
Interface for Numeric and Symbolic Solutions of ODE and ODE Systems


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A new interactive interface (Interactive ODE Analyzer) has been created for numeric and symbolic solutions of ODE and ODE systems. The Analyzer is easy to use, with many common options. In addition to computation of solutions and solution values, plots can also be generated. The Analyzer is suitable as an educational tool; it can provide the corresponding Maple commands needed to compute the solution or plot. For information on launching the Analyzer (and commandline options), see dsolve/interactive. For an illustrated description of the interface, see worksheet/interactive/dsolve.



Maplets Package


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Enhancements to the Maplets package enable you to interactively rotate 3D plots in Maplet applications.

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The cyclic option to the Maplet application Plotter element has been deprecated. The option 'cyclic'=true is interpreted as 'continuous'=true. The option 'cyclic'=false is ignored.



Plotting


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Maple 9 includes a new plot renderer, OpenViz, from Advanced Visual Systems (AVS). This renderer improves Maple plot quality.

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Most Maple plotting routines now accept a new $\mathrm{transparency}=t$ option, which controls the transparency of plot objects. The transparency t must be in the range 0.0 to 1.0, with 0.0 meaning ``not transparent'' and 1.0 meaning ``fully transparent''. For more information, see plot[options] and plot3d[options].


The corresponding plot data structure is $\mathrm{TRANSPARENCY}\left(t\right)$. For more information on PLOT and PLOT3D data structures, see plot[structure]. The following is an example that uses the plot3d command.

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plot3d([cos(t), sin(t), s], s=0..1, t=0..2*Pi, transparency=0.2);

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There is a new maplet plot device available. It displays plots in a separate window as a Maplet application (using the Maplet application Plotter element). This functionality is particularly useful in the commandline version. For more information, see plotdevice.

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The following three plotting routines have been updated to allow a list of curves or surfaces as input: plot3d, plots[implicitplot], and plots[implicitplot3d]. As a result, particular options can now take lists as values. An example using the plots[implicitplot] command follows. For more information and additional examples, see the help pages for the three commands.

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plots[implicitplot]([x^2+y^2=1, x^2+y^2=4], x=2..2, y=2..2,
color=[coral,blue], linestyle=[DOT,DASH]);

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The plots[animate] command has been redesigned to animate any Maple plotting command, including 3D plotting commands. (The plots[animate3d] command has been superseded by plots[animate].)


Consider the old format for the plots[animate] command.

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plots[animate](A*sin(x), x=0..2*Pi, A=0..2, frames=50);


This calling sequence still works and all existing plots[animate] commands work as well. Using the redesign, the plots[animate] command is the following.

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plots[animate](plot, [A*sin(x), x=0..2*Pi], A=0..2, frames=50);


In general, to animate a plotting command of the form plotcommand(f(t, x, y), f2, ..., fn) for the parameter t over the range $a..b$, you write plots[animate](plotcommand, [f(t, x, y), f2, ..., fn], t=a..b). The first argument is the plotting command, the second argument is the list of inputs to the plotting command, the third argument is the range for the animation parameter, and the remaining arguments are options for the animation. The following animation shows how the $xy$ term of an ellipse deforms a circle.

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plots[animate](implicitplot, [x^2+A*x*y+y^2=2, x=2..2, y=2..2,
grid=[50,50]], A=0..1, frames=25 );


The following is a 3D animation using the plot3d command.

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plots[animate](plot3d, [sin(A)*exp(x^2y^2), x=2..2, y=2..2],
A=0..2*Pi);


The following is an animation of two figures.

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plots[animate](plot, [{[sin(x), cos(x), x=0..t], [sin(2*x), cos(3*x),
x=0..t]}], t=0..2*Pi, frames=50);

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The plots[cylinderplot] and plots[sphereplot] routines have been superseded. The same functionality is available using the $\mathrm{coords}=\mathrm{cylindrical}$ or $\mathrm{coords}=\mathrm{spherical}$ option with the plot3d command. For information on plotting in various coordinate systems, see ?plot3d[coords]. Note that for backwards compatibility, the plots[cylinderplot] and plots[sphereplot] commands will continue to function.



Student


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The Precalculus subpackage in the Student package introduces a number of visualization tools for precalculus students. These visualization tools are interactive tutors, graphical user interfaces, that help you work through a particular precalculus problem. For more information, see Student[Precalculus].



