Functions of two or more variables

The concept of function of one variable can be extended to functions of two or more variables. Thus for example defines a function f which assigns to the number pair (x, y) the number z.

It’s familiar for some people with graphing in a 3-dimensional xyz coordinate system to obtain a surface. Sometime x and y are called independent variables and z a dependent variable. Occasionally it’s written rather than , using the system z in two different senses. however, no confusion should result.

The ideas of limits and continuity for functions of two or more variables pattern closely those for one variable.