The package demonstrated here is the result of a continuing project begun in December 1990 to make Mathematica graphics more powerful and easier to use. It is specifically aimed toward use by students and instructors in computer laboratories, but should be of interest to anyone using Mathematica graphics on a regular basis.
Steps are being taken to make the full package available commercially at a reasonable price. If you like what you see here, you can help this process by letting your favorite publisher of academic texts and software know you are interested!
The centerpiece of GUM is the PlotE (for “PlotExtended”) command, a major enhancement of the built-in Plot command which provides flexible syntax, automatic convenience features, and over 40 new options.
There are several other graphics utility commands, primarily useful in Calculus instruction: Zoom, Newton, Riemann, Trapezoidal, Simpson, PlotDirection, PlotConcavity, InterP, and Cobweb. Most of these are based on PlotE so that options and keywords for PlotE can be used with these as well. One example of each of these is given below. There are also a number of miscellaneous features not directly graphical in nature.
Note: In laboratory use the PlotE function is accessed via the command Plot. In this demonstration we will use PlotE explicitly, and Plot will give the standard Mathematica command, allowing comparison with PlotE.
PlotE can do things other than plotting functions; it can graph sequences, data sets, equations, and parametric equations, all at the same time. In fact, PlotE doesn't have to do anything at all! It can also create a variety of geometric objects. But first, let's show how to do nothing at all!
Which[0 <= x <= 1, x^2, 1 <= x <= 2, 2 - x, 2 <= x <= 4, E^(2 - x)]
;[o]
2 2 - x
Which[0 <= x <= 1, x , 1 <= x <= 2, 2 - x, 2 <= x <= 4, e ]
:[font = text; inactive; preserveAspect; ]
As you can see, Piece is in part a synonym for Which. It has the advantage that you donàt have to remember what comes first, the functions or the intervals:
