Maplesoft MAPLE 10 User Manual

Maple User Manual

Copyright © Maplesoft, a division of Waterloo Maple Inc. 2005.

Maple User Manual

Copyright

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trademarks of Waterloo Maple Inc.

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software on any medium except as specifically allowed in the agreement.

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Java and all Java based marks are trademarks or registered trademarks of Sun Microsystems, Inc. in the United

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All other trademarks are the property of their respective owners.
This document was produced using a special version of Maple and DocBook.
Printed in Canada
ISBN 1-894511-75-1

Contents

Preface .................................................................................................... xiii

1 Document Mode ...................................................................................... 1

1.1 Introduction ...................................................................................... 1

1.2 In This Chapter ................................................................................ 3

1.3 Simple Mathematical Expressions ................................................... 4

Rational Expressions (Fractions) ....................................................... 5

Powers ................................................................................................ 5

Products .............................................................................................. 5

Shortcuts for Entering Mathematical Expressions ............................. 6

Other Expressions .............................................................................. 7

1.4 Evaluating Expressions .................................................................... 8

1.5 Editing Expressions and Updating Output ...................................... 9

1.6 Entering Expressions ..................................................................... 10

Palettes ............................................................................................ 10

Symbol Names ................................................................................ 16

1.7 Performing Computations ............................................................. 19

Computing with Palettes ................................................................. 20

Context Menus ................................................................................ 20

Assistants and Tutors ....................................................................... 26

1.8 Document Mode Summary ............................................................ 30

1.9 Getting Help ................................................................................... 32

2 Worksheet Mode ................................................................................... 35

2.1 In This Chapter .............................................................................. 36

2.2 Input Prompt .................................................................................. 37

Suppressing Output .......................................................................... 38

1-D Math Input ................................................................................ 38

Input Separators ............................................................................... 39

2.3 Commands .................................................................................... 40

The Maple Library ........................................................................... 40

Top-Level Commands ...................................................................... 40

Package Commands ........................................................................ 42

2.4 Palettes .......................................................................................... 44

2.5 Context Menus .............................................................................. 46

2.6 Assistants and Tutors ..................................................................... 48

iii

iv • Contents

Launching an Assistant or Tutor ...................................................... 48

Example: Using the Interactive Plot Builder ................................... 49

2.7 Task Templates .............................................................................. 51

Viewing Task Templates .................................................................. 51

Inserting a Task Template ................................................................ 52

Performing the Task ......................................................................... 53

2.8 Text Regions ................................................................................... 54

2.9 Names ........................................................................................... 55

Assigning to Names ........................................................................ 55

Unassigning Names ........................................................................ 57

Valid Names .................................................................................... 58

2.10 Equation Labels .......................................................................... 59

Displaying Equation Labels ............................................................. 59

Referring to a Previous Result ......................................................... 59

Execution Groups with Multiple Outputs ........................................ 61

Label Numbering Schemes ............................................................. 61

Features of Equation Labels ............................................................ 62

3 Performing Computations .................................................................... 65

3.1 In This Chapter .............................................................................. 65

3.2 Symbolic and Numeric Computation ............................................ 66

Exact Computations ........................................................................ 67

Floating-Point Computations .......................................................... 68

Converting Exact Quantities to Floating-Point Values ................... 69

Sources of Error .............................................................................. 70

3.3 Integer Operations ......................................................................... 71

Non-Base 10 Numbers and Other Number Systems ........................ 74

3.4 Solving Equations .......................................................................... 78

Solving Equations and Inequations ................................................. 78

Other Specialized Solvers ................................................................ 88

3.5 Units, Scientific Constants, and Uncertainty ................................. 96

Units ................................................................................................ 97

Scientific Constants and Element Properties ................................ 105

Uncertainty Propagation ............................................................... 111

3.6 Restricting the Domain ................................................................ 115

Real Number Domain ................................................................... 115

Assumptions on Variables ............................................................. 117

Contents • v

4 Mathematical Computations .............................................................. 123

4.1 In This Chapter ............................................................................ 125

4.2 Algebra ........................................................................................ 126

Polynomial Algebra ...................................................................... 126

4.3 Linear Algebra ............................................................................ 135

Creating Matrices and Vectors ...................................................... 135

Accessing Entries in Matrices and Vectors ................................... 144

Linear Algebra Computations ....................................................... 145

Student LinearAlgebra Package .................................................... 152

4.4 Calculus ....................................................................................... 153

Limits ............................................................................................ 153

Differentiation ............................................................................... 155

Series ............................................................................................. 161

Integration ..................................................................................... 163

Differential Equations .................................................................... 166

Calculus Packages ......................................................................... 166

4.5 Optimization ............................................................................... 168

Point-and-Click Interface .............................................................. 169

Large Optimization Problems ....................................................... 171

MPS(X) File Support .................................................................... 173

Additional Information .................................................................. 173

4.6 Statistics ...................................................................................... 173

Probability Distributions and Random Variables .......................... 173

Statistical Computations ................................................................ 175

Plotting .......................................................................................... 177

Additional Information .................................................................. 179

4.7 Teaching and Learning with Maple ............................................ 180

Student Packages and Tutors ........................................................ 181

5 Plots and Animations .......................................................................... 189

5.1 In This Chapter ............................................................................ 189

5.2 Creating Plots .............................................................................. 190

Interactive Plot Builder ................................................................. 191

Context Menu ................................................................................ 204

Dragging to a Plot Region ............................................................. 207

The plot and plot3d Commands .................................................... 208

The plots Package ......................................................................... 211

vi • Contents

Multiple Plots in the Same Plot Region ......................................... 214

5.3 Customizing Plots ....................................................................... 216

Interactive Plot Builder Options ................................................... 216

Context Menu Options .................................................................. 217

The plot and plot3d Options ......................................................... 220

5.4 Analyzing Plots ........................................................................... 222

Point Probe, Rotate, Pan, and Scale Tools ..................................... 222

5.5 Creating Animations ................................................................... 223

Interactive Plot Builder ................................................................. 223

The plots[animate] Command ....................................................... 225

5.6 Playing Animations ..................................................................... 226

Animation Context Bar .................................................................. 226

5.7 Customizing Animations ............................................................. 228

Interactive Plot Builder Animation Options .................................. 228

Context Menu Options .................................................................. 228

The animate Command Options .................................................... 229

5.8 Exporting ..................................................................................... 230

5.9 Code for Color Plates .................................................................. 230

6 Creating Mathematical Documents ..................................................... 231

6.1 In This Chapter ............................................................................ 232

6.2 Document Formatting .................................................................. 233

Quick Character Formatting .......................................................... 233

Quick Paragraph Formatting .......................................................... 235

Copy and Paste ............................................................................... 236

Sections .......................................................................................... 237

Display Hidden Formatting Attributes ........................................... 238

Indentation and the Tab Key .......................................................... 238

Character and Paragraph Styles ..................................................... 239

Document Blocks ........................................................................... 247

Typesetting ..................................................................................... 252

Using Tables for Layout ................................................................. 252

Formatting Lists: Bullets, Numbers, and Indent ............................ 262

Bookmarks ..................................................................................... 264

Inserting Images ............................................................................. 265

Show or Hide Worksheet Content .................................................. 266

6.3 Embedded Components ............................................................... 268

Contents • vii

Adding Graphical Interface Components ...................................... 268

Editing Component Properties: General Process ........................... 269

Removing Graphical Interface Components .................................. 269

Example Component Properties .................................................... 270

Printing and Exporting a Document with Embedded Compon-

ents ................................................................................................. 271

6.4 Creating Graded Assignments ...................................................... 271

Creating a Question ........................................................................ 271

Viewing Questions in Maple .......................................................... 272

Saving Test Content ....................................................................... 272

6.5 Auto-Execute ................................................................................ 272

Setting the Auto-Execute Feature .................................................. 273

Removing the Auto-Execute Setting .............................................. 273

Repeating Auto-Execution ............................................................. 273

Security Levels ............................................................................... 273

6.6 Sketch Regions ............................................................................. 274

Insert a Sketch Pad ......................................................................... 274

Drawing .......................................................................................... 275

Canvas Style of Sketch Pad ............................................................ 275

Erase or Clear Content ................................................................... 276

Selection Tool ................................................................................ 277

6.7 Spell Checking ............................................................................. 277

How to Use the Spellcheck Utility ................................................. 278

Selecting a Suggestion ................................................................... 279

Spellcheck Usage and the Document ............................................. 279

User Dictionary .............................................................................. 279

6.8 Hyperlinks .................................................................................... 281

Inserting a Hyperlink in a Document ............................................. 281

6.9 Worksheet Compatibility ............................................................. 284

7 Maple Expressions .............................................................................. 285

7.1 In This Chapter ............................................................................ 285

7.2 Creating and Using Data Structures ............................................ 285

Expression Sequences ................................................................... 286

Sets ................................................................................................ 287

Lists ............................................................................................... 288

Arrays ............................................................................................ 289

viii • Contents

Tables ............................................................................................ 290

Matrices and Vectors ..................................................................... 291

Functional Operators ..................................................................... 292

Strings ........................................................................................... 297

7.3 Working with Maple Expressions ................................................ 298

Low-Level Operations ................................................................... 298

Manipulating Expressions ............................................................. 304

Evaluating Expressions ................................................................. 310

8 Basic Programming ............................................................................ 321

8.1 In This Chapter ............................................................................ 321

8.2 Flow Control ................................................................................ 322

Conditional Execution (if Statement) ........................................... 322

Repetition (for Statement) ............................................................. 325

8.3 Iterative Commands .................................................................... 333

Creating a Sequence ...................................................................... 333

Adding and Multiplying Expressions ........................................... 334

Selecting Expression Operands ..................................................... 335

Mapping a Command over a Set or List ....................................... 336

Mapping a Binary Command over Two Lists or Vectors ............... 336

Additional Information .................................................................. 337

8.4 Procedures ................................................................................... 338

Defining and Running Simple Procedures .................................... 338

Procedures with Inputs .................................................................. 339

Procedure Return Values ............................................................... 339

Displaying Procedure Definitions ................................................. 340

Displaying Maple Library Procedure Definitions ......................... 340

Modules ......................................................................................... 342

9 Maplets ................................................................................................ 343

9.1 In This Chapter ............................................................................ 343

9.2 Simple Maplet .............................................................................. 343

9.3 Using Maplets ............................................................................. 344

Maplet File .................................................................................... 344

Maple Document ............................................................................ 345

9.4 Authoring Maplets ...................................................................... 345

Maplet Builder .............................................................................. 346

Maplets Package ........................................................................... 355

Contents • ix

Saving ............................................................................................ 361

10 Input, Output, and Interacting with Other Products ......................... 363

10.1 In This Chapter .......................................................................... 363

10.2 Writing to Files ......................................................................... 363

Saving Data to a File ...................................................................... 363

Saving Expressions to a File .......................................................... 365

10.3 Reading from Files .................................................................... 366

Reading Data from a File ............................................................... 366

Reading Expressions from a File ................................................... 367

10.4 Exporting to Other Formats ...................................................... 369

Exporting Documents ................................................................... 369

MapleNet ........................................................................................ 372

Maple T.A. ..................................................................................... 373

10.5 Connectivity .............................................................................. 374

Translating Maple Code To Other Programming Languages ........ 374

Accessing External Products from Maple ...................................... 374

Accessing Maple from External Products ...................................... 375

Index ...................................................................................................... 379

x • Contents

List of Tables

Table 1.1: Shortcuts for Entering Mathematical Expressions .................... 6

Table 1.2: Entering a Definite Integral ..................................................... 13

Table 1.3: Symbol Completion Shortcut Keys ......................................... 17

Table 1.4: Summary of Document Mode Tools ....................................... 31

Table 1.5: Maple Help Resources ............................................................ 32

Table 3.1: Select Integer Commands ....................................................... 73

Table 3.2: Modular Arithmetic Operators ................................................ 76

Table 3.3: Overview of Solution Methods for Important Equation

Types ........................................................................................................ 78

Table 3.4: Sample Dimensions ................................................................ 98

Table 3.5: Scientific Constants ............................................................... 106

Table 4.1: Maple Resources for Mathematical Computation ................ 123

Table 4.2: Polynomial Arithmetic Operators ......................................... 127

Table 4.3: Polynomial Coefficient and Degree Commands ................... 132

Table 4.4: Select Other Polynomial Commands .................................... 134

Table 4.5: Additional Polynomial Help ................................................. 135

Table 4.6: Matrix and Vector Arithmetic Operators ............................... 146

Table 4.7: Select Matrix and Vector Operators ...................................... 148

Table 4.8: Select LinearAlgebra Package Commands ........................... 150

Table 4.9: Limits .................................................................................... 154

Table 4.10: Student and Instructor Resources ........................................ 180

Table 5.1: Windows of the Interactive Plot Builder ............................... 192

Table 5.2: Displaying a Plot of a Single Variable Expression ................ 193

Table 5.3: Displaying a Plot of Multiple Expressions of 1 Variable ..... 195

Table 5.4: Displaying a Plot of a Multi-variable Expression ................ 196

Table 5.5: Displaying a Conformal Plot ............................................... 198

Table 5.6: Displaying a Plot in Polar Coordinates ................................ 200

Table 5.7: Interactive Plotting ............................................................... 202

Table 5.8: The plot and plot3d Commands ............................................ 208

Table 5.9: Customizing Plots Using Interactive Plot Builder ................ 217

Table 5.10: Customizing 2-D Plots Using the Context Menu ................ 218

Table 5.11: Customizing 3-D Plots Using the Context Menu ................ 219

Table 5.12: Popular Plot Options ........................................................... 220

Table 5.13: Plot Analysis Options .......................................................... 222

xi

xii • List of Tables

Table 5.14: Creating Animations Using the Interactive Plot Builder ..... 223

Table 5.15: The animate Command ....................................................... 225

Table 5.16: Animation Options .............................................................. 226

Table 5.17: Customizing Animations Using the Context Menu ............ 229

Table 8.1: Default Clause Values ........................................................... 327

Table 8.2: Iterative Commands .............................................................. 333

Table 8.3: The seq Command ................................................................ 333

Table 8.4: The add and mul Commands ................................................ 334

Table 8.5: The select, remove, and selectremove Commands ............... 335

Table 8.6: The map Command ............................................................... 336

Table 8.7: The zip Command ................................................................. 337

T able 10.1: Summary of Content T ranslation When Exporting to Dif ferent

Formats .................................................................................................. 371

Preface

The Maple Software

The MapleTM software is a powerful system that you can use to solve comple x
mathematical problems. You can also create professional quality documents,
presentations, and custom interactive computational tools in the Maple en­vironment.

You can access the power of the Maple computational engine through a
variety of interfaces.

DescriptionInterface

Standard Worksheet

Classic Worksheet

Command-line version

MaplesoftTMGraphing Calculator
(Microsoft® Windows® only)

Full-featured graphical user interface offering features
that help you create electronic documents that show all
your assumptions, the calculations, and any margin of
error in your results; or hide the computations to allow
your reader to focus on the problem setup and final res­ults. The advanced formatting features help you create
the customized document you need. Because the docu­ments are live, you can edit the parameters and, with the
click of a button, compute the new results.

The User Manual was created using the Standard
W orksheet interf ace to Maple. An interacti v e version of
this manual is available in the Standard W orksheet inter­face. From the Help menu, select Manuals, Dictionary,
and more>Manuals>User Manual.

Basic worksheet environment for older computers with
limited memory.

Command-line interface, without graphical user inter­faces features, for solving very large complex problems
or batch processing with scripts.

Graphical calculator interface to the Maple computational
engine. Using it, you can perform simple computations
and create customizable, zoomable graphs.

xiii

xiv • Preface

DescriptionInterface

MapletTMApplications

Graphical user interface containing windows, textbox
regions, and other visual interfaces, which gives you
point-and-click access to the power of Maple. You can
perform calculations and plot functions without using
the worksheet or command-line interfaces.

This manual describes how to use the Standard Worksheet interface. Some
features are not available in the Classic Worksheet interface and Command­line version. The Standard Worksheet interface has two modes: Document
mode and Worksheet mode.

Document Mode - Using the Document mode, you can perform quick cal­culations. You can enter a mathematical expression, and then evaluate, ma­nipulate, solve, or plot with a few keystrokes or mouse clicks.

Worksheet Mode - The Worksheet mode is designed for:

• Interactive use through Maple commands, which may offer advanced
functionality or customized control not available using context menus
or other syntax-free methods

• Programmatic use of the powerful Maple language

Using either mode, you can create high quality interactive mathematical
presentations or documents.

In This Manual

This manual provides an overview of all Maple features including:

• Performing computations

• Creating plots and animations

• Creating interactive documents

• The Maple programming language

• Using and creating custom Maplet applications

Preface • xv

• File input and output, and using Maple with third party products

• Data structures
For a complete list of manuals, study guides, toolboxes, and other resources,

visit the Maplesoft Web site at http://www.maplesoft.com.

Audience

The information in this manual is intended for Maple users who have read
the Maple Getting Started Guide.

Conventions

This manual uses the following typographical conventions.

• bold font - Maple command, package name, option name, dialog, menu,

and text field

• italics - new or important concept

• Note - additional information relevant to the section

• Important - information that must be read and followed

Customer Feedback

Maplesoft welcomes your feedback. For suggestions and comments related
to this and other manuals, contact [e-mail]

xvi • Preface

1 Document Mode

Using the Maple software, you can create powerful interactive documents.
You can visualize and animate problems in two and three dimensions. You
can solve complex problems with simple point-and-click interfaces or easy­to-modify interactive documents. Y ou can also de vise custom solutions using
the Maple programming language. While you work, you can document your
process, providing text descriptions.

1.1 Introduction

Maple has two modes: Document mode and Worksheet mode.
Using Document mode, you can quickly perform calculations. You can enter

a mathematical expression, and then evaluate, manipulate, solve, or plot it
with a few keystrokes or mouse clicks. This chapter provides an overview
of Document mode.

Document mode sample:

Find the value of the derivative of at .

Integrate over the interval .

=

Worksheet mode is designed for interactive use through commands and
programming using the Maple language. The Worksheet mode supports the
features available in Document mode described in this chapter . After revie w-

1

2 • 1 Document Mode

ing the information in this chapter, see Chapter 2, Worksheet Mode (page 35),
for information on using Worksheet mode.

Worksheet mode sample:

Find the value of the derivative of at .

>

(1.1)

>

(1.2)

>

Integrate over the interval .

>

Important: In every Maple document, you can use Document mode and

Worksheet mode.
Using either mode:

1.2 In This Chapter • 3

• You have access to the full mathematical engine.

• You can create high quality interactive documents: easy-to-use compu­tational tools, presentations, or publications.

Interactive document features include:

• Embedded graphical interface components, like buttons, sliders, and
check boxes

• Automatic execution of marked regions when a file is opened

• Tables

• Character and paragraph formatting styles

• Hyperlinks

These features are described in Chapter 6, Creating Mathematical Docu-
ments (page 231).

Note: This chapter was created using Document mode. All other chapters
were created using Worksheet mode.

1.2 In This Chapter

TopicsSection

Simple Mathematical Expressions - Introduc­tion to Math and Text modes, and how to
easily enter simple expressions

• Text and Math Modes

• Rational Expressions

• Powers

• Products

• Shortcuts for Entering Mathematical Ex-

• Other Expressions

pressions

4 • 1 Document Mode

TopicsSection

Evaluating Expressions - How to evaluate
expressions

Editing Expressions and Regenerating Output

- How to update expressions and results

Entering Expressions - Overview of tools for
creating complex mathematical expressions

Performing Computations - Overview of
tools for computing and plotting

key Document mode features

in the Maple Help System

• Displaying the Value Inline

• Displaying the Value on the Following
Line

• Updating a Single Computation

• Updating a Group of Computations

• Updating All Computations in a Docu­ment

• Palettes

• Symbol Names

• Computing with Palettes

• Context Menus

• Assistants and Tutors

• Table of Document Mode ToolsDocument Mode Summary - Summary of

• Table of Maple Help ResourcesGetting Help - A list of resources available

1.3 Simple Mathematical Expres­sions

In Document mode, you can enter two types of content: Text and Math. The
Text mode and Math mode icons at the left end of the toolbar indicate the
current mode. The toolbar is located near the top of the Maple window, im­mediately below the menu bar.

To switch between Text and Math modes, press the F5 key. (Alternatively,
click the Text mode or Math mode toolbar icon.) Consequently, it is easy
to enter sentences containing text and inline mathematical expressions.

1.3 Simple Mathematical Expressions • 5

Entering mathematical expressions, such as , , and , is
natural in Math mode.

Rational Expressions (Fractions)

To enter a fraction:

1. Enter the numerator.

2. Press the forward slash (/) key.

3. Enter the denominator.

4. To exit the denominator, press the right arrow key.

Powers

To enter a power:

1. Enter the base.

2. Press the caret (^) key (Shift + 6).

3. Enter the exponent, which displays in math as a superscript.

4. To exit the exponent, press the right arrow key.

Products

To enter a product:

1. Enter the first factor.

2. Press the asterisk (*) key, which displays in math as .

3. Enter the second factor.

6 • 1 Document Mode

Implied Multiplication

In most cases, you do not need to include the multiplication operator, .
Insert a space character between two quantities to multiply them.

Note: In some cases, you do not need to enter the multiplication operator or
a space character. For example, Maple interprets a number followed by a
variable as multiplication.

Shortcuts for Entering Mathematical Expressions

T able 1.1 lists shortcut keys for entering and na vigating mathematical expres­sions.

Table 1.1: Shortcuts for Entering Mathematical Expressions

Math and Text
modes

Overscript

Square root

KeySymbol/Format

F5Switch between

/ (forward slash)Fraction

^ (caret)Exponent

_ (underscore)Subscript

• Ctrl + Shift + ", Windows and

UNIX®

• Command + Shift + ", Macin-

tosh®

Enter sqrt , and then press the com­mand/symbol completion shortcut. (See
the following row in this table.)

Automatically Generated in
Document

Example using fraction:

(Math) versus 1/4 (Text)

1.3 Simple Mathematical Expressions • 7

Automatically Generated in
Document

Command/symbol
completion

pression

KeySymbol/Format

• Ctrl + Space, Windows

• Command + Shift + Space,

Macintosh

• Ctrl + Shift + Space, UNIX

Arrow keysNavigating an ex-

For a complete list of shortcut keys, refer to the Math Shortcut and Hints
help page. To access this help page in the Maple software, in Math mode
enter ?MathShortcuts and then press Enter. For information on the Maple
Help System, see Getting Help (page 32).

Other Expressions

It is also easy to enter mathematical expressions, such as:

• Piecewise-continuous functions:

• Limits:

• Continued fractions:

and more complex expressions. For information, see Entering Expres-
sions (page 10).

8 • 1 Document Mode

1.4 Evaluating Expressions

To evaluate a mathematical expression, place the cursor in the expression
and press Ctrl + = (Command + =, for Macintosh). That is, pr ess and hold
the Ctrl (or Command) key, and then press the equal sign (=) key.

T o the right of the expression, Maple inserts an equal sign and then the v alue
of the expression.

=

You can replace the inserted equal sign with text or mathematical content.

To replace the equal sign:

1. Select the equal sign. Press Delete.

2. Enter the replacement text or mathematical content.
For example, you can replace the equal sign with the text "is equal to".

is equal to

In mathematical content, pressing Enterevaluates the e xpression and displays
it centered on the following line. The cursor moves to a new line below the
output.

By default, Maple labels output that is generated by pressing Enter. For in­formation on equation labels, see Equation Labels (page 59). In this manual,
labels are generally not displayed.

1.5 Editing Expressions and Updating Output • 9

In text, pressing Enter inserts a line break.

You can use the basic algebraic operators, such as and , with most
expressions, including polynomials—see P olynomial Algebr a (page 126)—and

matrices and vectors—see Linear Algebra (page 135).

=

=

1.5 Editing Expressions and Updat­ing Output

One important feature of Maple is that your documents are live. That is, you
can edit expressions and quickly recalculate results.

To update one computation:

1. Edit the expression.

2. Press Ctrl + = (Command + =, for Macintosh) or Enter.
The result is updated.

To update a group of computations:

1. Edit the expressions.

2. Select all edited expressions and the results to recalculate.

3. Click the Execute toolbar icon .
All selected results are updated.

To update all output in a Maple document:

10 • 1 Document Mode

• Click the Execute All toolbar icon .
All results in the document are updated.

1.6 Entering Expressions

Mathematical expressions can contain the following symbols.

• Numbers: integers, rational numbers, complex numbers, floating-point

values, finite field elements, , ∞, ...

• Operators: , , , /, , , , , ...

• Constants: π, e, ...

• Mathematical functions: sin(x), , Γ(2), ...

• Names (variables): x, y, z, α, β, ...

• Data structures: sets, lists, Arrays, Vectors, Matrices, ...
Maple contains over a thousand symbols. For some numbers, operators, and

names, you can press the corresponding key , for e xample, 9, =, >, or x. Most
symbols are not available on the keyboard, but you can insert them easily
using two methods.

To insert a symbol, you can use:

• Palettes

• Symbol names

Palettes

Palettes are collections of related items that you can insert by clicking or
dragging. Palettes contain:

• Numbers and constants, like i (the imaginary unit), π, and ∞. For example,

see the Common Symbols palette (Figure 1.1).

1.6 Entering Expressions • 11

• Layouts, like an item with a superscript and subscript. For example, see

the Layout palette (Figure 1.2).

• Mathematical operations, like a definite integral with placeholders for
the integrand, variable of integration, and endpoints of the interval of
integration. For example, see the Expression palette (Figure 1.3).

• Specialized tools. For example, see the Matrix palette (Figure 1.4). For
information on the Matrix palette, see Creating Matrices (page 135).

Figure 1.2: Layout PaletteFigure 1.1: Common Symbols Palette

12 • 1 Document Mode

Figure 1.4: Matrix PaletteFigure 1.3: Expression Palette

Using Palettes

To insert a palette item:

1. In the palette, click the item to insert. The item is inserted at the cursor
location.

2. If the item has colored placeholders, specify values for them.

• To move to the next placeholder, press the Tab key.

Note: You can drag palette items to any location in the document.
For example, to insert the constant π:

• In the Common Symbols palette, click the π symbol.
or

• From the Common Symbols palette, drag the π symbol to the appropriate

location in the document.

Table 1.2 shows how to enter a definite integral.

Table 1.2: Entering a Definite Integral

1. In the Expression palette, click the definite

integration item . Maple inserts the
definite integral. The left endpoint placeholder
is selected.

2. Enter 0, and then press Tab. The right end-
point placeholder is selected.

3. Enter 1, and then press Tab. The integrand
placeholder is selected.

1.6 Entering Expressions • 13

Result in DocumentAction

4. Enter , and then press Tab. The vari-
able of integration placeholder is selected.

5. Enter x.

To evaluate the integral, press Ctrl+= (Command+=, for Macintosh) or
Enter. For more information, see Computing with Palettes (page 20).