Tickmarks in multiples of $\mathrm{\pi }$ are now added to plots generated by the plot and plot3d commands when $\mathrm{\pi }$ is detected in the range arguments.

plot3d(cos(x)*sin(y), x=-Pi..Pi, y=-Pi..Pi, 'axes'='boxed');

The range argument for the plot command is optional. When this is omitted, the default range is now set to -2*Pi..2*Pi instead of -10..10 when a trigonometric function is detected in the expression to be plotted.

plot([cos(x), sin(x)]);

Plots created using the Plot Builder or through the context menu also set the default range to -2*Pi..2*Pi when a trigonometric function is detected.

When specifying $\mathrm{\pi }$ tickmarks with the tickmarks or axis option, you can now use the name piticks instead of the spacing suboption. Similarly, if you want to remove $\mathrm{\pi }$ tickmarks that were automatically added, you can use the decimalticks value for the tickmarks option.

plot(sin(x), x = 0 .. 2*Pi, tickmarks = [decimalticks, piticks]);

Visualization plots and tutors in the Student packages have improved captions, including formatted 2-D mathematics describing the graph.

For an introduction to these visualizations, see the Calculus1Visualization, MultivariateCalculus, LinearAlgebraVisualization, and StudentVectorCalculus example worksheets.

The new getdata command in the plottools package retrieves data from a 2-D or 3-D plot and returns it in the form of a Matrix or Array, along with the ranges of the data. More details are available in the plottools[getdata] help page.

plottools[getdata](plot([sin(x), x^2-2*x], x = -2 .. 2));

The DEplot3d command in the DEtools package has been enhanced, with the addition of 3-d field arrows, and the ability to animate either curves, arrows, or both.

Example of a command to plot field arrows:

with(DEtools,DEplot3d):

DEplot3d({diff(x(t),t)=y(t),diff(y(t),t)=-sin(x(t))},[x(t),y(t)],t=0..10,
[[x(0)=0,y(0)=.5],[x(0)=0,y(0)=1],[x(0)=0,y(0)=1.8],[x(0)=-2*Pi,y(0)=1],
[x(0)=2*Pi,y(0)=.5],[x(0)=-2*Pi,y(0)=2.1],[x(0)=2*Pi,y(0)=-2.1]],
orientation=[-5,85],linecolor=sin(t)-t,arrows=cheap);

Same system animating the solution curves:

DEplot3d({diff(x(t),t)=y(t),diff(y(t),t)=-sin(x(t))},[x(t),y(t)],t=0..10,
[[x(0)=0,y(0)=.5],[x(0)=0,y(0)=1],[x(0)=0,y(0)=1.8],[x(0)=-2*Pi,y(0)=1],
[x(0)=2*Pi,y(0)=.5],[x(0)=-2*Pi,y(0)=2.1],[x(0)=2*Pi,y(0)=-2.1]],
orientation=[-5,85],linecolor=sin(t)-t,animate=true);

See DEtools[DEplot3d] for more information.

The background and trace options for the animate command in the plots package have been improved. For more information, see the plots[animate] help page.

The background option now accepts a list of plots in addition to a single plot. The plots are automatically combined with the plots[display] command to form a single background plot.

Note: To run animations, right-click ( Command-click, Macintosh) the plot, and select Animation > Play.

plots[animate](plot, [t*x^2, x=-1..1], t=0..1, 'background'=[plot(.5, -1..1, 'color'="Blue"), plots[pointplot]([0, 0], 'symbol'='solidbox', 'color'="Green", 'symbolsize'=30)]);

The trace option now allows you to specify a list of the frames to be traced during the animation, as an alternative to having a number of equally spaced frames.

plots[animate](plot, [t*x^2, x = -1..1], t=0..1, 'trace'=[1, 2, 3, 23, 24, 25]);