Interactive Differential Equations (IDE)

IDE is available, for free, at http://www.aw-bc.com/ide

When we first, in the 1990s, became acquainted with Hubert Hohn and his wonderful interactive illustrations we knew immediately that he had found a real key to making our subject (and many others) come alive--not only for students, but for ourselves and our faculty colleagues.   Hohn is a master educator. 

Each of the 97 "tools" is carefully constructed to illuminate the very crux of a topic.  There is no syntax to learn – the tools are completely intuitive.  They operate entirely by simple point/click, or sometimes click/drag.  Simulations run simultaneously as graphs evolve; variables and their graphs are color-coded; parameters can be changed with a slider.  Multiple concepts are quickly and automatically assimilated.

In the Pendulums tool, we see various cases and can watch all aspects of the evolution of trajectories; in the Glider we change a parameter to see its effects.

Damped Nonlinear Pendulum		Forced Damped Pendulum
The Glider Tool		Parameter Plane Input Tool

The fourth figure above shows the tool that allows you to move across the trace-determinant parameter plane for a two-dimensional system and watch how the behaviors of the vector field and eigenvectors change, and the matrix updates. Go to http://www.aw-bc.com/ide and try IDE to see far more than these screen snaps can convey.

The equations and graphs illustrated in IDE are chosen carefully to illustrate certain points clearly, without missing the point, so IDE is not a solver in which you can enter your own equations. It is simply a package to clarify concepts, in a visual way that is entirely intuitive. Students quickly gain understanding of concepts that are too abstract without the pictures; they have the ability to control what happens when something changes, and to replay an evolution as often as they wish.

Finally, there is a set of 31 laboratory worksheets of several pages each, constructed by four of us who used IDE extensively in our courses. Each lab is a PDF file that can be downloaded and copied for your class. We hope you will find this approach as much fun as we have.

Beverly H. West, Cornell University
Steven Strogatz, Cornell University
Jean Marie McDill, California Polytechnic University
John Cantwell, St. Louis University

Note: An instructor’s version of the lab manual is available online at Pearson.com for faculty members who wish additional guidance – this can be a real help for those who have not had experience teaching a differential equations course with a component of computer exploration.