Vector Field (redirected from Integral curve of a vector field)

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.

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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(P) of the variable point 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