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Frequently in multivariate calculus, we encounter functions which take as their inputs points in the plane or points in three dimensional space, but return numbers.  These are scalar functions.  A typical example would be a function which describes the pressure at any point in a fluid.  However, a function which takes a point in a fluid and returns the direction of the flow at that point would NOT be scalar function because the information returned it not a number - we will examine these kinds of functions in the next lecture.

Frequently in multivariate calculus, we encounter functions which take as their inputs points in the plane or points in three dimensional space, but return numbers.  These are scalar functions.  A typical example would be a function which describes the pressure at any point in a fluid.  However, a function which takes a point in a fluid and returns the direction of the flow at that point would NOT be scalar function because the information returned it not a number - we will examine these kinds of functions in the next lecture.

 

Scalar functions on the plane are easily visualized.  For example, a scalar function on the plane which takes a point <math>(x,y) \ </math> and returns a number <math>z \ </math> can be visualized by constructing a surface consisting of points in three dimensional space <math>(x,y,z) \ </math>.  See illustration at right.

Scalar functions on the plane are easily visualized.  For example, a scalar function on the plane which takes a point <math>(x,y) \ </math> and returns a number <math>z \ </math> can be visualized by constructing a surface consisting of points in three dimensional space <math>(x,y,z) \ </math>.  See illustration at right.