Functions of two variables

Graphical, Numerical and Analytical Points of view

Functions of One variable

In first and second semester calculus, you studied functions of one variable. That is, one quantity depends on another quantity. For instance, the area of a circle depends only upon

its radius. The position of a moving object varies with time.

You have seen several ways of representing these relationships.

Functions of One Variable

Analytical representation

( ) sin( )f x x x

Graphical Representation

x y=f(x)

1 .841

2 1.82

3 .423

4 -3.03

5 -4.80

Numerical Representation

Dependance on more than one quantity Most quantities in life depend on a number of

different factors. Volume of a right circular cone depends on its height

and the radius of its base

The pressure of an ideal gas depends on the number of moles of the gas, the volume of the gas, the absolute temperature of the gas.

21

3V r h

nRT or P= ( is a constant)

VPV nRT R

Graphing Functions of Two Variables

Suppose that (2,3) 4f

(2,3)

When we do this with many points…

We get a surface instead of a curve!

In Calculus C. . .

We will study the calculus of functions of several variables. We will see how to picture these functions and

extract information from the graphs.We will analyze their rates of change

(differentiation)We will look at integration for these functions,

as well.