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How do I...
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Maple's Tutorials are designed to help you get started with Maple, learn about the key tools available in Maple, and lead you through a series of problems.
The How do I... topics cover essentials for doing mathematics in Maple. Learn more about Maple's tools and features, such as palettes and context-sensitive menus.
Refer to Help>Quick Reference for basic getting started tips.
Note for non-Windows users: The keystrokes given in this document are for Windows. There will be differences for other platforms. If you are using a different platform, see Help>Quick Help for the list of the most common keystrokes.
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How do I...
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This section explains how to perform basic tasks in Maple, including entering mathematical objects (such as simple expressions, functions, matrices, and complex numbers), evaluating expressions, and plotting functions.
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...enter a simple expression?
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In Maple, mathematical expressions, such as  , can be entered in a natural, textbook-like notation. In Maple, this is called 2-D Math notation. The following examples demonstrate the process of entering expressions.
To begin, create a new document in Document mode. To begin entering a 2-D mathematical expression, ensure that you are in Math mode. In this mode, the cursor is inside a box with a dotted outline that indicates the boundaries of the mathematical expression. By default, all new documents created in Document mode start in Math mode so that you can begin entering mathematical expressions immediately. To switch between Math mode and Text mode, press [F5].
A video demonstration of the following examples is available online.
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Example: 
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Ensure that you are in Math mode, and follow the steps below to enter the expression  .
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Step
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Description
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Illustration
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1
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Type  , then  . Maple's Math mode treats the juxtaposition of a constant and a variable as an implicit multiplication.
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Type the division [/] character.
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Type  .
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To bring the cursor back onto the base line, press the right arrow [→] key on your keyboard.
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Type [+]. There is no need to type a space, as Maple automatically adjusts the spacing for you.
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6
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Repeat steps 1 through 4 to type  .
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(7)
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If you wish to continue typing non-mathematical text, press [F5] to switch to Text mode.
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Example: 
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Ensure that you are in Math mode, and follow the steps below to enter the expression  .
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Step
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Description
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Illustration
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Click the  template in the Expression palette. The green placeholder is selected automatically.
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Type  , overwriting the  .
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To enter an exponent, type the common power character [^] using the key combination [Shift][6]. The cursor is now in the exponent position. Type  .
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To bring the cursor back onto the base line, press the right arrow [→] key on your keyboard.
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5
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Type [+]. There is no need to type a space, as Maple automatically adjusts spacing for you.
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Type the word pi, and press [Esc]. The command completion list appears, listing every available symbol and command whose name begins with  . For the Greek symbol for pi, Select  .
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(7)
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If you wish to continue typing non-mathematical text, press [F5] to switch to Text mode.
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Return to the top of the page
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...enter a function?
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Mathematical functions are represented in Maple as operators. There are various methods for entering a function: by using a template from the Expression palette, by using Maple's operator syntax directly, or by converting an existing expression into an operator.
Before you proceed, be sure to familiarize yourself with entering simple mathematical expressions. (See the subsection above.) Open a new worksheet in Document mode, and ensure that you are in Math mode.
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Using a template from the Expression palette
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Follow the steps below to enter the operator  and assign it to a variable whose name is  .
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Step
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Description
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Illustration
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Select the  template from the Expression palette. The green placeholder  is selected automatically.
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Type  , overwriting the green  .
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Move the cursor among placeholders by pressing [Tab]. The  is selected as you do so. Type  .
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Press [Tab] to select the final placeholder  . To type  , first type  . Use the common power character [^] ([Shift][6]) to bring the cursor into the exponent position and type  .
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To bring the cursor back onto the base line, press the right arrow [→] key on your keyboard.
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Type [-]. There is no need to type a space, as Maple automatically adjusts spacing for you. Type  .
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Press [Enter] to execute the statement. Maple displays and labels the result of an executed statement on a new line. (For more information, see the How do I subsection on evaluating expressions.)
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To see what  does, enter  and press [Ctrl][=] to evaluate it inline. As you can see, Maple evaluates the expression  at  , which yields  .
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When working with templates from the palettes, keep these tips in mind.
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If you accidentally move the cursor outside a template, simply move the cursor back into the template and press [Tab] to move to the next placeholder.
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Use [Shift][Tab] to move back to the previous placeholder, if you have not overwritten it yet.
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Using Maple's operator syntax
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Follow the steps below to enter  and assign it to a variable whose name is  .
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Step
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Description
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Illustration
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1
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Type  , followed by a colon [:] and an equal sign [=]. The colon-equals notation assigns the content on the right-hand side to a variable name on the left-hand side.
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Type  . This is the name of the independent variable. To type the arrow, first type a minus sign [-], then the right angular bracket [>]. Maple automatically converts these characters to an arrow.
Tip: "->" looks like a right arrow.
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Type  . For detailed instructions, see the above example, steps 4 to 6.
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Press [Enter] to execute the statement. Maple displays and labels the result of an executed statement in a new line. (For more information, see the How do I subsection on evaluating expressions.)
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To see what  does, enter  and press [Ctrl][=] to evaluate it inline. As you can see, Maple evaluates the expression  at  , which yields  .
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Converting an existing expression into an operator
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Suppose the expression  has already been typed. Follow the steps below to convert it to the operator  and assign the result to a variable whose name is  .
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Step
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Description
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Illustration
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Right-click any part of the expression (within the dotted outline). A context-sensitive menu is displayed. For more information, see the Context-Sensitive Menus subsection under the Tools and Features section of this document.
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Select Conversions → Operator →  . Maple will convert the expression to an operator of  .
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Right-click any part of the blue output; in the context-sensitive menu that appears, select Assign to a Name.
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A dialogue box appears; enter the name  . Click OK.
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To see what  does, enter  and press [Ctrl][=] to evaluate it inline. As you can see, Maple evaluates the expression  at  , which yields  .
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Return to the top of the page
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...enter a matrix?
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Entering matrices in Maple is very simple. This section demonstrates two methods for entering a matrix: by inserting a template from the Matrix palette and by using the Matrix-constructor shortcut syntax.
Before you proceed, be sure to familiarize yourself with entering simple mathematical expressions (see the subsection above). Open a new worksheet in Document mode, and ensure that you are in Math mode.
A video demonstration showing how to enter a matrix using the Matrix palette is available online.
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Using the Matrix palette to create a template
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Follow the steps below to enter the three-by-four matrix  and assign it to a variable whose name is  .
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Step
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Description
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Illustration
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Type  , followed by a colon [:] and an equal sign [=]. The colon-equals notation assigns the content on the right-hand side to a variable on the left-hand side.
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In the Matrix palette, either
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Click and hold the Choose... button and drag a three-by-four rectangle in the box that pops up, or
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Type  into the Rows field and  into the Columns field.
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Click Insert Matrix.
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Type  over the highlighted placeholder. To move to and highlight the next placeholder, press the [Tab] key.
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Continue to navigate through the placeholders using the [Tab] key and enter values for the entire matrix.
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Press [Enter]. Maple displays and labels the result of an executed statement in a new line. (For more information, see the How do I subsection on evaluating expressions and the Tools and Features subsection
Equation Labels.)
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When working with templates from the palettes, keep these tips in mind.
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If you accidentally move the cursor outside a template, simply move the cursor back into the template and press [Tab] to move to the next placeholder.
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Use [Shift][Tab] to move back to the previous placeholder, if you have not overwritten it yet.
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Using Maple's Matrix-constructor shortcut syntax
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Follow the steps below to enter the three-by-four matrix  and assign it to a variable whose name is  . For details about the special syntax used in these steps, see the associated help topic.
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Step
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Description
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Illustration
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Type  , followed by a colon [:] and an equal sign [=]. The colon-equals notation assigns the content on the right-hand side to a variable name on the left-hand side.
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Type two left angular brackets [<] [<], followed by  (separated by commas), and a right angular bracket [>]. The expression  represents the first column of the final matrix.
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Type the pipe character [|]. This character is usually typed by pressing [Shift][\], the backslash key. The pipe character separates the four columns in the final matrix.
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As before, type the columns  ,  , and  , separated by pipe characters [|]. Type a final right angular bracket [>]. The angular brackets are automatically formatted by Maple.
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Press [Enter]. Maple displays and labels the result of an executed statement in a new line. (For more information, see the How do I subsection on evaluating expressions and the Tools and Features subsection
Equation Labels.)
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When working with this shortcut syntax, keep these tips in mind.
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The comma [,] is used to separate elements in different rows, while the pipe symbol [|] is used to separate elements in different columns.
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As a result, the matrix could also be entered as  .
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Return to the top of the page
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...evaluate an expression?
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Maple can evaluate any mathematical expression and display the results in-line or on a new line. Maple can also evaluate an expression at a point.
Before you proceed, be sure to familiarize yourself with entering simple mathematical expressions. (See the subsection above.) Open a new worksheet in Document mode, and ensure that you are in Math mode.
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Evaluating an expression in-line
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Follow the steps below to evaluate  and display the result in-line.
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Step
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Description
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Illustration
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Type  . For instructions on entering this expression, see the subsection entering an expression above.
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Press [Ctrl][=] to evaluate the expression in-line.
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The in-line evaluation mechanism, when used with Maple's Context-Sensitive Menus, is one of the fastest methods to perform a string of successive computations.
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Evaluating an expression on a new line
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Follow the steps below to evaluate  and display the result on a new line.
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Step
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Description
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Illustration
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Type  . For instructions on entering this expression, see the subsection entering an expression above.
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Press [Enter]. Maple displays and labels the result of an executed statement on a new line. By default, if this result is the first label in the document, it will be shown as (1). For more information on labels, see the Equation Labels subsection of the Tools and Features section.
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Equation labels organize the flow of computations. Keep these tips in mind when working with labels.
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References can be made to any labeled result.
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Labels are automatically numbered in sequence; if any labeled result is removed, Maple automatically renumbers all equation labels and updates all equation label references.
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Evaluating at a point
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Follow the steps to evaluate  at  .
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Step
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Description
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Illustration
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Type  . For instructions on entering this expression, see the subsection entering an expression above.
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Right-click on the expression. In the context-sensitive menu that appears, select Evaluate at a Point.
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A dialog box appears; enter  .
The substitution is made.
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(4)
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Note that the result was calculated in symbolic form. If you prefer an approximation, right-click on the result and choose Approximate and the desired number of digits.
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You can also use the "evaluate at a point" template
from the Expression palette.
For example,
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Return to the top of the page
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...plot a function?
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Maple has extensive plotting functionality to help you visualize the behavior of mathematical functions. The examples below show how to construct a graph of the function  by using two different methods: by using Maple's Context Menu system and by using the interactive Plot Builder.
The generated plot can be manipulated; it can be scaled, zoomed, panned, and resized. For more details on plotting, refer to the comprehensive Maple Plotting Guide. For information about Maple commands used in plotting, see the help pages on plot, plot3d, and plottools.
Before you proceed, be sure to familiarize yourself with entering simple mathematical expressions (see the subsection above). Open a new worksheet in Document mode, and ensure that you are in Math mode.
A video demonstration of the first method (and of plotting in general) is available online.
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Using Maple's context menu system
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Follow the steps below to plot the function  .
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Step
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Description
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Illustration
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Type  .
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Right-click the equation, and from the Context Menu, select Plots → 2-D Plot of Right Side.
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Using the interactive Plot Builder
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Follow the steps below to plot the function  .
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Step
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Description
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Illustration
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Type the expression  . Do not type an equation, since the Plot Builder interprets equations as implicit plots.
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Right-click the expression, and from the Context Menu, select Plots → Plot Builder. The Plot Builder dialog opens. Note that if the Plot Builder is accessed from the main menu (Tools → Assistants → Plot Builder...), then the expression  must be entered manually.
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The plot type and plot ranges for independent variables can be set here. The Options button opens a window where the settings for this plot can be changed. For this example, the default settings suffice.
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Click Plot. The plot is displayed.
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Return to the top of the page
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...enter a complex number
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In Maple, the default representation of the imaginary unit  is I. Thus,  is a complex number in Maple. The example below demonstrates two ways to enter a complex number in Maple.
Maple provides a way to customize the way complex numbers are displayed. For instance, you may want to use i or j as the imaginary unit instead of I.
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Example: Multiply two complex numbers
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Maple uses I for the constant  . Multiply  by  and display the result inline.
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Step
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Description
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Illustration
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Type  . Put a space between 2 and  to signify multiplication. (Alternatively, use [*] for multiplication.)
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Enter a space (or *) and then type  .
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Press [Ctrl][=] to evaluate the expression in-line.
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Using the Palette
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You can also enter complex numbers using the Common Symbols palette. From the palette, the symbols  ,  , and  can all be used to enter a complex number.
Note that simply typing  will not produce the imaginary unit, but typing  will.
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When you type the letter i or j in Maple, it is understood as the name `i` or `j`. Only I is an initially known constant. This means:
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You can use i or j as variables. For instance, as the index in expressions such as  =  .
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Typing I results in the imaginary constant. Thus,  =  .
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Using a different symbol for the imaginary unit
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You can customize the setting that specifies which symbol represents the imaginary unit. This will enable you to simply type this symbol to get  . Furthermore, ordinarily in output the imaginary unit is displayed with a capital I, no matter which symbol was used for input. By changing this setting, you change the output display.
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Step
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Description
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To change the symbol used for the imaginary unit, (both for input and output), use the interface command. The calling sequence is interface(imaginaryunit=symbol);
Here, we set  to be the symbol for the imaginary unit.
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Thereafter, clicking on  ,  , or  in the Common Symbols palette, or typing the letter  will produce the imaginary unit, and its symbol as displayed in any output will be  .
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From the palette:
By typing:
In computations:
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Return to the top of the page
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Tools and Features
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This section details the point-and-click tools and core features available in Maple to help you accomplish tasks quickly and easily. These features include palettes, context sensitive menus, and assistants.
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Palettes
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Maple has over thirty palettes containing an extensive collection of symbols, templates, and other features. These palettes are located beside the Maple workspace.
A template is an editable expression containing placeholders that can be easily overwritten. Use the [Tab] key to move to and highlight the next placeholder in a template, and [Shift][Tab] to move back to the previous placeholder. The How do I... section contains many examples where a template from a palette is used.
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The Expression palette contains many common mathematical expressions—such as integrals, derivatives, exponents, subscripts,  th roots, elementary functions, operators, and piecewise functions—as easily editable templates. See the How do I... subsection on entering a simple expression for an example of its use.
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The Matrix palette is a tool used to insert a matrix template of a specified size, type, shape, and data type for entering a matrix quickly. See the How do I... subsection on entering a matrix for an example of its use.
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By default, not all palettes are shown; to show a hidden palette, navigate to View → Palettes → Show Palette, and select a palette. Alternatively, navigate to View → Palettes → Arrange Palettes... to show, hide, and rearrange palettes interactively. Note that as more palettes are enabled, you may want to display some palettes to the right of the Maple workspace.
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Context-Sensitive Menus
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One of the most useful features in Maple is the Context-Sensitive Menu, or Context Menu. Together with inline evaluation, the use of Context Menus is one of the fastest ways to perform a string of successive computations.
To access the Context Menu menu for a specific Maple object, right-click the object. The Menu will contain common operations associated with the object; for example, the Context Menu for a matrix will include the inverse operation, and for an expression, the Menu will contain the simplify operation.
Before you proceed with the example below, be sure to familiarize yourself with entering simple mathematical expressions (see the How do I... subsection on entering a simple expression). Open a new worksheet in Document mode, and ensure that you are in Math mode.
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Example: simplify and factor 
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Follow the steps below to simplify and factor the expression  .
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Step
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Description
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Illustration
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Right-click any part of the expression (within the dotted outline) and a Context Menu is displayed. Select Collect → Name → x.
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Right-click on the resulting expression and select Simplify>Simplify.
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Right-click on the resulting expression and select Factor.
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Note
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If you were working with an equation, some of these functionalities would not be available. Equations cannot be simplified or explicitly differentiated and must therefore first be converted into an expression. To do this, right-click the equation and select Right-hand side.
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Return to the top of the page
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Command Completion
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Command and symbol completion is a feature that automatically suggests a command to use as you enter a phrase in Maple. To access the command completion menu, press [Esc] after typing the phrase. A pop-up list displays commands that begin with the phrase typed. Maple lists symbols, commands, functions, and package names that match the entered text. To insert an item from this list, select it with the mouse or navigate to it by using the arrow keys and press Enter.
For example, to get the Greek letter  (rho), type rho and press [Esc]. Select 
This command completion list can include command completion templates. These provide the full syntax of common Maple commands including arguments, so that these commands can be easily entered. Simply choose the desired command completion template and replace the placeholders with the desired values.
For example, to get an integral, type int and press [Esc]. Select int(definite)
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Equation Labels
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Equation Labels are automatically generated after executing a Maple command on a new line. The result returned is labeled so that you can refer to it later in the document. As an example, compute the reduced row echelon form of a matrix using equation labels. Maple's equation labels are automatically re-numbered in sequential order if any labeled result is deleted or moved.
Before you proceed with the example below, be sure to familiarize yourself with entering simple mathematical expressions (see the How do I... subsection on entering a simple expression). Open a new worksheet in Document mode, and ensure that you are in Math mode.
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Computing the reduced row echelon form of a matrix
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Follow the steps below to find the reduced row echelon form of the three-by-four matrix  .
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Step
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Description
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Illustration
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Follow the instructions in either of the two examples given in the How do I subsection on entering matrices. Press [Enter], and the resulting Matrix is labeled.
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Type
![LinearAlgebra[ReducedRowEchelonForm]](/support/helpjp/helpview.aspx?si=3767/file02178/math3258.png)
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Now pass the Matrix as an argument to this procedure by typing a left parenthesis [(], followed by the equation label. To enter the equation label, either press [Ctrl][l] or select Insert → Label.... Type the label value into the dialogue box; in this case, since it is the first labeled result, the label value is  . Click OK. Now type a right parenthesis [)].
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Press [Enter]. The reduced row echelon form of this Matrix is displayed and labeled.
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Assistants
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Maple has many interactive assistants that provide graphical user interfaces to various Maple packages and functionalities. Here are some of the assistants available in Maple.
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Back-Solver
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Solve for an unknown parameter in an equation whose other parameters are known
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Curve Fitting
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Compute regressions and fit curves on a collection of data
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Data Analysis
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Display textual and graphical information about data sets, traverse data sets, and generate new data sets via standard operations on existing ones
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Equation Manipulator
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Perform a series of operations on an equation
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Import Data
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Import data from an external file into Maple as an rtable
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Installer Builder
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Build installers for your own toolboxes, or return a Build command which you can store and execute later
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Library Browser
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Manipulate the libraries in a specified directory
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ODE Analyzer
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Investigate and solve ordinary differential equations and ordinary differential equation systems
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Optimization
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Graphically minimize or maximize an objective function under given constraints
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Plot Builder
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Build a Maple plot interactively
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Scientific Constants
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Browse an extensive collection of physical constants and properties of chemical elements
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Special Functions
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View properties of over 200 special mathematical functions
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Units Calculator
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Convert between over 500 units of measurement
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Maple Help
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Maple's help system provides extensive help on topics and commands in Maple. Access the help system from the Help>Maple Help menu item. To find help on a particular topic, you can enter ?Topic in Math mode and then press [Enter].
This will open the help page on the Statistics package.
You can also put your cursor in a word and press [F2] to get help on that word.
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Plotting Guide
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The Plotting Guide provides a visual guide to Maple's plots and a summary of plotting features.
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Applications
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The sample application worksheets provide demonstrations of solutions to specific problems.
To see a list of applications, from the Help menu, choose Manuals, Resources, and more>Applications and Examples.
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Example Worksheets
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Maple provides a number of example worksheets to supplement the examples in the help pages. Example worksheets demonstrate the syntax of popular commands and packages, such as solve, Calculus, and Linear Algebra, as well as more sophisticated topics such as lexical scoping. You can execute all the commands in the example worksheets.
To view a list of example and application worksheets, see the examples index.
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Manuals
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Access the Maple User Manual and Maple Programming Guide within Maple.
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From the Help menu, select Manuals, Resources, and more.
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Select Manuals and then the desired manual.
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The manual opens with the Table of Contents displayed.
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Other Resources
Maple's Application Center offers over 1,500 Maple applications, Maplet applications, tutorials, Maple PowerTools, MapleSim models, and Maple packages for free download.
Maple Primes is a web community dedicated to sharing experiences, techniques, and opinions about Maple and related products, as well as general interest topics in math and computing.
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