Electronic Library: Software Alcove: Repository

The University of Arizona Software Collection

Click here to download the entire Arizona package from this site. You are advised to put it in a directory by itself. This is a large file, so go and get a cup of coffee or something while it is downloading. When you decompress it, it will take up about 11 megs of disk space. Also, we had some difficulty installing it according to the author's instructions (We don't know if the problem is with the installation software or with our local setup.) When you PKUNZIP the package, you will find a README file which tells how we successfully installed the program.

You can also download the individual pieces of the package and run them as stand-alone programs. We have modified the author's description so that you can click on any of the highlighted areas below to download that piece of the program.

(Author's description of) the University of Arizona Software Package

Our software falls into 3 categories: ARE YOU READY?, SLIDE SHOWS, and TOOLKITS.

ARE YOU READY?
The purpose of this series is to make available to students computer programs which review those materials from the prerequisite courses that are essential for success in the present course. In addition, the programs identify a student's weak areas and recommend appropriate action (usually references are to Schaum's Outlines because they are inexpensive and are not revised every few years). Programs available:

ARE YOU READY FOR INTERMEDIATE ALGEBRA?
ARE YOU READY FOR COLLEGE ALGEBRA?
ARE YOU READY FOR CALCULUS? (Also contains Are You Ready for Business Calculus?)
ARE YOU READY FOR AP CALCULUS (AB)?
ARE YOU READY FOR CALCULUS II?
ARE YOU READY FOR CALCULUS III?
ARE YOU READY FOR ODES?

SLIDE SHOWS
This is a collection of screen images, primarily graphical, which anyone can view. These are usually images of functions which would be difficult, or impossible, to draw on the board. Some of these are animated and some "zoom" in on the function. Programs available:

FUNCTIONS. This consists of graphs of functions which occur frequently in Calculus, such as sin(1/x), x sin(1/x), sin x/x, and, that old standby, an everywhere continuous nowhere differentiable function.
TROUBLE. This demonstrates the dangers associated with graphing a function by plotting "enough" points and then joining them.
NEWTON'S METHOD. This shows Newton's method graphically. Some images demonstrate how it works, while others display how it can go wrong.
TAYLOR SERIES (SLIDE SHOW). This displays the Taylor polynomials, of various degrees, corresponding to exp x, sin x, cos x, etc. It also contains some visual demonstrations of convergence and divergence.
ORDINARY DIFFERENTIAL EQUATIONS. This has examples from ordinary differential equations, including a one parameter family of curves, the US Population and logistic growth, the cooling of coffee and Newton's law, the Euler and Runge Kutta methods and their fallibility, damped free vibrations, building a function from its series solution, and Bessel functions.
FOURIER SERIES (SLIDE SHOW). This shows the partial sums of Fourier series for the triangular wave, the square wave, the saw tooth wave, the cosine expansion of sin x, and an interrupted square wave. The Gibbs phenomenon and other non-uniform convergence are quite apparent.
VIBRATING STRING. This is an animated set of displays which shows how two travelling waves generate a stationary wave.
PDE1, PDE2, and PDE3. This shows the exact solution of a wave equation for three different initial conditions (PDE1 a smooth hump, PDE2 a step function, PDE3 a triangular hump). Various numerical approximations are then superimposed on the exact solution so that the accuracy and stability of the numerical scheme can be visualized.

TOOLKITS
These are aids to instructors and students, both in and out of class. Some encourage experimentation via projects. All have drop down-menus and are self documenting, with online, context sensitive help. A 30 page manual, entitled A Manual for the Mathematical Toolkits Software is available from us for $3. For each toolkit the manual contains a description of the program, its purpose, the courses it targets, and suggestions for its use. Programs available:

BAYES' THEOREM - deals with Probabilities, Conditional Probabilities, Bayes' Theorem, and how they are used in Search and Rescue to look for a missing subject lost in a hostile environment.
COMPLEX NUMBERS - graphically displays the sum, product, quotient, conjugate, etc. of complex numbers. Also has game feature to test the user's understanding of these concepts.
CONICS - a program that plots conics in standard form, as well as quadratic curves. The constants that usually occur in these formula can be changed at will and the curves redrawn. Contains demos showing the construction of conics.
DIVISION ALGORITHM - user enters real polynomials with integer coefficients. This package will help the user find GCDs, as well as perform Sturm's algorithm, and Bezout's identity. The coefficients of all polynomials are stored and shown as rational numbers.
FEUERBACH'S THEOREM - allows you to experiment with the size of a triangle and see the resulting incircles, excircles, circumcircles and nine-point circles. It is designed to give a pictorial representation of Feuerbach's Theorem.
FINDPOLY - gives student any information about a selected polynomial (graph, derivative, zeros, value) - except what it is. The student has to identify the polynomial. Designed for Calculus I.
FORTUNE - a graphics package that plots f(x) and g(x) containing parameters a, b, and c. Then these parameters can be "tuned" and the graphs redrawn. Contains projects for ideas.
FOURIER SERIES (TOOLKIT) - plots the first 20 Fourier "polynomials" of the Fourier series of f(x). Will compute the Fourier coefficients numerically, or the user can supply them explicitly.
HISTOGRAM - calculates the mean, median, and standard deviation of a data set. It will also generate a histogram, a bar chart, a box and whisker plot, and a stem and leaf plot.
IDENTIFY - a program to test whether a student can identify polynomials, rationals, trig functions, exponentials, and logs. The computer will graph a function selected from its bank of functions. The student is to identify that function. Designed for pre-calculus.
IMPLICIT FUNCTIONS - plots implicit functions defined by f(x,y) 0, as well as contour lines for surfaces z = f(x,y).
INTEGRAL - performs numerical integration of f(x), by various techniques, (left endpoint, right endpoint, mid-point, trapezoidal, Simpson, Romberg, Gaussian, and Monte Carlo).