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• Vector_field abstract "In vector calculus, a vector field is an assignment of a vector to each point in a subset of Euclidean 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 vector_field.
• 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 wikiPageRevisionID "602247879".
• Vector_field alt "Dense vector field representation.".
• Vector_field alt "Sparse vector field representation".
• Vector_field footer "Two representations of the same vector field: v = −r. The arrows depict the field at discrete points, however, the field exists everywhere.".
• Vector_field hasPhotoCollection Vector_field.
• Vector_field id "p/v096420".
• Vector_field image "Radial_vector_field_dense.svg".
• Vector_field image "Radial_vector_field_sparse.svg".
• Vector_field title "Vector field".
• Vector_field width "140".
• Vector_field subject Category:Differential_topology.
• Vector_field subject Category:Vector_calculus.
• Vector_field comment "In vector calculus, a vector field is an assignment of a vector to each point in a subset of Euclidean 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_field label "Campo vectorial".
• Vector_field label "Campo vetorial".
• Vector_field label "Campo vettoriale".
• Vector_field label "Champ de vecteurs".
• Vector_field label "Pole wektorowe".
• Vector_field label "Vector field".
• Vector_field label "Vectorveld".
• Vector_field label "Vektorfeld".
• Vector_field label "Векторное поле".
• Vector_field label "حقل شعاعي".
• Vector_field label "ベクトル場".
• Vector_field label "向量場".
• Vector_field sameAs Vektorové_pole.
• Vector_field sameAs Vektorfeld.
• Vector_field sameAs Campo_vectorial.
• Vector_field sameAs Bektore-eremua.
• Vector_field sameAs Champ_de_vecteurs.
• Vector_field sameAs Campo_vettoriale.
• Vector_field sameAs ベクトル場.
• Vector_field sameAs 벡터장.
• Vector_field sameAs Vectorveld.
• Vector_field sameAs Pole_wektorowe.
• Vector_field sameAs Campo_vetorial.
• Vector_field sameAs m.0gxtc.
• Vector_field sameAs Q186247.
• Vector_field sameAs Q186247.
• Vector_field wasDerivedFrom Vector_field?oldid=602247879.
• Vector_field depiction VectorField.svg.
• Vector_field isPrimaryTopicOf Vector_field.