Hints for Computer Project 1

(Calculus IIIa, Fall 2000, Sections 001 & 002)

You are free to use any mathematical software you like to do computer project 1. You will need something that can plot 3-D space curves and also something that can do symbolic differentiation. Gyrographics is very nice for plotting 3-D space curves, and actually allows you to rotate the curves with your cursor, so you can visualize the curve very easily. The tutorials in the lab are very good. However, it is a bit cumbersome trying to print your graphs from Gyrographics. It requires copying the image into some word processing software (like WordPerfect). There are instructions posted on the walls in the computer lab explaining how to do this. But I recommend getting help from a lab TA.

You can also use Derive 5.0 to do your 3-D plotting. However, I found this was a bit tricky, so here is one method you can use to do this.

Consider the space curve r(t)=<cos t, sin t, t>. We can plot this curve using Derive 5.0 as follows:

1. Author the expression r(t):=[cos t, sin t, t]. (Don't forget the colon before "=").

(if you don't know how to author expressions, you should read one of the Derive tutorials in the computer lab).

(NOTE: at this stage, you could plot the space curve by highlighting the above expression, and then just doing a 3-D plot. Unfortunately, you will not be able to specify the range of t values for the curve. Thus, you will need to use the following, more cumbersome, procedure.

2. To plot the curve over the range 0<= t <= 3, author the following expression: vector(r(t),t,0,3*pi,0.1)

3. Highlight the expression above (actually, it will probably already be highlighted), then click the approximate button (looks like an approximately equal to symbol), which will generate a matrix with 3 columns. (each row of this matrix specifies a point on the space curve).

4. Highlight this matrix and then move to the 3-D plot window (by clicking on the 3-D plot icon, which looks like a set of 3-D coordinate axes).

5. Finally, plot the curve by clicking on the plot icon (which has probably moved, since you are now in the plot window).

At this stage, you should see a 3-D curve plotted in the plot window. And this curve will probably be plotted inside of a box. (Unless someone has changed the Derive default settings). Unfortunately, Derive may not have plotted the entire space curve. That is, the curve may not encompass the entire range of t values. You can tell if the curve appears to reach a side or edge of the box. To fix this problem, you need to change the plot range:

6. Click on Set, followed by Plot Range. This will bring up a window called "Set 3-D Plot Range".

7. In the "Set 3-D Plot Range" window, change the minimum or maximum values of each variable that you think may be bounding your curve. For example, when I did this, each variable started out ranging from -5 to 5. This caused a problem in the z direction, since at t=3*, the z-coordinate of the curve should be between 9 and 10. To fix this problem, I changed the maximum z-value to 10 in the "Set 3-D Plot Range" window.

If you have set the plot range large enough, then when you return to the plot window, your space curve should look like it is entirely within the box (instead of being cut off by a face of the box).

Now you are almost done. The last step is to get rid of the coordinate "box" and replace it with a set of coordinate axes. The following instructions describe how to do this:

8. Click on Options, and then click on Display. This will bring up a window called "Display Options".

9. In the "Display Options" window, click on the "axes" tab. Then click "on" to turn on the axes.

10. Next, click on the "box" tab in the "Display Options" window, and click "off" to turn off the box. Finally, click "ok".