Matches in DBpedia 2015-10 for { <http://dbpedia.org/resource/Vector_field> ?p ?o }
- Vector_field abstract "In vector calculus, a vector field is an assignment of a vector to each point in a subset of space. A vector field in the plane, for instance, can be visualized as a collection of arrows with a given magnitude and direction each attached to a point in the plane. Vector fields are often used to model, for example, the speed and direction of a moving fluid throughout space, or the strength and direction of some force, such as the magnetic or gravitational force, as it changes from point to point.The elements of differential and integral calculus extend to vector fields in a natural way. When a vector field represents force, the line integral of a vector field represents the work done by a force moving along a path, and under this interpretation conservation of energy is exhibited as a special case of the fundamental theorem of calculus. Vector fields can usefully be thought of as representing the velocity of a moving flow in space, and this physical intuition leads to notions such as the divergence (which represents the rate of change of volume of a flow) and curl (which represents the rotation of a flow).In coordinates, a vector field on a domain in n-dimensional Euclidean space can be represented as a vector-valued function that associates an n-tuple of real numbers to each point of the domain. This representation of a vector field depends on the coordinate system, and there is a well-defined transformation law in passing from one coordinate system to the other. Vector fields are often discussed on open subsets of Euclidean space, but also make sense on other subsets such as surfaces, where they associate an arrow tangent to the surface at each point (a tangent vector). More generally, vector fields are defined on differentiable manifolds, which are spaces that look like Euclidean space on small scales, but may have more complicated structure on larger scales. In this setting, a vector field gives a tangent vector at each point of the manifold (that is, a section of the tangent bundle to the manifold). Vector fields are one kind of tensor field.".
- Vector_field thumbnail VectorField.svg?width=300.
- Vector_field wikiPageExternalLink VectorField.html.
- Vector_field wikiPageExternalLink VectorField.html.
- Vector_field wikiPageExternalLink node2.html.
- Vector_field wikiPageExternalLink statbotl.html.
- Vector_field wikiPageExternalLink kidlington.aspx.
- Vector_field wikiPageExternalLink simusoft_vectorfields.html.
- Vector_field wikiPageID "62641".
- Vector_field wikiPageLength "24925".
- Vector_field wikiPageOutDegree "130".
- Vector_field wikiPageRevisionID "680119384".
- Vector_field wikiPageWikiLink 1-form.
- Vector_field wikiPageWikiLink Angular_momentum.
- Vector_field wikiPageWikiLink Atmospheric_pressure.
- Vector_field wikiPageWikiLink Barometric_pressure.
- Vector_field wikiPageWikiLink Category:Differential_topology.
- Vector_field wikiPageWikiLink Category:Vector_calculus.
- Vector_field wikiPageWikiLink Classical_field_theory.
- Vector_field wikiPageWikiLink Closed_manifold.
- Vector_field wikiPageWikiLink Compact_support.
- Vector_field wikiPageWikiLink Conservation_of_energy.
- Vector_field wikiPageWikiLink Conservative_field.
- Vector_field wikiPageWikiLink Conservative_vector_field.
- Vector_field wikiPageWikiLink Continuously_differentiable.
- Vector_field wikiPageWikiLink Covariance_and_contravariance_of_vectors.
- Vector_field wikiPageWikiLink Covector.
- Vector_field wikiPageWikiLink Curl_(mathematics).
- Vector_field wikiPageWikiLink Degree_of_a_continuous_mapping.
- Vector_field wikiPageWikiLink Del.
- Vector_field wikiPageWikiLink Derivation_(abstract_algebra).
- Vector_field wikiPageWikiLink Derivation_(differential_algebra).
- Vector_field wikiPageWikiLink Derivative.
- Vector_field wikiPageWikiLink Diffeomorphism.
- Vector_field wikiPageWikiLink Differentiable_function.
- Vector_field wikiPageWikiLink Differentiable_manifold.
- Vector_field wikiPageWikiLink Differential_calculus_over_commutative_algebras.
- Vector_field wikiPageWikiLink Differential_form.
- Vector_field wikiPageWikiLink Differential_geometry_of_curves.
- Vector_field wikiPageWikiLink Divergence.
- Vector_field wikiPageWikiLink Divergence_theorem.
- Vector_field wikiPageWikiLink Dual_space.
- Vector_field wikiPageWikiLink Eisenbud–Levine–Khimshiashvili_signature_formula.
- Vector_field wikiPageWikiLink Electromagnetic_field.
- Vector_field wikiPageWikiLink Equivalence_class.
- Vector_field wikiPageWikiLink Euclidean_space.
- Vector_field wikiPageWikiLink Euclidean_vector.
- Vector_field wikiPageWikiLink Euler_characteristic.
- Vector_field wikiPageWikiLink Exponential_map_(Lie_theory).
- Vector_field wikiPageWikiLink Exterior_derivative.
- Vector_field wikiPageWikiLink Field_line.
- Vector_field wikiPageWikiLink Field_strength.
- Vector_field wikiPageWikiLink Flow_(mathematics).
- Vector_field wikiPageWikiLink Fluid.
- Vector_field wikiPageWikiLink Fluid_dynamics.
- Vector_field wikiPageWikiLink Fluid_flow.
- Vector_field wikiPageWikiLink Force.
- Vector_field wikiPageWikiLink Fraktur.
- Vector_field wikiPageWikiLink Fraktur_(typeface_sub-classification).
- Vector_field wikiPageWikiLink Fundamental_theorem_of_calculus.
- Vector_field wikiPageWikiLink Geodesic.
- Vector_field wikiPageWikiLink Geodesic_flow.
- Vector_field wikiPageWikiLink Gradient.
- Vector_field wikiPageWikiLink Gradient_descent.
- Vector_field wikiPageWikiLink Gravitational_field.
- Vector_field wikiPageWikiLink Gravity.
- Vector_field wikiPageWikiLink Hairy_ball_theorem.
- Vector_field wikiPageWikiLink Inner_product.
- Vector_field wikiPageWikiLink Inner_product_space.
- Vector_field wikiPageWikiLink Invariant_(mathematics).
- Vector_field wikiPageWikiLink Iron.
- Vector_field wikiPageWikiLink Lie_algebra.
- Vector_field wikiPageWikiLink Lie_bracket.
- Vector_field wikiPageWikiLink Lie_derivative.
- Vector_field wikiPageWikiLink Lie_group.
- Vector_field wikiPageWikiLink Light_field.
- Vector_field wikiPageWikiLink Line_integral.
- Vector_field wikiPageWikiLink Line_of_force.
- Vector_field wikiPageWikiLink Linear_form.
- Vector_field wikiPageWikiLink Lines_of_force.
- Vector_field wikiPageWikiLink Lipschitz_continuity.
- Vector_field wikiPageWikiLink Magnetic_field.
- Vector_field wikiPageWikiLink Magnetism.
- Vector_field wikiPageWikiLink Magnitude_(mathematics).
- Vector_field wikiPageWikiLink Map_(mathematics).
- Vector_field wikiPageWikiLink MathWorld.
- Vector_field wikiPageWikiLink Mathworld.
- Vector_field wikiPageWikiLink Maxwells_equations.
- Vector_field wikiPageWikiLink Michael_Faraday.
- Vector_field wikiPageWikiLink Module_(mathematics).
- Vector_field wikiPageWikiLink Multivector.
- Vector_field wikiPageWikiLink One-form.
- Vector_field wikiPageWikiLink One-parameter_group.
- Vector_field wikiPageWikiLink One-parameter_subgroup.
- Vector_field wikiPageWikiLink Open_set.
- Vector_field wikiPageWikiLink Orthogonal_group.
- Vector_field wikiPageWikiLink Orthogonal_matrix.
- Vector_field wikiPageWikiLink P-vector.
- Vector_field wikiPageWikiLink Parametric_equation.
- Vector_field wikiPageWikiLink Picard–Lindelöf_theorem.