# Vector field

Assignment of a vector to each point in a subset of space.

- Vector field

305 related topics

## Differentiable manifold

Type of manifold that is locally similar enough to a vector space to allow one to apply calculus.

A locally differential structure allows one to define the globally differentiable tangent space, differentiable functions, and differentiable tensor and vector fields.

## Curl (mathematics)

In vector calculus, the curl is a vector operator that describes the infinitesimal circulation of a vector field in three-dimensional Euclidean space.

## Vector calculus

Vector calculus, or vector analysis, is concerned with differentiation and integration of vector fields, primarily in 3-dimensional Euclidean space The term "vector calculus" is sometimes used as a synonym for the broader subject of multivariable calculus, which spans vector calculus as well as partial differentiation and multiple integration.

## Line integral

Integral where the function to be integrated is evaluated along a curve.

The function to be integrated may be a scalar field or a vector field.

## Tangent bundle

Trivial.

A smooth assignment of a tangent vector to each point of a manifold is called a vector field.

## Magnetic field

A magnetic field is a vector field that describes the magnetic influence on moving electric charges, electric currents, and magnetic materials.

In vector calculus, the gradient of a scalar-valued differentiable function

of several variables is the vector field (or vector-valued function).

## Gravitational field

Model used to explain the influences that a massive body extends into the space around itself, producing a force on another massive body.

is a vector field consisting at every point of a vector pointing directly towards the particle.

## Scalar field

In mathematics and physics, a scalar field or scalar-valued function associates a scalar value to every point in a space – possibly physical space.

Scalar fields are contrasted with other physical quantities such as vector fields, which associate a vector to every point of a region, as well as tensor fields and spinor fields.

## Tensor field

In mathematics and physics, a tensor field assigns a tensor to each point of a mathematical space (typically a Euclidean space or manifold).

As a tensor is a generalization of a scalar (a pure number representing a value, for example speed) and a vector (a pure number plus a direction, like velocity), a tensor field is a generalization of a scalar field or vector field that assigns, respectively, a scalar or vector to each point of space.

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