Fundamental vector field information

fundamental vector fields are an instrument that describes the infinitesimal behaviour of a smooth Lie group action on a smooth manifold. Such vector...

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...

decomposition theorem or the fundamental theorem of vector calculus states that any sufficiently smooth, rapidly decaying vector field in three dimensions can...

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

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...

In vector calculus, a vector potential is a vector field whose curl is a given vector field. This is analogous to a scalar potential, which is a scalar...

vector boson is a boson whose spin equals one. Vector bosons that are also elementary particles are gauge bosons, the force carriers of fundamental interactions...

The concept of vector spaces is fundamental for linear algebra, together with the concept of matrices, which allows computing in vector spaces. This provides...

mathematical field of differential topology, the Lie bracket of vector fields, also known as the Jacobi–Lie bracket or the commutator of vector fields, is an...

the right we identified a vertical vector field and a Lie algebra element generating it (fundamental vector field), and σ ∈ { 1 , 2 } {\displaystyle \sigma...

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

then, writing X # {\displaystyle X^{\#}} for the fundamental vector field (i.e., vertical vector field) generated by X in g {\displaystyle {\mathfrak {g}}}...

constitutes a vector field. As the day progresses, the directions in which the vectors point change as the directions of the wind change. The first field theories...

assigning a vector to each point of space, called a vector field (more precisely, a pseudovector field). In electromagnetics, the term magnetic field is used...

curve (commonly arc length or, for a vector field, the scalar product of the vector field with a differential vector in the curve). This weighting distinguishes...

vector calculus, divergence is a vector operator that operates on a vector field, producing a scalar field giving the quantity of the vector field's source...

letters represent vectors and E is the electric field vector; H is the magnetic field's auxiliary field vector or magnetizing field. This expression is...

the first fundamental form of the surface. Consider a vector field v on a surface S, that is, for each r = (x, y, z) in S, v(r) is a vector. The integral...

theorem, also known as the fundamental theorem of calculus for line integrals, says that a line integral through a gradient field can be evaluated by evaluating...

Electric fields and magnetic fields are both manifestations of the electromagnetic field, Electromagnetism is one of the four fundamental interactions...

it is equivalent to the fundamental theorem of calculus. In two dimensions, it is equivalent to Green's theorem. Vector fields are often illustrated using...

of symmetric polynomials Fundamental theorem of topos theory Fundamental theorem of ultraproducts Fundamental theorem of vector analysis Carl Friedrich...

In three dimensions, the curl of a polar vector field at a point and the cross product of two polar vectors are pseudovectors. A number of quantities...

In vector calculus, the gradient of a scalar-valued differentiable function f {\displaystyle f} of several variables is the vector field (or vector-valued...

the flux the more fundamental quantity and call the vector field the flux density. Often a vector field is drawn by curves (field lines) following the...