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Plotting Capabilities for Engineers
Go to Maple Portal Maple Portal for Engineers
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Introduction
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Maple contains an extensive set of visualization tools and options, including many plots and options commonly used by engineers. This document demonstrates how to create and customize your plots using interactive techniques and command options, with an emphasis on options useful in a engineering context.
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Constructing Plots in Maple
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Plots can be created using both interactive, "clickable" techniques and through plotting commands. Both of these methods are demonstrated here.
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Clickable Plotting
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The clickable approach is based on using point-and-click tools such as menus and interactive assistants, rather than commands. Using this approach is possible even without knowledge of Maple's syntax or the underlying commands.
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Example
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Plot the function  from -15 to 15 using a clickable plotting approach.
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Action
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Result
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Enter the expression to be plotted.
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Right-click the expression and select Plots > Plot Builder. The interactive Plot Builder assistant appears.
Change the range of the  -axis to  to  .
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Click Plot.
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Tip: The Plot Builder is a good choice if you know in advance the options that you want to modify. Alternatively, you could also select Plots > 2-D Plot, and then use the context menus to change various options afterwards.
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Command Plotting
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The command-based approach involves using Maple commands to produce the plots. Options can be added to the command to customize the final appearance of the plot. The plotting command can be incorporated into larger scripts and custom Maple procedures.
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Example
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Plot a simple function using a command-based approach:
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Plotting Features
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Certain plotting features, such as the display command, are part of the plots
package, so we will begin by loading the package. This package contains a wide variety of specialized plots and options.
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To load the plots package, from the Tools menu, select Load Package>Plots
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Loading plots
Note: You can also load the package using the command with(plots):
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Feature
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Clickable-Based Approach
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Command-Based Approach
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Simple 2-D Plot
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Right-click an expression and select Plots > Plot Builder.
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Change the range of  to be from 0 to 2*Pi.
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Tip
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In the expression above,  is the imaginary unit. It is entered from the Common Symbols palette.
The symbols  ,  , and  from that palette represent the imaginary unit. Warning: Simply typing "j" will be understood as the name j, not the imaginary unit.
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Gridlines
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Right-click an expression and select Plots > Plot Builder.
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Ensure that the range of  is from 0 to 2*Pi.
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Right-click the plot; select Axes > Toggle Gridlines.
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Tip: When you click the plot, the Plot toolbar will be visible above. You can click the
button to toggle the gridlines on and off.
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Annotations
You can add annotations to your plot, such as titles, axis labels, legends, and more. Shown here are just some of the annotations you can make.
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Right-click an expression and select Plots > Plot Builder.
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Ensure that the range of  is from 0 to 2*Pi.
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Right-click the plot and select Title > Add Title.
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Name the plot Function Plot.
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Right-click the plot and select Axes > Labels > Edit Vertical.
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Name the vertical axis Value.
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Tip: You can also add annotations to your plot using the Drawing tools. Click your plot and select the
toolbar, and then you can choose from several options to annotate your plot.
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![plot(abs(1+exp(I*Pi*cos(theta))+exp((2*I)*Pi*cos(theta)))^2, theta = 0 .. 2*Pi, title = "Function Plot", labels = [theta, "Value"])](/support/helpjp/helpview.aspx?si=3835/file02183/math756.png)
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Logarithmic Scales
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Right-click an expression and select Plots > Plot Builder.
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Ensure that the range of  is from 0 to 2*Pi.
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Click Options, and Advanced Settings in the Axes section.
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Change the Mode for the second, unlabeled axis to Log.
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Click Apply, and then click Plot.
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![plot(abs(1+exp(I*Pi*cos(theta))+exp((2*I)*Pi*cos(theta)))^2, theta = 0 .. 2*Pi, axis[2] = [mode = log])](/support/helpjp/helpview.aspx?si=3835/file02183/math883.png)
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Specialty Tickmarks
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Right-click an expression and select Plots > Plot Builder.
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Ensure that the range of  is from 0 to 2*Pi.
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Click Options, and Advanced Settings in the Axes section.
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Change the Tickmarks setting for theta to spacing(Pi,0).
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Click Apply, and then click Plot.
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![plot(abs(1+exp(I*Pi*cos(theta))+exp((2*I)*Pi*cos(theta)))^2, theta = 0 .. 2*Pi, tickmarks = [spacing(Pi), default])](/support/helpjp/helpview.aspx?si=3835/file02183/math1012.png)
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Plot Multiple Expressions
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Begin with two expressions separated by a comma as shown. Right-click and select Plots > Plot Builder.
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Ensure that the range of  is from 0 to 2*Pi.
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Tip: To create a single plot with multiple expressions, you can also drag and drop expressions expressions from your document, or curves from separate plots, onto the same set of axes.
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Tip: To suppress the output of the assignments of A and B, you can place a colon at the end of your statement (as shown above).
Tip: The display command is used to display more than one plot on a set of axes. For more information on the display command, see display.
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Dual Axes
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Begin with two expressions separated by a comma. Right-click and select Plots > Plot Builder.
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Ensure that the range of  is from 0 to 2*Pi; click Plot.
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Right-click the plot; select Axes > Create second axis.
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Right-click a curve (for example, the green curve) and select Axes > Move to second axis.
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Specialized Plotting Examples
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Built into Maple are a wide array of standard engineering plots such as Bode plots, root-locus plots, and polar plots. See the Plotting Guide for information on all of Maple's built-in specialized plots.
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Bode Plots
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Bode plots are typically a combination of a magnitude plot and a phase plot. These plots provide us with information with regard to the frequency characteristic of a linear, time-invariant system. The command used to construct a Bode plot belongs to the Dynamic Systems package. To begin, load this package. This enables you to access Dynamic System commands in the context menu.
In this example, we enter a transfer function for a continuous system and then graph the Bode plot for the system. We demonstrate the clickable approach. For more details about using the Dynamic Systems package, including both clickable and command-based approaches, see Dynamic Systems in Maple.
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To begin, load the Dynamic Systems package (Tools>Load Package>Dynamic Systems). This enables you to access Dynamic System commands in the context menu.
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Enter the transfer function. Then, right-click the transfer function and select DynamicSystems>Plots>Bode Plot.
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Loading DynamicSystems
 
Tip: Specialized Maple functions like BodePlot can still be customized with various plotting options, allowing you to add titles and change colors and annotations, just as with any other Maple plot.
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Root Locus Plots
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Maple has the ability to plot the root-locus of a system using another command from the DynamicSystems package. Simply load the package, enter the transfer function of the system, and create the root-locus plot.
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To begin, load the Dynamic Systems package (Tools>Load Package>Dynamic Systems). This enables you to access Dynamic System commands in the context menu.
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Enter the transfer function. Then, right-click the transfer function and select DynamicSystems>Plots>Root Locus Plot.
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Loading DynamicSystems
 
The Dynamic Systems package also includes support for root-contour plots, phase plots, and more. See DynamicSystems for more details.
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Polar Plots
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To plot polar functions in Maple, you simply define your function and plot it using the Plot Builder.
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Action
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Result
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Enter the expression to be plotted.
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Right-click the expression and select Plot > Plot Builder. The interactive Plot Builder assistant appears.
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Click Plot.
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 Go to Maple Portal Maple Portal for Engineers
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