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...

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

force field F, defined everywhere in space (or within a simply-connected volume of space), is called a conservative force or conservative vector field if...

In vector calculus and physics, a vector field is an assignment of a vector to each point in a space, most commonly Euclidean space R n {\displaystyle...

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

force field is a vector field corresponding with a non-contact force acting on a particle at various positions in space. Specifically, a force field is a...

In vector calculus, a complex lamellar vector field is a vector field which is orthogonal to a family of surfaces. In the broader context of differential...

codomain, Conservative vector field, a vector field that is the gradient of a scalar potential field Hamiltonian vector field, a vector field defined for...

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

vectors at every point in space, which is in-turn called a vector field. A conservative vector field can be simply expressed as the gradient of a certain scalar...

{\displaystyle \phi } is a scalar potential for the irrotational/conservative vector field E → {\displaystyle {\vec {E}}} ) and A → ( x → , t ) {\displaystyle...

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...

field line is a graphical visual aid for visualizing vector fields. It consists of an imaginary integral curve which is tangent to the field vector at...

exact form. In 3 dimensions, an exact vector field (thought of as a 1-form) is called a conservative vector field, meaning that it is the derivative (gradient)...

that V is a scalar potential of the conservative vector field F. Scalar potential is not determined by the vector field alone: indeed, the gradient of a...

any C 1 {\displaystyle C^{1}} vector field that has the path-independence property (so it is a conservative vector field.) must also be irrotational and...

In mathematics, the vector flow refers to a set of closely related concepts of the flow determined by a vector field. These appear in a number of different...

curl, denoted ∇×, of the vector field vanishes. In the case of the gravitational field g, which can be shown to be conservative, it is equal to the gradient...

if the vector field F is the gradient of some scalar-valued function (i.e., if F is conservative), then F is a path-independent vector field (i.e., the...

In vector calculus, a Beltrami vector field, named after Eugenio Beltrami, is a vector field in three dimensions that is parallel to its own curl. That...

conservative vector field this integral evaluates to zero for every closed curve. That means that a line integral between any two points in the field...

point can be used. In classical electrostatics, the electrostatic field is a vector quantity expressed as the gradient of the electrostatic potential...

electric field between atoms is the force responsible for chemical bonding that result in molecules. The electric field is defined as a vector field that...

justification for belief Conservative force, a physical force whose work is path-independent Conservative vector field, a vector field that is the gradient...

in vector calculus on R 3 {\displaystyle \mathbb {R} ^{3}} . Given a vector field, the theorem relates the integral of the curl of the vector field over...

In science, a field is a physical quantity, represented by a scalar, vector, or tensor, that has a value for each point in space and time. A weather map...

its reciprocal density (ρ) Particle number (ni) Markov property Conservative vector field Nonholonomic system Equation of state State variable Callen 1985...

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...

of which is characterized by an irrotational solenoidal field or a conservative vector field. Control System Analysis: Control Systems - The application...

solving non-exact differential equations by making them exact Conservative vector field Laidler, Keith, J. (1993). The World of Physical Chemistry. Oxford...