Contents Previous Next Index
1 Getting Started
Don't worry about your difficulties in Mathematics. I can assure you mine are still greater.
Mathematics touches us every day—from the simple chore of calculating the total cost of our purchases to the complex calculations used to construct the bridges we travel.
To harness the power of mathematics, Maplesoft provides a tool in an accessible and complete form. That tool is Maple.
1.1 In This Chapter
Introduction to Maple - The main features of Maple's Standard Interface
Starting the Standard Document Interface
Entering commands and mathematical expressions
Copy and drag keys
Saving Maple documents
Entering Expressions - Methods of entering expressions in 1-D and 2-D Math
Math Mode and Text Mode
Point-and-Click Interaction - An introduction to the point-and-click features in Maple
Commands - An introduction to the commands of the Maple language
Using commands from the Maple library
The Maple Help System - Accessing help on commands, packages, point-and-click features, and more
How to access help for Maple features
Interacting with help pages
Viewing and interacting with examples
Available Resources - Both online and from within Maple
New user resources, including tutorials and the Maple Portal
Maple website resources
1.2 Introduction to Maple
Working in Maple
With Maple, you can create powerful interactive documents. The Maple environment lets you start solving problems right away by entering expressions in 2-D Math and solving these expressions using point-and-click interfaces. You can combine text and math in the same line, add tables to organize the content of your work, or insert images and sketch regions. You can visualize and animate problems in two and three dimensions, format text for academic papers or books, and insert hyperlinks to other Maple files, websites, or email addresses. You can embed and program graphical user interface components, as well as devise custom solutions using the Maple programming language.
Figure 1.1: The Maple Environment
Starting the Standard Document Interface
To start Maple on:
From the Start menu, select All Programs → Maple 2023 → Maple 2023.
Double-click the Maple 2023 desktop icon.
From the Finder, select Applications and Maple 2023.
Double-click Maple 2023.
Enter the full path, for example, /usr/local/maple/bin/xmaple
Add the Maple directory (for example, /usr/local/maple/bin) to your command search path.
When the first Maple session opens, a Start Page displays shortcuts to useful tasks and topics.
To start a Maple session:
In the Start Page, select New Document or New Worksheet. A blank document displays.
From the File menu, select New, and then either Document Mode or Worksheet Mode. A blank document displays.
You can opt to start Maple with a blank document instead of the start page. You can also replace the default start page with a custom start page. For instructions, refer to the startpage help page.
To invoke the Start Page at any time, click the home button (
) on the worksheet toolbar.
Document and Worksheet Modes
Maple offers two modes, Document Mode and Worksheet Mode. Using either mode, you can create high quality interactive mathematical documents. Each mode offers the same features and functionality; the only difference is the default input region of each mode.
Document mode uses Document Blocks as the default input region to hide Maple syntax. A Document Block region is indicated by two triangles located in the vertical Markers column along the left pane of the Maple Document,
. If the Markers column is not visible, open the View menu and select Markers. This allows you to focus on the problem instead of the commands used to solve the problem. For example, when using the context-sensitive operations from the Context Panel on Maple input in Document mode (invoked by moving your mouse cursor over your input expression, then selecting the appropriate operation from the displayed context panel), input and output are connected using an arrow or equal sign with self-documenting text indicating the calculation that had taken place. The command used to solve this expression is hidden.
To create a new document, select File → New → Document Mode.
Worksheet mode uses a Maple prompt as the default input region. The Maple input prompt is a red angle bracket,
. When using context-sensitive operations on input in Worksheet mode, all commands are displayed.
To create a new worksheet, select File → New → Worksheet Mode.
Full Flexibility in Either Mode
Regardless of which mode you begin working in, you have the opportunity to use both document blocks and command prompts.
For example, you can hide commands in Worksheet Mode by adding a document block from the Edit menu, Edit → Document Blocks → Create Document Block (see Document Blocks), or you can show commands in Document mode by adding a Maple prompt from the Insert menu, Insert → Execution Group → Before / After Cursor (see Input Prompt).
This chapter discusses features common to both modes. Specific aspects of Document mode are explained in Document Mode, and aspects of Worksheet mode are explained in Worksheet Mode.
The Maple Workbook
The Maple Workbook acts as a container that lets you collect Maple worksheets, library archives and language files, data (such as images or spreadsheets), and other items into a single file, stored in the .maple file format. This lets you better organize your Maple-based projects. For more information, refer to the Workbook Overview help page.
Navigation of Workbook files is accomplished through the workbook Navigator palette, available in the Workbook tab. For more information, refer to The Workbook Navigator help page.
Entering 2-D Math
In documents, the default format for entering mathematical expressions is 2-D Math. This results in mathematical expressions that are equivalent to the quality of math found in textbooks. Entering 2-D Math in Maple is done using common key strokes or palette items. For more information on palettes, see Palettes. An example of entering an expression using common key strokes is presented in the following section. An example of entering an expression using palette items is presented in Example 3 - Enter an Expression Using Palettes.
Entering mathematical expressions, such as 3599⁢+⁢19, x2⁢+⁢x, and x⋅y is natural in 2-D Math.
To enter a fraction starting with the numerator:
Enter the numerator.
Press the forward slash (/) key.
Enter the denominator.
To leave the denominator, press the right arrow key.
To enter a fraction starting with the denominator:
Press // (two forward slashes).
To leave the numerator, press the right arrow key.
To enter a power:
Enter the base.
Press the caret (^) key.
Enter the exponent, which displays in math as a superscript.
To leave the exponent, press the right arrow key.
To enter a product:
Enter the first factor.
Press the asterisk (*) key, which displays in 2-D Math as a dot, ⋅.
Enter the second factor.
In general, the best practice is to enter a multiplication symbol (*) for multiplication in any calculation. In some cases, you can instead insert a space character between two quantities to multiply them. This is called implicit multiplication. For example, in the expression −b+b2−4 a c2 a a space is used for the multiplication 4*a*c and 2*a.
In the case of a number followed by a variable, Maple interprets the expression as meaning multiplication even without the presence of * or a space character.
However, it's easier to identify and correct mistakes in your formulas if you use the multiplication symbol (*) regularly.
Important: Maple interprets a sequence of letters, for example, xy, as a single variable. To specify the product of two variables, you must insert a space character (or multiplication operator), for example, x⁢y or x⋅y. For more information, refer to the 2DMathDetails help page.
Shortcuts for Entering Mathematical Expressions
x2−7 x y+3 y2 x y
Shift + *
/ (forward slash)
// (two forward slashes)
Shift + ^
Ctrl + Shift + _ (Command + Shift + _ in Mac)
literal subscript (subscripted variable name)
__ (two underscores)
command / symbol completion3
Esc in Mac, Windows, and Linux
Ctrl + Space in Windows
Ctrl + Shift + Space in Linux
sqrt and then command completion
exp and then command completion
enter / exit 2-D Math
Math and Text icons in the toolbar
14 versus 1/4
1 required for products of numbers
2 use the right arrow key to leave a denominator, numerator, superscript, or subscript region
3 for more information, see Command Completion.
For a complete list of shortcut keys, refer to the 2-D Math Shortcut Keys and Hints help page. For information on the Maple Help System, see The Maple Help System.
Example 1 - Enter and Evaluate an Expression Using Keystrokes
Review the following example:
In this example, you will enter x2+y22 and evaluate the expression.
Result in Document
To enter the expression:
Press Shift + ^ . The cursor moves to the superscript position.
Press the right arrow key. The cursor moves right and out of the superscript position.
Enter the + symbol.
Press Shift + ^ to move to the superscript position.
Enter 2 and press the right arrow key.
With the mouse, select the expression that will be the numerator of the fraction.
Enter the / symbol. The cursor moves to the denominator, with the entire expression in the numerator.
Press the right arrow key to move right and out of the denominator position.
To evaluate the expression and display the result inline:
Press Ctrl + = (Command + = in Mac).
x2+y22 = x22+y22
To execute 2-D Math, you can use any of the following methods.
Pressing Ctrl + = (Command + = in Mac). That is, press and hold the Ctrl (or Command) key, and then press the equal sign (=) key. This evaluates and displays results inline.
Pressing the Enter key. This evaluates and displays results on the next line and centered.
Select the input and from the context panel, select Evaluate and Display Inline. See The Context Panel for more details.
Using the Evaluate menu items Evaluate and Evaluate and Display Inline.
The Maple toolbar offers easy access to a number of actions. See Table 1.2.
Equivalent Menu Option or Command
Create a new Maple document
From the File menu, select New and then Document Mode
Open an existing document or worksheet
From the File menu, select Open...
Save the active document or worksheet
From the File menu, select Save...
Print the active document or worksheet
From the File menu, select Print...
Print preview the active document or worksheet
From the File menu, select Print Preview...
Toggle the Print Layout Mode
From the File menu, select Print Layout Mode.
Cut the selection to the clipboard
From the Edit menu, select Cut
Copy the selection to the clipboard
From the Edit menu, select Copy
Paste the clipboard contents into the current document or worksheet
From the Edit menu, select Paste
Undo the last operation
From the Edit menu, select Undo
Redo the last operation
From the Edit menu, select Redo
Insert the Code Edit Region
From the Insert menu, select Code Edit Region
Inserts plain text after the current execution group.
From the Insert menu, select Text.
Inserts Maple Input after the current execution group. For details, refer to Execution Groups.
From the Insert menu, select Execution Group and then After Cursor
Encloses the selection in a document block. If nothing is selected, it creates a new document block.
From the Edit menu, select Document Blocks and then Create Document Block
Encloses the selection in a subsection. For details, refer to Sections.
From the Format menu, select Insert Section
Remove one level of indentation enclosing the selection.
From the Format menu, select Remove Section
Move backward to previous document in the hyperlink history
Open the start page
Move forward to next document in the hyperlink history.
Executes all commands in the worksheet or document
From the Execute menu, select Execute Worksheet.
Executes a selected area.
From the Evaluate menu, select Execute Selection.
Interrupt the current operation.
Debug the current operation
Clears Maple's internal memory. For details, refer to the restart help page.
Add and edit Maple code that is executed each time the worksheet is opened. For details, refer to the startupcode help page.
From the Edit menu, select Startup Code.
Adjusts the display size of document content. Note: Plots, images, and sketches remain unchanged.
From the View menu, select Zoom Factor and then a zoom size.
Reset zoom level.
From the View menu, select Zoom Factor → Default.
Opens the Maple help system in a new window. For details, refer to The Maple Help System.
From the Help menu, select Maple Help.
Search box provides quick access to the help system.
Access to the MapleCloud on the web.
The Context Bar shows icons that are relevant to the location of the cursor in the document. For example, place the cursor at an input region and the Text and Math tools are accessible. See Table 1.3 for a list of the tools available in each icon.
Context Bar Tools
2-D Plot tools
3-D Plot tools
Text and Math icons
Drawing and Plot icons
Drawing, Plot, and Animation icons
Drawing Canvas and Image regions
The Text and Math icons allow you to enter text and math in the same line by choosing the appropriate input style at each stage when entering the sentence, such as the following sentence:
The graph of y=x−22−1 is a parabola that opens up with vertex at 2,1.
For a step-by-step example of creating a sentence with text and math, see Example 6 - Enter Text and 2-D Math in the Same Line Using Toolbar Icons.
The meaning of the Text and Math icons differs while at a Maple input prompt. The Math icon displays input as 2-D Math, whereas the Text icon displays Maple input. For details, refer to Math Mode vs. Text Mode.
To access the tools available in the Plot and Drawing icons, click a plot region. These tools allow you to manipulate the plot or draw shapes and enter text on the plot region. By clicking an animation region, you have the same features available for a plot region, in addition to tools for playing the animation in the Animation icon. For details on plots and animations, refer to Plots and Animations.
For the description of any icon, hover the mouse over the icon to display at tooltip.
The Context Panel and Copy & Drag
Maple dynamically generates a collection of applicable options when you select or hover your mouse over an object, expression, or region. The options are organized and collectively displayed in the context panel to the right-hand side of the Maple user interface. The options available in the context panel depend on the selected input region. For example, you can manipulate and graph expressions, enhance plots, format text, manage palettes, structure tables, and more. When using menu items from the context panel to perform an action on an expression, the input and output are connected with a self-documenting arrow or equal sign indicating the action that had taken place. For more information, see The Context Panel.
Copy & Drag
With Maple, you can drag input, output, or curves in a plot region into a new input region. This is done by highlighting the input or selecting the curve and dragging it with your mouse into a new input region. Dragging the highlighted region will cut or delete the original input. To prevent this, use the copy and drag feature.
Ctrl + drag, Windows and Linux
Command + drag, Mac
That is, highlight the region you want to copy. Press and hold the Ctrl key while you drag the input to the new region using the mouse. The analogous operation on Mac uses the Command key.
Example 2 - Solve and Plot an Equation Using Context Panel Options and Copy & Drag
5 x−7=3 x+2
In this example, you will enter the equation and then solve and plot the equation using the context panel and the copy & drag feature. This example will only refer to the keystrokes needed on a Windows operating system to invoke the context panel and the copy & drag feature. For your operating system, refer to section Shortcut Keys by Platform for the equivalent keystrokes.
To solve the equation:
Enter the equation.
Click the equation and select Move to Left.
5 x−7=3 x+2→move to left2⁢x−9=0
A brief description, "move to left" is displayed above the arrow that connects the input and output.
Right-click the output from the previous action, 2 x−9=0, and select Solve → Isolate Expression for → x.
5 x−7=3 x+2→move to left2⁢x−9=0→isolate for xx=92
Now that we have solved the equation, we can plot it. To do this, we will copy the equation 2 x−9=0 to a new document block and use the context panel again.
From the Edit menu, select Document Blocks→ Create Document Block.
To copy the expression 5 x−7=3 x+2, highlight this expression from the previous line. Press and hold the Ctrl key and drag the expression to the new document block region.
To plot the expression:
From the context panel, select Plot both sides.
5 x−7=3 x+2→Plot both sides [5*x-7, 3*x+2]
Saving a Maple Document
To save these examples you created, from the File menu, select Save. Maple documents are saved as .mw files.
Saving a Maple Document as a Workbook
To save these examples you created as part of a new Maple workbook, from the Workbook tab, click Save As Workbook. For more information about saving Maple content refer to the worksheet,managing,saving help page.
1.3 Entering Expressions
An execution group is a grouping of Maple input with its corresponding Maple output. It is distinguished by a large square bracket, called a group boundary, at the left. An execution group may also contain any or all of the following: a plot, text, embedded components, and a drawing canvas.
Execution groups are the fundamental computation and documentation elements in the document. If you place the cursor in an input command and press the Enter or Return key, Maple executes all of the input commands in the current execution group.
Math Mode vs. Text Mode
The default mode of entry in Document or Worksheet mode is Math Mode, which displays input in 2-D Math. In Worksheet Mode or at a prompt, you can opt to use Maple Input (1-D Math). This is 1-D math input:
sum(a[k]*x^k, k=0..m)=product(b[j]*x^j, j=0..n);
In Document Mode, to enter input using Maple Input mode, insert a Maple prompt by clicking
in the toolbar, and then click the Text button in the context bar. In Worksheet Mode, simply click the Text button. See Figure 1.2.
Figure 1.2: Text and Math Buttons on the Toolbar
Maple's default setting. Executable standard math notation. This is also referred to as 2-D Math Input.
∫x2+2 x+6 ⅆx
Executable Maple notation. This is referred to as 1-D Math Input or Maple Input.
Access from the Insert → 2-D Math menu.
Access from the Insert → Maple Input menu.
When using 2-D Math, the Math mode icon is highlighted in the toolbar,
When entering Maple Input or text in a text region, the Text mode icon is highlighted in the toolbar,
In Document Mode (or a document block), input is entered in a document block with a slanted cursor,
In Document Mode (or a document block), text is entered with a vertical cursor, as plain text,
In Worksheet Mode, input is made at an input prompt with a slanted cursor,
In Worksheet Mode, input is made at an input prompt with a vertical cursor,
To convert a 2-D Math expression to 1-D Math, click the expression, then from the context panel select 2-D Math → Convert To → 1-D Math Input.
To convert a 1-D Math expression to 2-D Math, click the expression, then from the context panel select Convert To → 2-D Math Input.
Palettes make entering expressions in familiar notation easier than entering foreign syntax and reduces the possibility of introducing typing errors.
Using palettes while in 1-D Math teaches you the related Maple command syntax.
If you prefer 1-D Math input in Worksheet mode, you can change the default math input notation.
To change math input notation for a session or globally across all documents:
From the Tools menu, select Options. The Options Dialog opens.
Click the Display tab.
In the Input Display drop-down list, select Maple Notation.
Click the Apply to Session or Apply Globally button.
This changes the default input math notation at the prompt (
Important: The new input display becomes the default setting after pressing the Enter key.
Palettes are collections of related items that you can insert into a document by clicking or drag-and-dropping. The Maple environment provides access to over 30 palettes containing items such as symbols ∞, layouts Ab, mathematical operations ∫abfⅆx,and much more.
By default, palettes are displayed in the left pane of the Maple environment when you launch Maple. If the palettes are not displayed,
From the View menu, select Palettes.
Select Expand Dock.
Right-click (Control-click, Mac) the palette dock. From the context menu, select Show Palette. Alternatively, from the main menu, select View → Palettes → Show Palette.
A list of potential palettes is displayed, with currently displayed palettes dimmed.
Select a palette.
Alternatively, select View → Palettes → Show All Palettes.
You can create a Favorites palette of the expressions and entities you use often by right-clicking (Control-click, Mac) the palette template you want to add and selecting Add To Favorites Palette from the context menu.
Roman Extended Upper Case
Roman Extended Lower Case
Palettes for constructing expressions
Constants and Symbols
Punctuation - insert punctuation symbols, such as inserting the registered trademark and copyright symbols
into text regions
Miscellaneous - insert miscellaneous math and other symbols outside the above categories
Expression - construct expressions such as logarithms
Matrix - enter the number of rows and columns required, designate type, such as zero-filled, and designate shape, such as diagonal.
Layout - add math content that has specific layout, such as expressions with one or more superscripts and subscripts
Calculus - construct expressions such as integrals
Handwriting - an easy way to find a desired symbol.
Units - select a unit and insert into document, such as
Accents - insert decorated names, such as an x with an arrow over it to denote a vector
Trigonometric & Hyperbolic - a palette for constructing expressions containing trigonometric and hyperbolic functions
Student Random Variables - a palette for constructing random variables based on distributions in the Student Statistics package
Group Constructors - a palette for constructing groups based on the Group Theory package
Components - embed graphical interface components such as a button into your document or worksheet. Components can be programmed to perform an action when selected such as executing a command when a button is clicked.
Favorites - add templates that you use most often from other palettes.Variables - manage all of your assigned variables in your current Maple session.
Live Data Plots - templates for visual representation of your data.
eBook Metadata - markup tags for use when creating eBooks from Maple worksheets
Tasks - a palette where you can store tasks that you have created
Viewing and Arranging Palettes
By default, palettes display in palette dock in the left pane of the Maple window. To view and manage palettes and palette docks, see Table 1.7.
To view the palette dock:
From the View menu, select Palettes, and then Expand Dock. The dock is in the left pant of the window.
To add a palette:
Right-click the palette dock. Maple displays a context menu near the palette.
From the context menu, select Show Palette and then select the palette.
To expand or collapse a palette in the palette dock:
Click the triangle at the left of the palette title.
To move a palette in the palette dock:
Move the palette by clicking the title and dragging the palette to the new location.
To expand or collapse the pane containing the palette dock:
Select the appropriate triangle at the top right side of the palette region.
Example 3 - Enter an Expression Using Palettes
∑i=1107 i2−5 i = 2420
In this example, we will enter ∑i=0107 i2−5 i and evaluate the expression.
Place the cursor in a new document block. In the Expression palette, click the summation template
. Maple inserts the summation symbol with the range variable placeholder highlighted.
Enter i and then press Tab. The left endpoint placeholder is selected. Notice that the color of the range placeholder has changed to black. Each placeholder must have an assigned value before you execute the expression. The Tab key advances you through the placeholders of an inserted palette item.
Enter 1 and then press Tab. The right endpoint placeholder is selected.
Enter 10 and then press Tab. The expression placeholder is selected.
Enter 7 i2−5 i. For instructions on entering this type of expression, see Example 1 - Enter and Evaluate an Expression Using Keystrokes.
Press Ctrl + = (Command + = for Mac) to evaluate the summation.
∑i=1107 i2−5 i = 2420
You can add to the Favorites palette any expressions that you use most often.
To add an entry from another palette to the Favorites palette, simply drag the entry to the Favorites palette.
To add a custom expression, select the expression in the worksheet and select Add Selection to Favorites Palette from the Context Panel.
Each symbol has a name and some have aliases. By entering its name (or an alias) in Math mode, you can insert the symbol in your document. All common mathematical symbols, including all Greek characters, π, and the square root symbol (), are recognized by Maple.
Note: If you hover the mouse pointer over a palette item, a tooltip displays the symbol's name.
To insert a symbol, enter the first few characters of a symbol name using a keyword that is familiar to you and then press the completion shortcut key, Esc (see Shortcut Keys by Platform). Symbol completion works in the same way as command completion (see Command Completion).
If a unique symbol name matches the characters entered, Maple inserts the corresponding symbol.
If multiple symbol names match the characters entered, Maple displays the completion list, which lists all matches, including commands. To select an item, click its name or symbol.
Example 4 - Square Root
To find the square root of 603729:
In a new document block, enter sqrt.
Press the symbol completion shortcut key, Esc. Maple displays a popup list of exact matches.
In the completion list, select
. Maple inserts the symbol with the x placeholder selected.
Enter 603729 into the placeholder.
Press Ctrl + = (Command + =, Mac).
603729 = 777
Example 5 - Complex Numbers
In Maple, the default display for imaginary i is a capital I. When you simply type the letter i in Math mode, it is in italics. This letter is just a variable, and is not the same as the imaginary unit −1,denoted by I or ⅈ in Maple.
Because of this, i can be used as a variable, for instance sumi,i=1..4 = 10
Multiply two complex numbers, −0.123+0.745 ⅈ and 4.2−ⅈ:
We will compute the result two ways, using I and then using ⅈ. The first way is the quickest to enter.
In a new document block, enter −0.123+0.745 I⋅4.2−I
Use * to enter multiplication between the two complex numbers.
Press Ctrl + = (Command + =, Mac) to evaluate the product.
−0.123+0.745 I⋅4.2−I = 0.2284+3.2520⁢I
The next method, while not as quick to enter, displays the computation using lowercase i.
In a new document block, enter (−0.123+0.745 i.
Press the symbol completion shortcut key, Esc. Maple displays a popup list of partial and exact matches, including symbols and commands.
Select the imaginary unit,
Close the parentheses, enter * (for multiplication), and type the second expression in parentheses, using symbol completion for the second imaginary number.
−0.123+0.745 ⅈ⋅4.2−ⅈ = 0.2284+3.2520⁢I
For more information on entering complex numbers, refer to the HowDoI/EnterAComplexNumber help page.
In the introduction section, you learned about the toolbar icons and context toolbars available in Maple (see Toolbar Options). The toolbar can be used to format your document, alter plots and animations, draw in a canvas, write in both Math and Text modes in one line and much more. The last of these is demonstrated in the next example.
Example 6 - Enter Text and 2-D Math in the Same Line Using Toolbar Icons
Enter the following sentence:
Evaluate ∫153 x2+2 x+3x3 ⅆx and write in simplest terms.
To enter this sentence:
Select the Text icon and enter "Evaluate ".
Select the Nonexecutable Math icon.
From the Calculus palette, select the definite integration template,
. The expression is displayed with the first placeholder highlighted.
With the first placeholder highlighted, enter 1, then press Tab.
Enter 5 and press Tab to highlight the integrand region.
Enter (3x^2 and press the right arrow to leave the superscript position.
Enter + 2.
Press the Space bar for implicit multiplication. Enter sqrt and press Esc to show the command completion options. Maple displays a popup list of exact matches. Select the square root symbol, x.
Maple inserts the symbol with the x placeholder selected. (Alternatively, select the square root symbol from the Expression palette.)
Enter x, then press the right arrow to leave the square root region.
Enter + 3, and then press the Space bar.
Select the n-th root symbol from the Expression palette,
Enter 3, then press Tab.
Enter x, then press the right arrow to leave the root region.
Enter ), then press Tab.
Enter x for the integration variable.
Put the cursor after the expression and click the Text icon in the toolbar, then enter the rest of the sentence: " and write in simplest terms."
Note: When an expression is intended for display purposes only, as in this example, it can be displayed in nonexecutable math. This is indicated by the gray background. For more information on executable and nonexecutable math, refer to the 2DMathDetails help page.
1.4 Point-and-Click Interaction
Maple contains many built-in features that allow you to solve problems quickly without having to know any commands.
Maple offers a set of assistants in the form of graphical user interfaces to perform many tasks without the need to use any syntax.
Using the Tools → Assistants menu, you can access tools to help you accomplish various tasks. See Figure 1.3. In some cases, you can launch an assistant by entering an expression and selecting the assistant from the options in the Context Panel.
Figure 1.3: Accessing the Assistants from the Tools Menu
Descriptions of Assistants
The available assistants are described below. Some of the assistants are interfaces to package commands. For more information on package commands, see Package Commands.
CAD Link - an interface to explore the properties of models from supported CAD applications (available on Microsoft Windows only).
Code Generation - an interface to automatically transform Maple expressions and programs to other languages.
Data Set Search - an interface for searching built-in and online data sources.
eBook Publisher - an interface to the eBook Publisher tools.
Import Data - an interface to read data from an external file into Maple.
Installer Builder - an interface to the InstallerBuilder package in which you can create installers for your Maple toolboxes.
Library Browser - an interface to manipulate the libraries in a specified directory.
Maplet Builder - an interface to the Maplets package. The Maplets package contains commands for creating and displaying Maplet applications (point-and-click interfaces). Using the Maplet Builder, you can define the layout of a Maplet, drag-and-drop elements (visual and functional components of Maplets), set actions associated with elements, and directly run a Maplet application. The Maplet Builder is available in the Standard interface only.
Plot Builder - an interface for creating two and three-dimensional plots, animations, and interactive plots.
Scientific Constants - an interface to over 20 000 values of physical constants and properties of chemical elements. All of these constants come with the corresponding unit and, if applicable, with the uncertainty or error, that is, how precisely the value of this constant is known.
Special Functions - an interface to the properties of over 200 special functions, including the Hypergeometric, Bessel, Mathieu, Heun and Legendre families of functions.
Thermophysical Properties Calculator - Calculate state-dependent and independent thermophysical properties.
Units Converter - an interface to convert between 500 units of measurement.
Worksheet Migration - an interface to convert worksheets from Classic Maple (.mws files) to Standard Maple (.mw files).
Maple provides over 50 interactive tutors and assistants to aid in the learning of
These tutors are easily accessible in the Tools menu by selecting Tutors. See Figure 1.4.
Figure 1.4: Accessing Tutors from the Tools Menu
Some of the tutors can also be accessed through the Student package. The Differential Equations tutor, DE Plots, is accessible through the DEtools package. For a definition of the term package, see Package Commands.
The Student package is a collection of subpackages designed to assist with the teaching and learning of standard undergraduate mathematics. The subpackages contain many commands for displaying functions, computations, and theorems in various ways, and include support for stepping through important computations.
The interactive commands help you explore concepts and solve problems using a point-and-click interface. These commands launch tutors that provide a graphical interface to some of the visualization and computation commands described above. See Figure 1.5 for an example of one of the tutors.
Figure 1.5: Calculus - Single Variable → Differentiation Methods Tutor
The Practice Sheets Assistant, found under Tools → Tutors→ Basics, lets you construct a practice sheet of math problems. It's easy to interactively construct a randomized set of problems arithmetic, algebra, calculus, factorization and more. Students can then do the problems, check their solutions, and even generate another set of problems.
For more information on the tutors and related resources for mathematics education, see Teaching and Learning with Maple.
Maple provides Math Apps that offer interactive, entertaining ways to explore mathematical concepts, ranging from Precalculus to Physics to Economics. A guide to these demonstrations is accessible in the Tools menu by selecting Math Apps.
The Context Panel
The context panel is a dynamically generated list of tools and actions that are applicable for the region on which it is invoked. These tools and actions are further organized into menus. Use the context panel to perform calculations and manipulations on expressions without using Maple syntax. To display the context panel, select an object, expression, or region. Context panel options are available for many input regions, including:
expressions to perform calculations, manipulations, or plotting
plot regions to apply plot options and manipulate the plot
tables to modify the table properties
text regions to add annotations and format text
When performing calculations or manipulations on an expression, a self-documenting arrow or equal sign connects the input and output, indicating the action that took place. See Figures 1.8 and 1.9 for two examples of context-sensitive operations.
Figure 1.6: Click the expression to see applicable operations in the context panel
Figure 1.7: Click the plot to see plot options in the context panel
Task templates help you perform specific tasks in Maple, such as:
performing a mathematical computation such as solving an equation symbolically or numerically, or determining the Taylor approximation of a function of one variable
constructing a Maple object such as a function
creating a document such as an application
Each task contains a description along with a collection of content that you can insert directly into your document. Content consists of 2-D mathematics, commands, embedded components (for example, buttons), and plots. You specify the parameters of your problem and then execute the commands in the document. See Figure 1.8 for an example of a Task Template.
Figure 1.8: Browse Tasks Dialog
To preview Maple tasks,
From the Tools menu, select Tasks, and then Browse. The Browse Tasks dialog opens and displays the list of tasks.
The tasks are sorted by subject to help you quickly find the desired task. In the Browse Tasks dialog, you can view tasks without inserting them into your document.
Inserting a Task into the Document
To insert a task into your document,
Select the Insert into New Worksheet check box to insert the task into a new document.
Click one of the insert buttons.
Click the Insert Default Content button. Maple inserts the default content. The default content level is set using the Options dialog. For instructions, refer to the usingtasks help page.
Click the Insert Minimal Content button. Maple inserts only the commands and embedded components, for example, a button to launch the related assistant or tutor.
Click the Copy Task to Clipboard button. Place the cursor where you want to insert the task, and then paste the task. Maple inserts the default content. Use this method to quickly insert a task multiple times.
Note: You can view the history of previously inserted tasks. From the Tools menu, select Tasks. Previously selected task names are displayed below the Browse menu item.
Before inserting a task, Maple checks whether the task variables have assigned values in your document. If any task variable is assigned, the Task Variables dialog opens to allow you to modify the names. Maple uses the edited variable names for all variable instances in the inserted task.
By default, the Task Variables dialog is displayed only if there is a naming conflict. You can set it to display every time you insert a task.
To specify that the Task Variables dialog be displayed every time you insert a task:
From the Tools menu, select Options.
In the Show task variables on insert drop-down list, select Always.
Click Apply to Session or Apply Globally, as necessary.
Updating Parameters and Executing the Commands
In inserted Task Templates, parameters are marked as placeholders (in purple text) or specified using sliders or other embedded components.
Specify values for the parameters in placeholders or using graphical interface components. You can move to the next placeholder by pressing Tab.
Execute all commands in the task by:
Placing the cursor in the first task command, and then pressing Enter repeatedly to execute each command.
Selecting all the template commands, and then clicking the execute toolbar icon
If the template contains a button that computes the result, click it.
For more information on task templates, refer to the tasks help page.
The Exploration Assistant allows you to interactively make parameter changes to expressions and view the result. The assistant can be used with almost any Maple expression or command that has at least one variable or parameter.
To launch the Exploration Assistant:
Enter an expression or command.
Click the expression or command. From the context panel, select Explore.
The Explore parameter selection dialog appears, where you can select the parameters to explore and the range for each parameter.
If you enter integer ranges, only integer values are allowed for parameters. To allow floating-point values, enter floating-point ranges.
Select skip for any of the parameters to leave that parameter as a variable.
Click Explore to continue to the Exploration Assistant. The assistant creates a table in the document. You can use the slider or sliders to vary the parameters and see your changes as the expression output is updated.
Once you are finished interacting with the assistant, you can copy and paste the results into your document, or save the interactive document for later use.
Example 7 - Use the Exploration Assistant to Explore a Plot
In this example, we will explore how the plot of sina x−b cosxx changes as we vary the parameters a and b.
Enter the plot command shown.
plotsina x−b cosxx,x=1..10
Click the expression and select Explore from the context panel.
In the Explore parameter selection dialog, set the ranges a = 0..10.0 and b = -5..5.0.
Click Explore. The Exploration Assistant creates a table in the document. Move the sliders to see the plot as the parameters change.
Tip: Since decimal numbers were used for the ranges in step 3, the slider uses decimal numbers. If you use integers for the ranges, the slider uses integer numbers.
Even though Maple comes with many features to solve problems and manipulate results without entering any commands, you may find that you prefer greater control and flexibility by using the set of commands and programming language that Maple offers.
The Maple Library
Commands are contained in the Maple library, which is divided into two groups: the main library and packages.
The main library contains the most frequently used Maple commands.
Packages contain related commands for performing tasks from disciplines such as Student Calculus, Statistics, or Differential Geometry. For example, the Optimization package contains commands for numerically solving optimization problems.
For details on top-level and package commands, see Commands.
If you want to interact with Maple using commands, simply enter the command using 2-D math. Notice that commands and variable names display in italics. Maple commands are constructed in a format similar to command(arguments), based on the command you are using.
For example, to factor an expression, enter:
To differentiate an expression, enter:
To integrate an expression on the interval 0, 2 π, enter:
int2 x+cosx, x=0..2 π
To plot an expression, enter:
plotsinx x2, x=−10..10
For a list of the top commands in Maple, see Top Commands.
There are two ways to access commands within a package, using the long form of the package command or the short form.
Long Form of Accessing Package Commands:
The long form specifies both the package and command names using the syntax package[command](arguments).
Short Form of Accessing Package Commands:
The short form makes all of the commands in the package available using the with command, with(package). If you are using a number of commands in a package, loading the entire package is recommended. When you execute the with command, a list of all commands in the package displays. To suppress the display of all command names, end the with(package) command with a colon. Alternatively, you can load packages through the Tools menu, by selecting Load Package, and then the package name.
After loading a package, you can use the short-form names, that is, the command names, without the package name.
LSSolvex−2, x−6, x−9
For a list of the top packages in Maple, see Top Packages.
To help with syntax and reduce the amount of typing when entering Maple commands, you can use command completion. Command completion displays a list of all Maple packages, commands, and functions that match the entered text. If there are multiple ways to call a command, then the command completion list contains each one, with appropriate placeholders.
To use command completion:
Begin entering a command or package name.
Select Tools → Complete Command or use the shortcut key Esc (see Shortcut Keys by Platform). If there is a unique completion, it is inserted. Otherwise, a list of possible matches is displayed.
Select the correct completion from the list.
Some inserted commands have placeholders, denoted by purple text. The first placeholder is highlighted after you insert it into the document. Replace it with your parameter, then move to the next placeholder by pressing the Tab key.
Equation labels help to save time entering expressions by referencing Maple output. See Figure 1.9.
By default, equation labels are displayed. If equation labels are not displayed,
From the Tools menu, select Options, and click the Display tab. Ensure that the Show equation labels check box is selected.
From the Format menu, select Equation Labels. Ensure that both Execution Group and Worksheet are selected.
Figure 1.9: Equation Label
To apply equation labels:
Enter an expression and press Enter. Note that the equation label is displayed to the right of the answer in the document.
In a new execution group, enter another expression that will reference the output of the previous execution group.
From the Insert menu, select Label. Alternatively, press Ctrl+L (Command+L, for Mac) to open the Insert Label dialog. Enter the label number in the Insert Label dialog and click OK. The item is now a label. See Figure 1.10.
Figure 1.10: Inserting an Equation Label
Press Enter to obtain the result.
To change the format of equation labels:
Select Format → Equation Labels → Label Display. In the Format Labels dialog, select one of the numbering schemes. Numbering can be flat numbers for the entire worksheet, or by section, so that equations in section 1 are labeled (1.1), (1.2), and so on.
Optionally, enter an appropriate numbering prefix.
Figure 1.11: Controlling Equation Label Format
The Label Reference menu item allows you to switch between the label name and its reference content. Place the cursor on the referenced equation label and select Format → Equation Labels → Label Reference.
Figure 1.12: Label Reference
The label is associated with the last output within an execution group.
You cannot apply equation labels to the following:
Error, warning, and information messages
Tables, images, plots, or sketches
In Document mode, content is created as a series of document blocks. Document blocks allow you to hide the syntax used to perform calculations, which in turn lets you focus on the concept presented instead of the command used to manipulate or solve the problem. You can also create document blocks in Worksheet mode to perform the same function. Document blocks are typically collapsed to hide the Maple code, but these regions can also be expanded to reveal this code.
To create a document block:
From the Edit menu, select Document Blocks → Create Document Block. If text or math in one or more execution groups is selected, then a document block is created that contains those execution groups. If not, a new document block is created after the current execution group. For more information, see the next example.
Document block regions are identified using markers that are located in a vertical bar along the left pane of the document. See Figure 1.13. In addition to document block boundaries, these markers (icons) indicate the presence of hidden attributes in the document such as annotations, bookmarks, and numeric formatting.
To activate markers:
From the View menu, select Markers. See Figure 1.13.
Figure 1.13: Document Block Markers
To view code in a document block:
Place the cursor in a document block to be expanded.
From the Edit→Document Blocks menu, select Show Command.
Figure 1.14: Expanded Document Block
With the Document Block expanded, you can see the Maple command that was used to perform this calculation. In Figure 1.14, the solve command was used.
Also notice a red prompt (>) before the original expression and the solve command. Entering commands outside of a document block region is done at this input region. To insert an input region, click the
button in the toolbar menu.
In Figure 1.14, an equation label was used to refer to the expression. For more information, see Equation Labels.
To collapse a Document Block:
With your cursor inside the document block, from the Edit → Document Blocks menu, clear the check box for Show Command.
You can use this process of expanding document blocks to view and edit Maple commands within a document block.
Changing the Display:
You can specify which parts of the input and output are displayed when the document block is collapsed. For each execution group in the block, you can choose to display either the input or the output.
Place the cursor in the execution group.
From the Edit → Document Blocks menu, select Toggle Input/Output Display.
Also, you can choose to display output either inline or centered on a new line.
From the Edit → Document Blocks menu, select Inline Document Output.
1.6 The Maple Help System
The Maple program provides a custom help system consisting of almost 5000 reference pages. The help system is a convenient resource for determining the syntax of Maple commands and for learning about Maple features.
Accessing the Help System
There are several ways to access the Maple help system:
Enter a search term in the search box in the worksheet toolbar.
in the toolbar.
To get help on a specific word:
In a document, place the insertion point in a word for which you want to obtain help. From the Help menu, select Help on .... Alternatively, press F2 (Control + ?, for Mac) to access context-sensitive help.
In a document, execute the command ?topic, for example, enter ?LinearAlgebra and press Enter.
The Maple help system opens in a separate window with two panes. The left pane contains the Help Navigator where you initiate searches and browse the table of contents, and the right pane displays the final search result, such as a specific help page.
Figure 1.15: Sample Help Page
Every help page in Maple lists the command's calling sequence, parameters, and a description, with examples of the command at the end of the page. Some help pages also contain hyperlinks to related help pages and hyperlinks to dictionary definitions. Hyperlinks to dictionary definitions display in red to distinguish them from hyperlinks to help pages.
Using the Help Navigator
Use the search field in the Help Navigator to find information on Maple commands and features.
Search for a known help topic, a command name, or a keyword or phrase.
If you have any add-on products, you can restrict the search to Maple, MapleSim, or any combination of those products and their add-ons.
You can search all of the help system or specific Resources such as Help Pages, Tasks, Math Apps, and Manuals by selecting the Page Types drop-down menu.Search results are displayed as a list in the Search Results tab of the left pane. Click the Table of Contents tab to view a structured list of all topics in the help system.
Note that some tutorials open in a Maple window instead of in the Help window.
In the left pane, the type of resource is indicated by an icon. Table 1.10 describes the icons.
A folder icon in the Table of Contents tab indicates that a topic can be expanded into subtopics.
Question mark icon indicates a help page and displays the associated help page in the right pane when selected.
WS icon indicates an example worksheet or tutorial. These worksheets open in a new tab in the Maple document.
D icon indicates a definition and displays the associated dictionary definition in the right pane when selected.
T icon indicates a Task template and displays the associated Task Template in the right pane when selected.
Viewing Help Pages as Documents
In the help system, examples are not executable.
The Maple help system allows you to open help pages as documents that you can execute.
To open a help page as a worksheet:
With the help page displayed in the right pane of the help system, from the View menu, select Open Page as Worksheet. A new worksheet tab opens and displays the help page as an executable document.
Alternatively, in the help system toolbar, click the open current help page in a worksheet window icon.
Viewing Examples in 2-D Math
You can choose to view the examples in most help pages in either 2-D math or 1-D Math (Maple input) mode. The default is 2-D Math.
To change the math mode:
In the Maple help system:
From the View menu, select or clear the Display Examples with 2D math input check box.
Click the 2-D Math icon,
Note: Some input in help pages displays as 1-D Math, no matter which option you have chosen. This is for Maple procedures and other code that is best input in 1-D Math. For more information, refer to the helpnavigator help page.
Instead of opening the entire page as a document, you can copy the Examples section only.
To copy examples:
With the help page displayed in the right pane of the help system, from the Edit menu, select Copy Examples.
Close or minimize the Help Navigator and return to your document.
In your document, place the cursor at the location where you want to paste the examples.
From the Edit menu, select Paste. The Examples section of the help page is inserted as executable content in your document.
1.7 Available Resources
Your work with Maple is supported by numerous resources.
Resources Available through the Maple Help System
Use the help system to find information about a specific topic, command, package, or feature. For more information, see The Maple Help System.
More than 5000 mathematical and engineering terms with over 300 figures and plots.
From the Help menu, select Maple Help.
Enter a search term. Dictionary entries that match your query are displayed in the left pane with a
Tutorials and the Maple Portal
The Maple Portal includes material designed for all Maple users, from new users to users who want more advanced tutorials. The Maple Portal also includes specific sections for students and engineers. The Maple Portal includes:
How Do I... topics that give quick answers to essential questions.
Tutorials that provide an overview of topics from getting started to plotting, data manipulation, and interactive application development.
Navigation to portals with specialized information for students and engineers.
Access the portal in the Table of Contents under Getting Started.
Applications and Example Worksheets
Sample applications demonstrate how Maple can be used to find and document a solution to a specific problem. Some applications allow for input or contain animations that you can run; however, their primary use is for demonstrations. Topics include Bouncing Ball, Digital Filter Design, Frequency Domain System Identification, Harmonic Oscillator, Image Processing, Radiator Design with CAD Systems, and Sunspot Periodicity.
Example worksheets are executable documents covering topics that demonstrate syntax or invoke a user interface to make complex problems easy to solve and visualize. You can copy and modify the examples as needed. Topics include Algebra, Calculus, Connectivity, Discrete Mathematics, General Numerics and Symbolics, and Integral Transforms.
Explore the available topics in the Table of Contents under Applications and Example Worksheets.
You can access all of Maple's manuals from within Maple, including the Maple Programming Guide and this manual. You can execute examples, copy content into other documents, and search the contents using the Maple Help System.
Access the manuals in the Table of Contents under Manuals.
Maple's manuals are also available as PDFs on the Maplesoft website.
Set of commands with placeholders that you can use to quickly perform a task. For details, see Task Templates.
From the Tools menu, select Tasks, and then Browse.
Quick Reference Card
The Quick Reference Card is a table of commands and information for new users that opens in a new window. It contains hyperlinks to help pages for more information.
From the Help menu, select Quick Reference. Alternatively, press Ctrl + F2 (Command + F2, for Mac).
Student Help Center
The Student Help Center offers a Maple student forum, online math Oracles, training videos, and a math homework resource guide.
Teacher Resource Center
The Teacher Resource Center is designed to ensure you get the most out of your Maple teaching experience. It provides sample applications, course material, training videos, white papers, and tips.
Maple website resource for free applications related to mathematics, education, science, engineering, computer science, statistics and data analysis, finance, communications, and graphics. Many applications are available in translations (French, Spanish, and German).
Maplesoft offers a comprehensive set of complementary training materials. From complete training videos to recorded training seminars to downloadable documentation, you have many options to get familiar with Maplesoft products. In addition, custom training sessions can be created to meet your needs.
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.
All of Maple's help pages are available online.
A Maple website containing FAQs, downloads and service packs, links to discussion groups, and a form for requesting technical support.
For a complete list of resources, refer to the MapleResources help page.
Download Help Document