**GETTING STARTED WITH DPGraph**

These instructions are intended to help you familiarize yourself with the plotting software DPGraph. You should be sitting in front of a computer with DPGraph running in front of you.

Suppose you want to graph a particular surface, analyze some of its properties, and then print out your results for turning in. Consider the following simple problem.

* Problem.* Describe and sketch the surface:

*Solution*. Since the variable y is missing, this is
a cylinder with rulings parallel to the *y*-axis. A graph of this
cylinder is given below:

The
cross section in the *yz*-plane is a parabola
(also easy to see from the given equation), so we have a parabolic cylinder.
Here is how you generate the above graph:

1. Download the surface-default graph by clicking its name, then click "Edit";

2. In the very last line of the Edit window, delete all the equations inside the "graph3d(...)" statement, and enter your own equation (in this case, the one given in the above problem);

3. Click "Execute" to get a color graph;

4.
With the default domain *-3 < x,y,z
<3*, you notice that the graph is cut off at the top. Increase the
positive z value until the graph completes (here you should realize that the
parabola's vertex is at *z = 4*, so just change the value of
"graph3d.maximumz" from *3* to a number greater than or equal
to *4*). Now *save your graph* (on a floppy disk, if NOT using
your own computer); click "Save as" then choose a directory (or the
floppy drive), enter a name for your file and press "OK". The file
will be saved with extension ".dpg".

5. Change the view by pressing down one of the "arrow" keys on your keyboard (this will rotate the graph) until you are satisfied that you have seen all aspects of the surface and have obtained the best view in your opinion.

*EXPLORE*!
*At this stage, with the graph in front of you, you can further analyze its
various properties. Click edit and change the "Resolution" to a
higher or a lower number to see the effect on the graph (generally, the higher
the resolution, the smoother the graph). Then try slicing the graph up to see
the "traces" of the surface by clicking "Scrollbar" then
"Z slice". This give you one cross section
orthogonal to the z-axis. Use the scrollbar at the far right of the screen to
move this cross section up or down; do you understand what is happening and
why? Next, click "Scrollbar" then "Y slice"; this time you
see the unchanging parabolic cross section whose equation was given in the
problem.*

6. Go back to the ideal view you obtained earlier in step 5. You are ready to print your result as far as this problem is concerned. If you are not using a COLOR printer, then you must first turn you graph into black and white. This is easy; just click "Color" then "White". Then click "Clipboard" then "OK". Now to print out your graph, and possibly annotate it also, go back to the "software page" and follow the "printing with Paint" instructions.

**Remark**. The buttons "Help",
"Clipboard", "Print" and "Animate" in DPGraph are for information. They should answer most, if
not all, of your questions regarding operation with the software. Ask me if you
still have a question; send e-mail or stop by my office.

The following useful facts are from the DPGraph help menu:

*COMMON ERRORS*: The seven most common mistakes when creating graphs
in the EDIT dialog box are: 1) leaving out asterisks for multiplication; 2)
leaving out equals signs or inequality signs; 3) leaving out the parentheses
for lists; 4) trying to use equalities in intersections (DPGraph
can only intersect inequalities, i.e. regions of space); 5) putting a space
inside the two-character symbols :=, >=, or <=; 6) using the parametric
variables u or v in implicit graphs; and 7) using the implicit variables x, y,
z, r, theta, rho, or phi in parametric graphs.

** wrong**: ---

graph3d( 3x = z^2 ) --- graph3d( 3*x = z^2 )

graph3d( x^2+y^2 ) --- graph3d( z = x^2+y^2 )

graph3d( x=1, y=1 ) --- graph3d( ( x=1, y=1 ) )

graph3d( x=1 & y=1 ) --- graph3d( x>1 & y>=1 )

graph3d( z^2> =x^2 ) --- graph3d( z^2 >= x^2 )

graph3d( z=u^2+v^2 ) --- graph3d( z=x^2+y^2 )

graph3d( rectangular(x,y,sin(x+y)) ) --- graph3d( rectangular(u,v,sin(u+v)) )

graph3d.resolution := 30

For parametric surfaces:

graph3d.stepsu := 50

graph3d.stepsv := 50

You may find it useful to use the technique described in the previous section on DEFAULTS.DPG.

Binary DPG files are compressed and contain error detection information for more reliable transmission. ASCII DPG files are readable and editable by Notepad and many other text editors. Each line in the file is a separate command for DPGraph. For example, a file might look like this:

graph3d.view:=top

graph3d.perspective:=false

graph3d(z=3*sin(x*y))

Each command must be on a separate line.