As computer based learning becomes a major part of educational technology there is great demand for applications which enhance and enrich teaching and produce a learning environment which promotes intelligent questions by illustrating complex situations using simple interactive graphics. Such applications are ideal for shifting the emphasis from teaching to learning by encouraging students to go beyond a typically passive learning role to discover explorative mathematics. The applications Differential Equations and Phase Portraits are both excellent examples which do precisely this. They were developed by Herman Gollwitzer, Drexel University. The user is able to enter their own function, f, select a method and then use the mouse to click at any point and observe the solution.
All graphical parameters are adjustable, as is the type and range of the axes.
The interface is typically Macintosh and can be entirely mouse driven with the exception of typing in the form of the differential equation. First we can examine the direction field but using the field marks option from the Screen options menu. From this the general form of the solution curves can be seen. Next we can determine an approximate solution by any of a variety of methods. For example using a 4th order adaptive Runge-Kutta we can determine the solution through any point simply by clicking the mouse button at the required point.