Functions of Several Variables

Constructing Functions of Several Variables

• The temperature at points in the xy-plane is proportional to the square of the distance of the point to the origin. Write the temperature as a function of x and y.

Constructing Functions of Several Variables

• The ideal gas law states that the pressure of a gas is proportional to its temperature and inversely proportional to its volume. Write a function that represents the pressure of a gas in terms of its temperature and volume.

Graphs of Functions of Several Variables

)y,x(f,y,x

z

y

x

0,y,x

Examples

Combinations of Functions

Level Curves of Graphs

Examples

Level Curves

Surfaces

Level Surfaces