Vector field Totally Explained

Everything about Vector Field totally explained

In mathematics a vector field is a construction in vector calculus which associates a vector to every point in a (locally) Euclidean space.
Vector fields are often used in physics 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.
In the rigorous mathematical treatment, (tangent) vector fields are defined on manifolds as sections of a manifold's tangent bundle. They are one kind of tensor field on the manifold.

Definition

Vector fields on subsets of Euclidean space

Given a subset S in Rⁿ, a vector field is represented by a vector-valued function

V_x: S 	o mathbf (M)

(a fraktur "X").

Further Information

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