JIM HENRIQUES: PROFESSOR, PHYSICS, CERRITOS COLLEGE, NORWALK, CALIFORNIA
You are free to use these applications with no fees or restrictions. I
merely ask that, for ego's sake, you credit me with authorship.
This is actually used for my pre-algebra class. I supply them with the data
sets (after a discussion of graphing of course) as assign the graphing by
hand (my pre-algebra students are notoriously computerphobes). The next day I
hand out the ASA plots and we compare. In a similar fashion we explore
frequency distribution and basic statistics:
One prepares a similar spreadsheet similar to FREQDIST complete with macros. I
have a Las Vegas Day where the students draw cards, throw dice, etc. Once
plotted they get views of probabilities and distributions. I also have them
anonymously write down their ages, heights, income, etc., and plot the class
data for display (we have a big VGA monitor, so a small class can get a good
picture). Both these spreadsheets seems to get the point across.
One of the first things I show my engineering students is the power of the
spreadsheet to do statistical interpretation. We do a freefall experiment with
HORRIBLE equipment, get reams of crummy data, then analyze it with some
spreadsheet statistics. They use STATDEML as a guide for creating their own
programs. It's good practice in learning a program, statistics, and data
analysis. Notice that the linear regression is rather more tedious than need
be--I don't tell them about the regression package until another lab!! This
lab they do reasonably well.
This is a simple radial plot of the radiation pattern (intensity vs.
azimuthal angle) for two antennae separated a certain distance, radiating at a
certain frequency. These parameters are easily changed, and PROFOUNDLY affect
the radiation pattern. However, even after showing my engineering students how
to do this plot, they could not reproduce it during an open book test! In some
ways my pre-algebra students are brighter than my engineers.
I haven't used this in lab yet, as I am still experimenting. The program is a
simple real number recursion over several increments that show unexpected
convergence to several "attractors". The numbers in column A are the seeds. I
print this data to a file and have MathCAD to the plotting. The bifurcation is
quite apparent, and will be more interesting when ASA5.0 expanded memory
capacity allows me to use more, smaller increments.
This is probably the most complicated .WKS file included. I won't go into a
treatise on Fourier synthesis, but here is a brief outline: I chose a simple
square wave (f(x)) to reconstruct using a Fourier series. The function has a
period of 10, and is piecewise continuous from -5 to 0 and from 0 to 5. There
is a discontinuity at zero, so the student must integrate the Fourier
amplitude coefficients in two parts. The integration is trivial, with one set
of coefficients vanishing as well as the even harmonics of the surviving
terms. Differential displacements fill the column to the left of the discreet
instantaneous amplitudes, and the harmonics are shown in a row across the top.
The sums of the amplitudes of each harmonic are in a column to the right of
the data. It is easy to show the gradual "squaring" of the series as one adds
more harmonics by adjusting the range or the @SUMS. In theory you could
calculate as many harmonics and as fine a differential as computer memory will
allow. When ASA5.0 comes out, the LIMits will be even higher (sorry about the
pun). My best students get a real kick out of making this program cook.
One final note for now: we use Vernier Software for much data collection
(temperature probes, timers, voltage probes). Vernier allows for the data to
be stored as a text file, with optional extension ".P". This allows importing
by ASA. Once in, the excess labels can be erased, and the data parsed (if
necessary) and analyzed more completely that Vernier's "Graphical Analysis".
I would be happy to hear from other physics/math people with other ideas
and/or improvements on my work. ENJOY!