just a picture -- but
this applet and many others are cataloged below!
GRAPHING APPLETS FOR CALCULUS
The pages contain a collection of applets designed for teaching Calculus,
two packages of java classes used for writing such applets, and full
documentation of the packages and their use. Source code is provided for
all the sample applets in the documentation below.
Above is a screen shot of one of the applets. This one is for experimenting
on Newton's method in one dimension and finding basins of attraction. The
basin of attraction to which each point on the x-axis
belongs is indicated by color; the code is on the right. The depth of the line indicates
how many steps it took to converge to the specified accuracy.
You can see
that the number of steps is large if you start near a maximum or minimum,
but what about the
other places its big? what's going on there?
It is this type of question that these for which
these applets were designed -- I wanted to bring experiments related to such
questions into my calculus classes.
These applets have a lot of features to facilitate experimentations -- both
to provide feedback, and to premit the user to make changes in the set-up.
For example,
the badge up above the graph gives the
coordinates of the cursor. The textfield at the bottom can be used to
enter new functions, and one can "zoom in" for a closer view, and change
the region shown with simple mouse clicks and drags...
Further instructions on the use of these applets is provided on the individual pages containing
them.
All code was written by Eric Carlen and is copyrighted. It is however placed
here for public non-comercial use -- you are free to use it as long as
you do not include it in or bundle it with (in any way) any product
being sold at any price. So academic use and freeware is fine.
That out of the way, here's what's here:
Also on this page is a link for downloading the
class files for the packages graphingApplet and functionParser.
Use this page if
your browser
does not read class files out of jar files.
Some files commented more thoroughly than others. The code for the first one,
on the basins of attraction for Newton's method is especially fully commented.
the design goals that shaped them,
and some discussion of what can be done with them. After that,
it provides introduction to the individual classes in the
packages graphingApplet and functionParser, with an
overview of the indiviual classes, explaing how each fits into the scheme of
things as described in the sections above. There is a very simple architechture
unerlying all of the example applets -- and many more that have been written
with these packages -- and this section explains the "how" issues: how the
classes work together, and how to use them to write applets like the example applets.
The packages are however quite flexible, and could be used to do many more
things. But that will be, as it must be, left to your imagination! For convenience,
the "how" part of the write up is on a separate page, presented as a
"cookbook" for writing math applets
using these classes. However, it is probably best, the first time around, to
read the introduction to the packages, and to to follow the links there to
the cookbook. The recipes will be clearer that way.