Gray

Mezzino

Pinsky

Installation and Contents of the CD-ROM


Configuring Your HTML Browser


This CD-ROM is designed to be used with an HTML compatible browser, typically Netscape Navigator or Microsoft Internet Explorer. Any HTML compatible browser will allow you to move throughout the various folders with ease. The file called "ode.htm" is the main entry point to the entire electronic extension to the book.

H O W E V E R,

unless you configure your browser to automatically launch Mathematica when you select files with a ".ma" or ".nb" extension, you will not be able to fully realize the seamless nature of this resource. For the two most popular browsers, Netscape and Microsoft, the following comments and instructions will help you with this one-time-only task.

MIME (Multipurpose Internet Mail Extension) is a standardized method for organizing file formats. Netscape Navigator and Microsoft Internet Explorer uses the MIME type to establish whether the file format can be read by the browser's built-in capabilities or, if not, whether a suitable helper application is available to read the file. When reading from this CD-ROM, Netscape Navigator and Microsoft Internet Explorer interpret the file's extension. For example, a ".zip" extension suggests a compressed file, a ".ma" file suggests a Mathematica 2.0-2.2 notebook, a ".nb" file suggests a Mathematica 3.0 notebook, and so on.

Configuring MIME Types for Netscape Navigator


You can view and configure the mappings of all MIME types to helper applications by choosing Options | General Preferences and then click on Helpers. Here, you will see the complete list of helper applications which are associated with a specific file extension. If entries similar to following exist,

application/mathematica    Math            ma
application/mathematica    Mathematica     nb
then you are already configured and nothing more is required. If one of these is not present, then you should add it. Let's suppose that the first one must be added. To add this new MIME type, follow the following steps, where the quoted expressions are entered without the quotes.

(1) Click on the button labeled Create New Type
(2) For Mime Type, enter "application"
(3) For Mime SubType, enter "mathematica"
(4) Click OK
Then, in the Helpers Panel,

(5) For File Extensions, enter "ma"
(6) Click Launch the Application
(7) Enter the complete path to the Mathematica 2.2 executable or, if you don't know it, click Browse to search for it. On a typical Microsoft Windows installation, it is usually

c:\wnmath22\math.exe

(8) Finally, click OK
If you must add the second line, then repeat steps (1)--(8) but at step (5), change your entry to "nb", and at step (7), enter the complete path to the Mathematica 3.0 executable or, if you don't know it, click Browse to search for it. On a typical Microsoft Windows 95 installation, it is usually

C:\Program Files\Wolfram Research\Mathematica\3.0\Mathematica.exe

Configuring MIME Types for Microsoft Internet Explorer


The current release of Microsoft Internet Explorer, available from Microsoft's web site, http://www.microsoft.com/ie/download , is already configured to recognize the ".ma" extension and the ".nb" extension.

File Naming Convention


To create a set of files which can be read by anyone, we have used lowercase filenames throughout this CD-ROM. However, all references to the Mathematica package called "ode.m" on the CD-ROM will be "ODE.m" to maintain consistency with the book and its supporting documents.

Mathematica Requirements


This CD-ROM and its corresponding web site of new files and bug fixes located at http://math.cl.uh.edu/ode/ode.html contain several hundred megabytes of Mathematica notebooks and packages and other related files. To fully utilize this resource, you must have Mathematica running on your computer. However, you only need MathReader, a free program from Wolfram Research, to view the various notebooks and play the Mathematica movies. You may download MathReader by clicking on http://www.wolfram.com and following the directions.

Installing ODE.m


In order for Mathematica to be able to access the programs in ODE.m, that file must be put in a directory known to Mathematica. These directories can be determined in a Mathematica session by typing $Path. Either ODE.m can be put into one of these directories, or the directory containing ODE.m, call it xxx, can be added to the Mathematica-accessible directories using the command AppendTo[$Path,"xxx"]. It is particularly useful to put this last command into the file init.m, which is the user's Mathematica initialization file.

Folders on the CDROM


For your convenience, the following links will take you to the platform independent Mathematica 3.0 notebooks and related files for each of the sections:

1. Examples (examples)

This directory includes the Mathematica solution to every example in the book, in the form of Mathematica notebooks organized by chapter and appendix. To find a specific example, say Example 5.10, open chap05.ma and then search for Example 5.10.

2. Exercises (exercise)

This directory includes a subdirectory for each chapter and appendix in the book. Each subdirectory contains a set of Mathematica notebooks representing solutions to the computational exercises for the sections within the chapter. To find a specific exercise, say Exercise 3 in Section 14.5, select subdirectory chap14, then open sec1405.ma and search for Exercise 3.

3. Lab Assignments (labs)

This directory contains seven sample lab assignments to be done using Mathematica. Each one includes a brief review of the theory covering the topic, an example problem, and then the exercise. These sample assignments cover the following topics:
First order differential equations
Cell growth and first order equations
Second order equations with constant coefficients
Numerical solutions to differential equations
Laplace transforms
Series solutions to differential equations
Linear systems of differential equations
4. Miscellaneous Notebooks (misc)

This directory contains an assortment of Mathematica notebooks describing several interesting facets of differential equations using ODE.
Various direction fields
2-dimensional and 3-dimensional phase portraits from Chapter 16
A tour of the ODE.m package showing most of the features
Phase portraits for the pendulum
Other pendulum-like puzzles
Example of resonance using Mathematica's Play function
Animation examples generated by ODE.m
5. Movies (movies)

The Movies directory contains subdirectories reflecting the mathematical significance of each topic. For PCs and Macs, there are Mathematica and Quicktime versions of the movies.

The LinearSystems (linear) subdirectory contains Mathematica movies of 2-dimensional and 3-dimensional phase portraits reflecting the characteristic behavior of each of the possible solutions to 2-dimensional linear systems. These movies correspond to the examples in Chapter 16.

The NonlinearSystems (nonlin) subdirectory contains Mathematica movies of several well known 2-dimensional and 3-dimensional phase portraits. These include examples of a spring, a pendulum, the Lorenz attractor, the van der Pol attractor and predator-prey modeling. These movies correspond to the examples in Chapters 18 and 19.

The SeriesApproximations (series) subdirectory contains a Mathematica movie which animates the behavior of the Picard series approximation to y' = t 2 - y, y(1) = 2 on the interval (-2,6).

The VectorFields (vectors) subdirectory contains a Mathematica movie which animates the behavior of the flow in the vector field defined by y' = sin(t)/y on a rectangle centered at the origin.

6. Mathematica Packages (packages)

This directory contains the Mathematica packages which are referenced in the book. The main package is called ODE.m which includes the frequently used Mathematica functions. An auxiliary package called ODEx.m includes functions which are useful but which are not mentioned in the book.

7. ODE Reference Manual (ref)

This directory contains the manual which documents the Mathematica code in ODE.m. It was written primarily to serve as a beginners handbook and quick reference manual for ordinary differential equations. Although this manual can be read with any HTML browser, it is also present in postscript form in the "psrefman" folder for those with a postscript viewer or postscript printer.