Vector fields

integral calculus extend naturally to vector fields. When a vector field represents force, the line integral of a vector field represents the work done by a force...

In vector calculus, a conservative vector field is a vector field that is the gradient of some function. A conservative vector field has the property...

metric tensor. Killing vector fields are the infinitesimal generators of isometries; that is, flows generated by Killing vector fields are continuous isometries...

time-varying electric currents. Electric fields and magnetic fields are both manifestations of the electromagnetic field. Electromagnetism is one of the four...

In vector calculus, the curl, also known as rotor, is a vector operator that describes the infinitesimal circulation of a vector field in three-dimensional...

tuples is called a coordinate vector space. Many vector spaces are considered in mathematics, such as extension fields, polynomial rings, algebras and...

In mathematics, the discussion of vector fields on spheres was a classical problem of differential topology, beginning with the hairy ball theorem, and...

vector calculus a solenoidal vector field (also known as an incompressible vector field, a divergence-free vector field, or a transverse vector field)...

Vector calculus or vector analysis is a branch of mathematics concerned with the differentiation and integration of vector fields, primarily in three-dimensional...

the power flow in electromagnetic fields. In Poynting's original paper and in most textbooks, the Poynting vector S {\displaystyle \mathbf {S} } is defined...