explore mathematical expressions, plots, or images that depend upon parameters - Maple Help

Explore - explore mathematical expressions, plots, or images that depend upon parameters

 Calling Sequence Explore(expr) Explore(expr, opts )

Parameters

 expr - anything; the expression or function call to explore opts - options, described below

Description

 • The Explore command takes an arbitrary Maple expression or function call and displays an interactive application to explore its evaluation at varying values of its dependent parameters. The interactive application for the exploration is comprised of various embedded components within a Standard GUI Table.
 Slider components allow for the values of the parameters to be changed. The result of evaluating the expression or function call at the values specified by the controllers is displayed either as an expression in a MathContainer, a plot in a PlotComponent, or as an image on a Label.
 A plotting command to be explored can be a function call to plot, plot3d, a command in the plots package, or any user-defined procedure which returns a two- or three-dimensional plot structure or an Array of such plot structures.
 • The resulting exploration application is not the return value of the Explore command. The default return value is NULL.
 • The Explore command can also be applied using the right-click context-sensitive menus.
 Note: This feature only works in the Maple Standard Worksheet interface.

Examples

See the Explore example worksheet for addtional discussion and examples of the various command options.

 > $\mathrm{Explore}\left(\mathrm{plot}\left(\frac{\left(b+0.7\right)\mathrm{sin}\left(\frac{x}{a+1}\right)}{x}+b,x=-12..12,\mathrm{view}=-2..6\right),\mathrm{parameters}=\left[a=-2.0..0.0,b=0.0..3.0\right]\right)$
 > $\mathrm{Explore}\left(\mathrm{factor}\left({x}^{a}-1\right),\mathrm{parameters}=\left[a=2..20\right],\mathrm{initialvalues}=\left[a=4\right]\right)$
 > $\mathrm{Explore}\left(\mathrm{plot}\left(\mathrm{sin}\left(ax\right)\mathrm{cos}\left(bx\right),x=0..1,y=-1..1\right),\mathrm{title}="sin\left(a*x\right) * cos\left(b*x\right)"\right)$

In the next example, select the skip check box for the variable x in the pop-up dialog.

 > $\mathrm{Explore}\left(∫{\mathrm{sin}\left(x\right)}^{a}{\mathrm{cos}\left(x\right)}^{b}\phantom{\rule[-0.0ex]{0.3em}{0.0ex}}ⅆx\right)$
 > $\mathrm{Explore}\left({{∫}}_{0}^{\mathrm{π}}a\mathrm{sin}\left(bx\right)\phantom{\rule[-0.0ex]{0.3em}{0.0ex}}{ⅆ}x,\mathrm{numeric},\mathrm{parameters}=\left[a=0..\sqrt{2},b=1.0..5.0\right]\right)$

In the next example select the check box numeric in the pop-up dialog to force use of numerical integration (quadrature).

 > $\mathrm{Explore}\left({{∫}}_{0}^{\mathrm{π}}a\mathrm{sin}\left(bx\right)\phantom{\rule[-0.0ex]{0.3em}{0.0ex}}{ⅆ}x,\mathrm{initialvalues}=\left[a=7,b=3\right]\right)$