Needham Multivariable Calculus: Domain of Function of Several Variables

When you dealt with functions of a single variable, it was enough to specify intervals over which the functions existed. Now that you're dealing with functions of MORE than one variable, you need to develop a vocabulary that can address the question of their domain. Because the domain of these functions consists of more than one variable (generally, x and y), the shape of their domain actually needs to be drawn on a plane, instead of specified as intervals of real numbers.