# DiffEq Support Notes

DiffEq is one of the dynamical systems exploration tools in MacMath 9.2. MacMath 9.2 was developed locally by Professor John Hubbard and Beverly West, and has been commerically sold by Springer Verlag. It specializes in exploring 1 dimensional (non-autonomous)  differential equations dx/dt=f(x,t).

Related programs include DiffEq, Phase Plane and DiffEq, 3D Views which specialize respectively in the two and three dimensional cases. By appending an equation like dy/dt=1, the two dimensional programs can also be utilized to study many aspects of one dimensional  equations such as those entered in DiffEq.

The program Planar Systems in MacMath 9.6 is an incomplete update of DiffEq, Phase Plane, with many nice additional features but incomplete support for basics like printing.

### Basic operation

of the program involves entering an equation and then clicking at various locations to see the trajectories going through those points. By default trajectories first continue forward until a window boundary is encountered. Then  a trajectory backwards (negative time) from the initial point is traced. Clicking the mouse while a trajectory segment is being traversed terminates that direction of traversal immediately.

DiffEq gives very rich graphical displays but has no support for providing large amounts of numerical data.

## Some Frequently Asked Questions

Axes and Tickmarks
are added from the Settings menu.
Equations
are also changed from below the Change menu.
Numerical Integration
methods available under the Change menu are Euler, Heun (midpoint Euler) , and Runge-Kutta.
The Point Window
contains the coordinates where the mouse was last clicked.
Rescaling
operations may require a carriage return to take effect.
Slope Marks
are available from the Settings menu. The program Planar Systems is notable for improving the algorithm used in drawing these.
Step Sizes
by default are very large because the program was written many years ago. Choose something smaller
from  below the Change menu.
Special Functions Supported include
• Option-p for pi.
• abs(),  sqrt(),  sgn(),  ln(),  exp(),  atan(),  and floor().
• ^ is exponentiation.
Zooming
is accomplished by selecting Blow Up fromt the Task menu and then selecting a rectangle while holding down the mouse button.

### Location

In the folder  MacMath 9.2 toplevel on all Macintoshes in the lab.

### Printing

Most MacMath programs have some difficulty printing in the lab. Screen Dumps should always be viewed as the backup technique when difficulties are encountered. Turning background printing off may also help this program.

### Documentation

A manual (yellow) for MacMath 9.2 is available in the lab bookcase.

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Last Update: September 2, 1998