematics) wikiPageWikiLink Riemannian_metric.
- Curl_(mathematics) wikiPageWikiLink Right-hand_rule.
- Curl_(mathematics) wikiPageWikiLink Right-handed_coordinate_system.
- Curl_(mathematics) wikiPageWikiLink Rotation.
- Curl_(mathematics) wikiPageWikiLink Scalar_field.
- Curl_(mathematics) wikiPageWikiLink Smooth_function.
- Curl_(mathematics) wikiPageWikiLink Smoothness.
- Curl_(mathematics) wikiPageWikiLink Special_orthogonal_Lie_algebra.
- Curl_(mathematics) wikiPageWikiLink Spherical_coordinate_system.
- Curl_(mathematics) wikiPageWikiLink Spherical_coordinates.
- Curl_(mathematics) wikiPageWikiLink Surface_integral.
- Curl_(mathematics) wikiPageWikiLink Symmetry_of_second_derivatives.
- Curl_(mathematics) wikiPageWikiLink Tangent_vector.
- Curl_(mathematics) wikiPageWikiLink Unit_vector.
- Curl_(mathematics) wikiPageWikiLink Vector_(geometry).