MATH 261, Spring 2001 Due Date: Name(s):
Project 15.1c: Graphs of Functions
Objective
The objective of this project is to illustrate some techniques we can use to visualize the graph of a function
of two real variables.
Narrative
If you have not already done so, read Section 15.1 in the text.
In this project we introduce the commands plot3d in Maple's plots package. This command allows us
to plot the graph of a function of two real variables over a specified range of values.
Tasks
1. a) Type the command lines below into Maple; they produce a graph of f(x, y) = e-x2
-y2
.
> # Project 15.1c: Graphs of Functions
> restart; with(plots):
> setoptions3d(axes=normal,color=red,grid=[50,50],
orientation=[80,80],lightmodel=light1):
> f := (x,y) -> exp(-x^2-y^2);
> plot3d(f(x,y),x=-3..3,y=-3..3,style=patch);
b) Continue by typing the following command line into Maple; note that the effect of the %; is to
produce two copies of the same graphic.
> plot3d(f(x,y),x=-3..3,y=-3..3,style=patchcontour); %;
Adjust the first graphic so that you get a good perspective view of the graph, and rotate the second
graphic so that the second view is from directly overhead (that is,  = 0).
2. Repeat both parts of Task 1 for f(x, y) = -5x/(x2
+ y2
+ 1).
At this time make a hardcopy of your typed input and Maple's responses. Then, ...
3. By hand, draw a level curve (other than one of the ones produced by Maple) on the second graphic
you produced in Task 1 (the "patchcontour" graphic that is in perspective), and the corresponding level
curve on the third graphic you produced in Task 1 (the "patchcontour" graphic for which  = 0).
4. By hand, draw a level curve (other than one of the ones produced by Maple) on the second graphic
you produced in Task 2 (the "patchcontour" graphic that is in perspective), and the corresponding level
curve on the third graphic you produced in Task 2 (the "patchcontour" graphic for which  = 0).
Comments
Since a computer is not always available to help you visualize the graph of a function, it is wise to study
the graphics produced by computer and try to produce them by hand. One of the things you can add to a
graphic that help in visualization are x- and y-curves, particularly those that might bound the region over
which the graph is drawn. Another thing you can draw are the occluding contours: the curves on a surface
consisting of those points at which the normal to the surface is perpendicular to the line determined by the
viewer's eye and the point.