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The ODE Library has dozens of pre-programmed, editable, and interactive ODE files covering a wide range of topics from mathematics, physics, chemistry, population biology, and epidemiology. There are also many ODEs to illustrate points such as data compression, ODEs with singular coefficients, bifurcations, limit cycles, and so on. Each Library file has explanatory text along with the equations and includes an illustrative graph or graphs. The Library files are organized into folders by topic and they have descriptive titles to facilitate browsing. These files also provide a marvelous way to learn how to use the tool.
ODE Architect was developed with partial support from the NSF/DUE,1 by the Consortium for ODE Experiments (C-ODE-E), Intellipro, Inc., and John Wiley & Sons, Inc. C-ODE-E saw to the mathematical side of things, Intellipro rendered C-ODE-Es work into an attractive multimedia software package, and John Wiley coordinated the efforts of both teams.
As in any project like this, we owe a debt of gratitude to many people: reviewers, beta testers, students, programmers, and designers. Specifically, we want to thank the other members of the C-ODE-E Evaluation Committee, Barbara Holland (John Wiley & Sons), Philippe Marchal (Intellipro), Michael Moody (Harvey Mudd College), and Beverly West (Cornell University). Without the many hours of hard work they put in on this project, it could not have been done.
We especially want to thank Professor L.F. Shampine for providing the excellent solver codes (developed by himself and his colleague, Ian Gladwell), and for his continuing support of the project. Thanks to Mark DeMichele at Intellipro, who wrote the code for the Architect and the implementation of the Shampine/Gladstone solver codes, and who put up with our constant “advice”. Another very special thanks to David Richards for designing and implementing the LTeX macros for the Companion book and for his patience and meticulous attention to detail during the many revisions. We also very much appreciate the reviewers, editors, and evaluators Susan Gerstein, Zaven Karian, Mario Martelli, Lang Moore, Douglas Quinney, David Cook, and Robert Styer for their many helpful comments and suggestions.
Finally, a big “thank you” to our students Tiffany Arnal, Claire Launay, Nathan Jakubiak, John Lu, Joel Miller, Justin Radick, Paul SanGiorgio, Treasa Sweek, and many others who read chapters, tested modules, and commented freely (even favorably) on what they experienced.
Robert L. Borrelli Courtney S. Coleman Claremont, CA
1 The work on ODE Architect and its Companion book was supported in part by the National Science Foundation under Grant Numbers DMI-9509135 and DUE-9450742. Any opinions, findings, conclusions, or recommendations expressed in this material are those of the authors and do not necessarily reflect the views of the National Science Foundation.
Modules/Chapters 1-3 are all introductory modules for first-order ODEs and simple systems of ODEs. Any of these modules/chapters can be used at the beginning of an ODE course, or at appropriate places in elementary calculus courses.
Modules/Chapters 4-9 involve higher-order ODEs and systems and their applications. Once students understand how to deal with two-dimensional systems graphically, any of these modules/chapters is easily accessible.
Modules/Chapters 10-12 apply two-dimensional systems to models that illustrate more advanced techniques and theory; the multimedia approach makes them nevertheless quite accessible. The modules are intended to enable students to get much further with the technical aspects explained in the chapters than would be otherwise possible.
Module/Chapter 13 treats discrete dynamical systems in an introductory fashion that could be used in a course in ODEs, calculus, or even a non-calculus course.
A Multimedia appendix on numerical methods gives insight into the ways in which numerical solutions are constructed.
Description/Prerequisites for Individual Modules/Chapters
We list below for each Module/Chapter its prerequisites and some comments on its level and goals. In general, each module progresses from easier to harder submodules, but the first section of nearly every module is at an introductory level.
The modules can be accessed in different orders. It is not expected that they will be assigned in numerical order. Consequently, we have tried to explain each concept wherever it appears, or to indicate where an explanation is provided. For example, Newton’s second law, F = ma, is described every time it is invoked.
There is far more material in ODE Architect than could possibly fit into a single course.
Module/Chapter 1: Modeling with the ODE Architect
Assumed concepts: Precalculus; derivative as a rate of change
This module is unlike all the others in that it is not divided into submodules, and it provides a tutorial for learning how to navigate ODE Architect. It carries that tutorial process along in tandem with an introduction to modeling that assumes very little background.