A scalar function 8 is a single-valued function which is defined in some domain D of space, and whose value at any point P of D is a real number.

The value of 8 depends only on the position of P, and not on the coordinate system used to specify it. The domain of definition D of 8 may be a curve, a surface or a region in space. We say 8 defines a scalar field in D, since it associates a scalar 8 (P ) with each point P in D.