1. Functions of Several Variables

2. 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.

3. 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.

4. Graphs of Functions of Several Variables z y x

5. Examples

6. Combinations of Functions

7. Level Curves of Graphs

9. Examples

10. Level Curves

11. Surfaces

12. Level Surfaces