Functions of two variables

Abstract

We have studied functions of one variable and vector functions of one variable. In each case, the value of the variable defines the value of the function. We now turn to functions of two real variables, where the values of two variables must be given before we can evaluate the function. As in the case of a function of one variable, we define a function f of two variables, x and y, say, by its value at all points of the domain. Thus the domain has to be described in terms of both variables x and y. The following definition enables us to do this.