# Vector Field

(redirected from*Gradient field*)

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Related to Gradient field: Gradient of a scalar

## vector field

[′vek·tər ‚fēld] (mathematics)

The field of vectors arising from considering a system of differential equations on a differentiable manifold.

A function whose range is in a vector space.

(physics)

A field which is characterized by a vector function.

## Vector Field

a region, at each point *P* of which a vector **a( P)** is assigned. Mathematically, a vector field can be defined in a given region

*G*by the vector function

**a(**of the variable point

*P*)*P*of this region. A whole series of physical phenomena and processes (for example, the vectors of the velocities of a moving fluid’s particles at each moment of time form a vector field) lead to the concept of a vector field. Vector-field theory has been extensively developed and has diverse applications in various branches of natural science.

### REFERENCE

Budak, B. M., and S. V. Fomin.*Kratnye integraly i riady,*2nd ed.Moscow, 1967.

E. G. POZNIAK