Parameter_Plane – with Initial Value Problems

The screen shot above shows a module using Parameter_Plane to study the effects of two parameters – the coefficient of friction and the spring constant – on an initial value problem. This is almost identical to the use of Parameter_Plane to study the effects of two parameters on function except in this use the functions are defined by initial value problems rather than by formulas.

The applet call for this example is shown on the next page. The code highlighted in red specifies the ranges and labels for the variables and axes. The internal names for the horizontal and vertical axes for the blue graph are a and b, respectively but you will normally change these. The internal names for the horizontal and vertical axes for the green graph (the one on which the solutions to the initial value problems are drawn) are x and y. You may specify up to ten curves. The parameters are essentially self-explanatory. Your names for variables must begin with a letter and may contain letters and numbers but no special characters.

The code highlighted in blue gives the number of initial value problems (the number of curves) to be drawn, their appearance (color and thickness), labels, and differential equations, and initial conditions. These parameters are self-explanatory. The thickness of each curve is specified by and integer 0, 1, or 2 with 0 being the thinnest and 2 the fattest.

Colors for the various elements of the display are specified in the form RRRGGGBBB where each of RRR, GGG, and BBB is a three digit integer between 000 and 255 specifying the red, green, and blue components of the color. Leading zeros may not be omitted.

The other parameters in the applet call above do the following.

  • margin determines the spacing around and between the two graphs.
  • background_color determines the color of the applet’s background.
  • de_sw and mark_point_sw must have the values that are shown for a phase plane graph like this one.

This applet has additional parameters that are described in the user’s manual.

To use this applet, include the applet call above in your html page, making the appropriate changes. Include the file Parameter_Plane.jar in the same directory (or folder) as your html page.