Click Back to return
THE MATHWRIGHT LIBRARY NEWSLETTER, August 2002, VOL
4, #5
A publication of Bluejay Lispware
James E. White, Editor
The official publication of the New Mathwright Library and Café:
In this issue:
Featured Microworlds this Month!
Free 30 Day Preview Version of Mathwright32 Author for Members of the Library
1) Featured Microworlds this Month!
A
Primer on Derivatives
by Ravinder Kumar, Alcorn State University
This
36-page Microworld
is an Active Introduction to one of the most basic concepts of the Calculus:
the Derivative. It develops this idea with many simulations, illustrations,
examples and exercises. Throughout the book, readers may ask their own questions
and study their own examples. But the book is equipped with countless automatically
generated example questions that can provide many hours of stimulating and
challenging activities.
Rational
Matrix WorkBench
by Dan Kalman, The American University
This
Microworld is a workbench that you may use to create exact rational
matrices and perform a variety of operations on them, such as adding or multiplying
them, inverting square matrices, row reducing them in a single step, finding
characteristic polynomials and determinants of square matrices, and many more.
It is well suited for laboratory and classroom work and for independent study
and experimentation. You may create any matrix objects you like, and then
perform command-line calculations on those objects. Operations are exact (rational)
by default but may also be done in decimal mode.
Surfaces
of Revolution
by James White, The Mathwright Library
This
Microworld is designed to illustrate how our new OpenGL based 3D Graphics
Objects may be used to support visualization. For Mathwright authors, it provides
a few examples that may guide them in the construction of their own dynamic
3D Microworlds. And for students, there are some utilities that they can use
to visualize a few interesting constructions in geometry.
Method
of Bisection
by Kwok-Wai Mok, Munsang College, Hong Kong
The
method of bisection is one of the simplest and most reliable ways to find
numerical solutions to equations. Suppose
you want to solve an equation in the form: f(x) = 0 for x. We assume that
f is a continuous function on an interval of numbers [a, b]. Suppose also
that f(a) is a negative number and that f(b) is a positive number. Then since
f is continuous on the interval by assumption, we may conclude that the graph
crosses the x axis at some point (z,0). This means that f(z) = 0, and z is
a solution to the equation f(x) = 0.
Of
course, there may be many such solutions, but we are not greedy. We seek only
one. How
can we approximate it? The Bisection method gives a simple (foolproof) recipe.
If we bisect the interval [a,b] at the point m = (a+b)/2 then either
f(m) will be 0, or the sign of f(m) will be different from that of f(a) or
of f(b). In the first case, m would be a solution, so we would be done. And
in the second case, we have two possibilities. If f(m) > 0 then we begin
again with the interval [a, m] and we know that since f(a) and f(m) have different
signs, there is a solution in the smaller interval, [a,m]. On the other hand,
if f(m) < 0, then we begin again with [m, b] and we know again that since
f(m) and f(b) have different signs, there is a solution in that interval.
And on and on...
Rocket
Science 101
by James White, The Mathwright Library
Your
Mission, Rocket Fans, should you choose to accept it, is to dock the Space
Shuttle with the "Novi Mir" Space Station. You will learn right
away the first lesson of space flight. In Space, flying is coasting. Let momentum,
inertia, and gravity do most of the work. You should use your engines only
when you have to make course corrections. Continually move the cursor near
the blue Shuttle avatar to fire the rockets. You will see and hear the engines
light. The shuttle velocity will slowly change as you correct the course.
Finally,
you must approach within 250 Kilometers of the Station before you hand the
job over to the pilot to dock. If your velocity does not match closely enough
to the Station's velocity, you will hear a short message from Arnold.
2) Free 30-Day Preview Version of Mathwright32 Author for Members of the Library
Create
Microworlds easily and painlessly with our 30-Day Free
Trial Mathwright32 Author
Did
you ever want to build an Applet for your own website? Daunted by Java? Java
is an elegant and powerful language, but
it is difficult to learn from scratch.
Now Library members may try our new Java authoring tool without any obligation
to purchase it. Mathscript creates Java code, but it speaks Mathematics. There
is no need to learn any Java at all to write interactive and "smart"
Microworlds like the ones at the Library.
Now
you can create interactive mathematical Microworlds like the ones in the Library
for your own web pages. That's right, you can build
powerful and highly interactive Mathematical Microworlds, and put them on
your website. And you can do it in a few hours (instead of months)
with our revolutionary point-and-click
Mathwright32 Microworld Builder.
Our
Microworld Builder is the first (and only) Author Platform of its kind available
for teachers today. Read our "Introducing
Mathwright Microworlds" paper in the Journal of Online Mathematics
to learn more. There is no longer a reason not to build rich and colorful,
smart and interactive learning environments for your web pages, like the ones
at the Library. The books you create are yours to distribute as you like.
They are royalty-free, and your readers use the free Personal MathwrightWeb
Player to read them. You distribute the Player, as you distribute your books
from your own website, with no strings attached to the Library.
Now
you can try it out for free so that you can decide whether our authoring program
is for you before you invest in it. The 30-Day trial
version of Mathwright32 Author has all the authoring functionality
and capabilities of Web Microworld Builder, and will give you the opportunity
to judge for yourself whether it is a tool you would like to use. It is available
to Library members only.
As
you step through the 10 Tutorial Chapters at our Online
Mathscript Help Center (or if you download the Help to read
on your machine) please feel free to send questions you have to us at
the Library on our Contact
Us page. We want to convince you how easy it is to learn and use and will
answer your questions promptly.
You
may also open any Mathwright32 Documents that you download from the Library
or other Mathwright site and modify them as you like. In fact, you might like
to take a look at some other Mathwright
sites for ideas.
The
Mathwright32 Documents that you create with it will be fully functional within
this trial version of the author program. They will not, however, be publishable
MathwrightWeb or Mathwright32 Reader. To publish those documents and make
them readable on the web or in Mathwright32 Reader, you simply reopen them
later in MWAuthor32 (after purchase) and save them from there.
At
the end of 30 days, the trial version will cease to function. At any time,
you may uninstall it, or you may purchase MWAuthor32 at the Library
Store and simply install that over the trial version for full functionality
and publishing. Once you do that, you may open and save any projects you built
with the trial version.
James E. White, Ph.D.
Library Director