What is mean by scalar point function?

Def. Scalar function. A scalar function is a function that assigns a real number (i.e. a scalar) to a set of real variables. Its general form is

u = u(x1, x2, ... , xn)

where x1, x2, ... , xn are real numbers.

ORDef. Scalar point function. A scalar point function is a function that assigns a real number (i.e. a scalar) to each point of some region of space. If to each point (x, y, z) of a region R in space there is assigned a real number u = Φ(x, y, z), then Φ is called a scalar point function.

Examples. 1. The temperature distribution within some body at a particular point in time. 2. The density distribution within some fluid at a particular point in time