1. Surfaces

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 Variablesz y x

5. Examples

6. Quadratic Surfaces

7. Ellipsoid

8. Sketching Surfaces
A trace of a surface is the intersections of a surface with a plane.
A sequence of traces for a surface form a wire mesh that represents the surface.

9. Ellipsoid

10. Elliptic Cone

11. Hyperboloid of Two Sheets

12. Hyperboloid of One Sheet

13. Elliptic Cylinder

14. Hyperbolic Cylinder

15. Parabolic Cylinder

16. Hyperbolic Paraboloid

17. Elliptic Paraboloid

18. Identify and Sketch the Surfaces