Remarks on Grading Assignment #3
First Posted: Wed Sep 28 09:14:24 MDT 2005
Stuff Added: Wed Sep 28 09:40:42 MDT 2005

Here are some observations I've made from grading #3:

1. I did not make clear enough the outer game of examples 2 and 3 and our in-class Least-Squares. Herewith let me try to fix this up.

   If you compare the pictures on pages 42 and 43, you see that the page-42 parabola exactly fits the three points given.

   But the page-43 parabola does not fit the points given: it is just the "best" that can be done in the sense that it is the parabola which

   minimizes the sum of the squares of the differences between the data y-coordinates and the parabola y-coordinates.

   Euclid knew that three points determined a unique parabola with a vertical axis of symmetry. For more than three points, there may be no such parabola passing through all the points. Least Squares just tries something that might be close in a reasonable way.
2. I did not make clear the relation between Example 2, page 42, and the in-class Maple worksheet:

   	Preview .html	Maple .mws
   In-Class Least-Squares Example 2	.html	.mws

   The stats and statplots packages used in the text are long-established parts of Maple. Their syntax is hideous. So recently Maple re-wrote the interface to the stats package so that it's more user-friendly and looks more like other Maple commands. That's where

   with(CurveFitting, LeastSquares);

   comes in.

   The in-class worksheet was intended to demo this newer interface. Make your lives easier, like.

   It was my intention that the Assignment-#3 problems be done with the new interface.

3. Watch that you do all parts of the problem. Problem 4 asked for three different sorts of least-squares curves.
4. Remove stuff that is not directly relevant to the problem at hand.
5. Dont remove too much stuff, though. Some wanted to de-garbage their worksheet through use of the colon : terminator. This is laudable, BUT
   • Run the statement with the ; terminator first. Like, make sure the thing's doing what you intend before you turn off its output. Don't hide errors from yourself.
   • Don't turn off results that your audience needs to see (such as the quadratic-fit of the force-displacement data).
6. The word "replicable" as applied in MATH 171 means that I should be able to type in exactly what I see on your handed-in submimssion and get exactly the same result that I see on your handed-in submission.
7. Several did problem 4 without reference to problem 4's input data.
8. It's a good idea to proofread your data. In problem 6, there were four temperatures and four specific heats.

   The zip command doesn't complain if one list is short -- it just stops, short.

9. Strive for relevant plot-window sizes. The problem-4 data had a very narrow horizontal spread. This horizontal spread should dictate the plot range

   0.01..0.28.

   It's on this range that you can see enough to decide which of the curves is maybe the best fit.
10. It's nicer if you can get the plot to show up on the same page as the commands which generated it.

    Maple allows you to insert pagebreaks by means of Control-Enter. If you get it in the wrong place, use the delete key to remove it.

    Maybe this is how you do it:

    • Use Control-J or Control-K to open an "execution group" at the place you want the page break.
    • At the beginning of the new group, do Control-T to turn on the black-writing mode, and then
    • Control-Enter to put in the pagebreak.

    Experiment with this before the eleventh hour finds you.

11. The commands
    • display
    • implicitplot
    • textplot
    are not part of "regular" Maple. You have to put with(plots): up at the start, say right after your restart; so that they work for you.

    Maple is indirect about telling you this: it just echoes back the command, sort of, if you don't have the "with".

12. When you resume work on a saved worksheet, you need to hit the !!! button to rerun the worksheet and put Maple in the know about your prior work.