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Teaching Software at ESG

This page contains links to other pages and sources that give information on how to use software available on Athena (and some other sources), as demonstrated at the Tutor Training Seminar.

Most of these links are to web pages for subjects that use the software in question and which include introductory instructions as part of the course material, and so the specific uses are those that pertain to specific subjects. Some links of more general interest, primarily links to Athena help pages, are included via those links. Applications on Athena change quite frequently; such is the nature of software, and for the most part that's a good thing. For an updated summary of what's available, see What Runs Where, Numerical/Math software. To see recents changes, see What's New.

The applications considered here are:

• Maple on Athena.
• Xess on Athena.
• Stella, a dynamic systems modeling program available as an application on the older Macintosh computers at ESG (anyone with access to a newer version?).

Maple

These instructions have been updated to reflect the upgrade of the default release on Athena to Release 6; Release 6 commands will work on Release 7 as well.

The commands that generated all of the figures and processes shown in the demonstration are in the ASCII file Demonstration Commands. The purpose of putting the commands into this format is that the commands can be cut and pasted directly into a Release 3 Maple session, or cut and pasted into another buffer (such as a scratch Emacs buffer) and then into a Release 6 Maple session. The demonstration used Maple Version 5 Release 3 exclusively.

Worksheets for the examples given in the demonstration may now be downloaded:

• Orthogonal Ellipses and Hyperbolas

  Download maple files for Release 3 or Release 6.

The set of ellipses

and the hyperbolas

have the same foci, and it is somewhat challenging (unless the trick is known) to show that at the intersection of one of the ellipses with a branch of any of the hyperbolas, the respective curves are orthogonal.

For further investigation, the parameter h can be considered a variable ranging from -c² to infinity, thus defining a surface. Such a surface is plotted here; the Maple Release 3 worksheet that created the plot is at Shapes, and shows how to make the plot both implicitly and by solving for h as a function of x and y in order to plot the surface more efficiently.

 

• Hypocycloid Animation

  Download maple files for Release 3 or Release 6.

The Hypocycloid of Three Cusps, defined parametrically by

is shown to be generated by a circle rolling inside a larger circle of twice the radius.

 

• "Clamshell" Surfaces

  Download maple files for First-Release 3, Variation-Release 3, or Release 6 (the Release 6 worksheet has commands for both figures).

The ``First'', which was shown in the demonstration, is a plot of the surface defined by

a perhaps familiar function that has the property that the first partial derivatives are not continuous at the origin.

The ``Variation'' contains plots of two surfaces,

where the first is a function which has well-defined first partial derivatives with respect to both x and y at the origin, but the derivatives are not continuous. The second function, the plot of which is a simple plane, would be the ``tangent plane'' if the derivatives were continuous; the point of the simultaneous plot is to show that this plane is certainly not tangent to the first surface.
These worksheets show how to plot two functions simultaneously.

 

• DC Resistive Circuit Anaylsis

  Download maple files for Release 3 or Release 6.

  These show how to use Maple to do the linear algebra needed to find the currents in a two-loop DC circuit, given the EMFs and resistances. While the physics may vary from circuit to circuit, the worksheets may be used as templates for solving other problems. The worksheets demonstrate both symbolic and numerical solution, including the substitution of numbers into a symbolic answer.

• Lorenz Attractor

  Download maple files for Release 3 or Release 6.

The by now ``standard'' system,

where s, r and b are constant parameters. The worksheets allow variation of these parameters, as well as the starting points and step sizes. This is a situation where the Release 6 commands are markedly different from the Release 3 commands.

• Fourier Animations

  Two Types:

  • We already know the coefficients, Triangle Wave, Release 3 or Triangle Wave, Release 6.
    The coefficients were taken from the 8.03-ESG text and notes, representing the amplitudes of the harmonics for a plucked string.
  • We get Maple to find the coefficients, Square Wave, Release 3 or Square Wave, Release 6.
    If we can input the function at time t = 0, Maple will integrate to find the coefficients and display the animation in one session.

• Vibrating String Animation

  Download maple files for Release 3 or Release 6.

  Shows the kinetic, potential and total energy density per unit length for a string vibrating as a standing sinusoidal wave.

• Surprise Figure

  Download maple files for Release 3 only. There's also Animated Surprise

Links to other pages with Maple instructions:

• 18.01-ESG Indpendent Study : Besides the documents explaining Maple, there are other uses of and references to other Maple uses.
• 18.02-ESG Independent Study contains further examples and commands for plots.
• 18.023 at ESG Course Notes: Extended uses of Maple, mainly for plotting surfaces. Further examples, including the ``Clamshell Figure'', are included in the notes.
• 18.03 at ESG Course Notes: Mainly but not exclusively the use of Maple to display solutions of differential equations.
• Numerical Methods, Xdvi or PDF for solving Differential Equations includes instructions for Maple, Matlab, XphaseD on Athena and Stella on the Macintoshes.
• The above are collected, with other links, at Using Maple for ESG subjects

A few further examples are contained in Craig Watkins' Public Directory on Athena; see the ASCII file.

/mit/watko/Public/Maple_Inst

Xess

Xess on Athena has vast resources that are sometimes hard to find. Instsructions for a simple version of a linear regression, as demonstrated, are in Introduction to Statistics on Xess, Xdvi or Postscript. In these notes, reference is made to the derivation and notation used in the subject 18.023. The file for that example is in Simple Linear Regression, and must be downloaded by clicking "Shift-Left" or from the menu by right-clicking.

Online help is available at Xess Help on Athena.

The other example demonstrated, that of analyzing the data from a photo of a bouncing ball, is part of the answers to an assignment in the subject 8.01L at MIT, and will not be made available on this web page.

Stella

An introduction to the use of Stella for modeling solutions to Differential Equations is contained in Numerical Methods, Xdvi or PDF, which also includes introductions to Maple (mentioned above), Matlab and XphaseD on Athena.

This page will certainly change and expand in the future, and possibly become a site of its own. Such an endeavor needs contributions from many interested parties. Such folks are asked to send Comments and suggestions.

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