Maple User Manual
Contents
Preface
Maple Software
Shortcut Keys by Platform
Command Completion
In This Manual
Audience
Conventions
Customer Feedback
1 Getting Started
1.1 In This Chapter
1.2 Introduction to Maple
Working in Maple
Starting the Standard Document Interface
Document and Worksheet Modes
The Maple Workbook
Entering 2-D Math
Common Operations
Shortcuts for Entering Mathematical Expressions
Example 1 - Enter and Evaluate an Expression Using Keystrokes
Toolbar Options
The Context Panel and Copy & Drag
Context Panel
Copy & Drag
Example 2 - Solve and Plot an Equation Using Context Panel Options and Copy & Drag
Saving a Maple Document
Saving a Maple Document as a Workbook
1.3 Entering Expressions
Execution Groups
Math Mode vs. Text Mode
Palettes
Viewing and Arranging Palettes
Example 3 - Enter an Expression Using Palettes
Favorites Palette
Symbol Names
Example 4 - Square Root
Example 5 - Complex Numbers
Toolbar Icons
Example 6 - Enter Text and 2-D Math in the Same Line Using Toolbar Icons
1.4 Point-and-Click Interaction
Assistants
Descriptions of Assistants
Tutors
Math Apps
The Context Panel
Task Templates
Previewing Tasks
Inserting a Task into the Document
Updating Parameters and Executing the Commands
Exploration Assistant
Example 7 - Use the Exploration Assistant to Explore a Plot
1.5 Commands
The Maple Library
Entering Commands
Package Commands
Equation Labels
Document Blocks
1.6 The Maple Help System
Accessing the Help System
Using the Help Navigator
Viewing Help Pages as Documents
Viewing Examples in 2-D Math
Copying Examples
1.7 Available Resources
Resources Available through the Maple Help System
Help Pages
Dictionary
Tutorials and the Maple Portal
Applications and Example Worksheets
Manuals
Quick Reference Card
Website Resources
Student Help Center
Teacher Resource Center
Application Center
Training
MaplePrimes
Online Help
Technical Support
2 Document Mode
2.1 In This Chapter
2.2 Introduction
2.3 Entering Expressions
Example 1 - Enter a Partial Derivative
Example 2 - Define a Mathematical Function
2.4 Evaluating Expressions
2.5 Editing Expressions and Updating Output
2.6 Performing Computations
Computing with Palettes
Computing with the Context Panel
Approximating the Value of an Expression
Solving an Equation
Using Units
Assistants and Tutors
Example 3 - Using the Context Panel to Open the Linear System Solving Tutor
3 Worksheet Mode
3.1 In This Chapter
3.2 Input Prompt
Suppressing Output
1-D Math Input
Input Separators
3.3 Commands
Top-Level Commands
Mathematical Functions
Top Commands
Top Packages
3.4 Palettes
3.5 The Context Panel
Example - Using the Context Panel
3.6 Assistants and Tutors
Launching an Assistant or Tutor
3.7 Task Templates
3.8 Text Regions
3.9 Names
Assigning to Names
Protected Names
Unassigning Names
Valid Names
3.10 Equation Labels
Displaying Equation Labels
Inserting Equation Labels
Execution Groups with Multiple Outputs
Label Numbering Schemes
Features of Equation Labels
4 Basic Computations
4.1 In This Chapter
4.2 Symbolic and Numeric Computation
Exact Computations
Floating-Point Computations
Converting Exact Quantities to Floating-Point Values
Sources of Error
4.3 Integer Operations
Non-Base 10 Numbers and Other Number Systems
Non-Base 10 Numbers
Finite Rings and Fields
Gaussian Integers
4.4 Solving Equations
Solving Equations and Inequations
Symbolically Solving Equations and Inequations
Numerically Solving Equations
Working with Solutions
Other Specialized Solvers
Ordinary Differential Equations (ODEs)
Partial Differential Equations (PDEs)
Integer Equations
Integer Equations in a Finite Field
Solving Linear Systems
Solving Recurrence Relations
4.5 Units, Scientific Constants, and Uncertainty
Units
Overview of Units
Unit Conversions
Applying Units to an Expression
Performing Computations with Units
Changing the Current System of Units
Extensibility
Scientific Constants and Element Properties
Overview of Scientific Constants and Element Properties
Scientific Constants
Element Properties
Value, Units, and Uncertainty
Performing Computations
Modification and Extensibility
Uncertainty Propagation
Quantities with Uncertainty
Performing Computations with Quantities with Uncertainty
Additional Information
4.6 Restricting the Domain
Real Number Domain
Assumptions on Variables
The assume Command
The assuming Command
5 Mathematical Problem Solving
5.1 In This Chapter
5.2 Algebra
Polynomial Algebra
Arithmetic
Sorting Terms
Collecting Terms
Coefficients and Degrees
Factorization
Other Commands
5.3 Linear Algebra
Creating Matrices and Vectors
Creating Matrices
Creating Vectors
Viewing Large Matrices and Vectors
Creating Matrices and Vectors with Specific Properties
Accessing Entries in Matrices and Vectors
Matrices
Vectors
Linear Algebra Computations
Matrix Arithmetic
Point-and-Click Interaction
LinearAlgebra Package Commands
Numeric Computations
Student LinearAlgebra Package
5.4 Calculus
Limits
The limit Command
Numerically Computing a Limit
Differentiation
The diff Command
Differentiating an Operator
Directional Derivative
Series
Integration
The int Command
Numeric Integration
Calculus Packages
VectorCalculus Package
Student Calculus Packages
Differential Equations
Student ODEs Package
5.5 Optimization
Point-and-Click Interface
Large Optimization Problems
MPS(X) File Support
Optimization Package Commands
5.6 Statistics
Probability Distributions and Random Variables
Adding Custom Distributions
Statistical Computations
Example 1 - Interquartile Range
Example 2 - Hazard Rate
Plotting
Student Statistics Package
5.7 Teaching and Learning with Maple
Student Packages and Tutors
Calculus Problem Solving Examples
Problem
Check for Existing Tools: Tutor
Check for Existing Tools: Task Template
Check for Instructions: Help Page and Example Worksheet
Check for Other Ready-To-Use Resources: Application Center
5.8 Clickable MathTM
Smart Popups
Drag-to-Solve
Examples
Example 1 - Graph a Function and its Derivatives
Example 2 - Solve for x in a Quadratic Equation
Example 3 - Solve a Quadratic Trig Equation
Example 4 - Find the Inverse Function
Example 5 - Methods of Integration - Trig Substitution
Example 6 - Initial Value Problem
6 Plots and Animations
6.1 In This Chapter
6.2 Creating Plots
Interactive Plot Builder
Launching the PlotBuilder
Example 1 - Display a plot of a single variable expression
Example 2 - Display a plot of multiple expressions in 1 variable
Example 3 - Display a plot of a multivariate expression
Example 4 - Display a conformal plot
Example 5 - Display a plot in polar coordinates
Example 6 - Interactive plotting
The plot and plot3d Commands
Maple commands from Creating Plots: Interactive Plot Builder
Display a Parametric Plot
Display a 3-D Plot
The plots Package
The pointplot Command
The matrixplot Command
The contourplot Command
Multiple Plots in the Same Plot Region
Dragging to a Plot Region
List of Expressions
The display Command
6.3 Customizing Plots
Interactive Plot Builder Options
Context Panel Options
2-D Plot Options
3-D Plot Options
The plot and plot3d Options
6.4 Analyzing Plots
Point Probe, Rotate, Pan, and Zoom Tools
6.5 Representing Data
6.6 Creating Animations
The plots[animate] Command
Maple Syntax for Creating Animations: Interactive Plot Builder Example
Animate a 2-D plot
The plot3d(...,viewpoint) Option
6.7 Playing Animations
Animation Context Bar
6.8 Customizing Animations
Interactive Plot Builder Animation Options
The animate Command Options
6.9 Exporting
7 Creating Mathematical Documents
7.1 In This Chapter
7.2 Document Formatting
Copy and Paste
Quick Character Formatting
Attributes Submenu: Setting Fonts, Character Size, and Attributes
Quick Paragraph Formatting
Attributes Submenu: Spacing, Indent, Alignment, Bullets, Line Break, and Page Break
Character and Paragraph Styles
Applying Character Styles
Creating and Modifying Character Styles
Applying Paragraph Styles
Creating and Modifying Paragraph Styles
Style Set Management: Saving Styles for Future Use
Sections
Using the Insert Menu to Add Sections
Tips for Adding Sections and Subsections
Using the Indent and Outdent Toolbar Icons
Headers and Footers
Show or Hide Worksheet Content
Using the Show Contents Dialog
Command Output Versus Inserted Content
Indentation and the Tab Key
7.3 Commands in Documents
Working with Document Blocks
Inline Document Output
View Document Code
Typesetting
Auto-Execute
Setting the Auto-Execute Feature
Removing the Auto-Execute Setting
Repeating Auto-Execution
Security Levels
7.4 Tables
Creating a Table
Cell Contents
Navigating Table Cells
Modifying the Structural Layout of a Table
Modifying the Physical Dimensions of a Table
Modifying the Appearance of a Table
Table Borders
Alignment Options
Cell Color
Controlling the Visibility of Cell Content
Printing Options
Execution Order Dependency
Editable Tables
Additional Examples
Table of Values
Formatting Table Headers
2-D Math and Plots
7.5 Drawing Canvas
Insert a Drawing Canvas
Drawing
Drawing Canvas Style
Inserting Images
ImageTools Package
7.6 Hyperlinks
Inserting a Hyperlink in a Document
Linking to a Webpage
Linking to an Email Address
Linking to a Worksheet
Linking to a Help Page
Linking to a Task
Linking to a Dictionary Topic
Linking to a Maplet Application
Linking to a Workbook Attachment
Linking to a Workbook File
Example
Bookmarks
Inserting, Renaming, and Deleting a Bookmark
Go to a Bookmark
7.7 Embedded Components
Adding Graphical Interface Components
Task Template with Embedded Components
7.8 Spell Checking
How to Use the Spellcheck Utility
Selecting a Suggestion
User Dictionary
Adding a Word to Your Dictionary
8 Maple Expressions
8.1 In This Chapter
8.2 Creating and Using Data Structures
Expression Sequences
Accessing Elements
Sets
Using Sets
Lists
Accessing Entries
Using Lists
Arrays
Creating and Using Arrays
Large Arrays
Tables
Defining Tables and Accessing Entries
Matrices and Vectors
Functional Operators
Defining a Function
Distinction between Functional Operators and Other Expressions
Multivariate and Vector Functions
Using Operators
Strings
Accessing Characters
Using Strings
8.3 Working with Maple Expressions
Low-Level Operations
Expression Types
Accessing Expression Components
Manipulating Expressions
Simplifying
Factoring
Expanding
Combining
Converting
Normalizing
Sorting
Evaluating Expressions
Substituting a Value for a Subexpression
Numerical Approximation
Evaluating Complex Expressions
Evaluating Boolean Expressions
Applying an Operation or Function to All Elements in a List, Set, Table, Array, Matrix, or Vector
Levels of Evaluation
Delaying Evaluation
9 Basic Programming
9.1 In This Chapter
9.2 Flow Control
Conditional Execution (if Statement)
Syntax
Simple if Statements
else Clause
elif Clauses
elif and else Clauses
Repetition (for Statement)
for/from Loop
for/in Loop
while Loop and until Loop
General Loop Statements
Infinite Loops
9.3 Iterative Commands
Creating a Sequence
Adding and Multiplying Expressions
Selecting Expression Operands
Mapping a Command over a Set or List
Mapping a Binary Command over Two Lists or Vectors
9.4 Procedures
Defining and Running Simple Procedures
Procedures with Inputs
Procedure Return Values
Displaying Procedure Definitions
Displaying Maple Library Procedure Definitions
Modules
Objects
9.5 Programming in Documents
Code Edit Region
Startup Code
9.6 Additional Information
10 Embedded Components and Maplets
10.1 In This Chapter
10.2 Using Embedded Components
Interacting
Component Descriptions
Example 1 - Using Embedded Components
Printing and Exporting a Document with Embedded Components
10.3 Creating Embedded Components
Inserting Components
Editing Component Properties: General Process
Removing Graphical Interface Components
Integrating Components into a Document
Example 2 - Creating Embedded Components
10.4 Using Maplets
Maplet File
Maple Document
10.5 Authoring Maplets
Simple Maplet
Maplet Builder
Example 3 - Design a Maplet Using the Maplet Builder
Maplets Package
Example 4 - Design a Maplet Using the Maplets Package
Saving
11 Input, Output, and Interacting with Other Products
11.1 In This Chapter
11.2 Writing to Files
Saving Data to a File
Saving Expressions to a File
Saving Data as Part of a Workbook
11.3 Reading from Files
Reading Data from a File
Import Data Assistant
ImportMatrix Command
Reading Expressions from a File
Reading Data From Workbook Attachments
11.4 Exporting to Other Formats
Exporting Documents
HTML
LaTeX
Maple Input
Maplet Application
Maple Text
PDF
Plain Text
Rich Text Format (RTF)
Summary of Translation
MapleNet
Overview of MapleNet
MapleNet Documents and Maplets
Custom Java Applets and JavaServer PagesTM Technology
11.5 Connectivity
Translating Maple Code To Other Programming Languages
Code Generation
Accessing External Products from Maple
External Calling
Mathematica Translator
Matlab Package
Accessing Maple from External Products
Microsoft Excel Add-In
OpenMaple
MapleSim
Sharing and Storing Maple Content
The MapleCloud
Index
List of Figures
Figure 1.1: The Maple Environment
Figure 1.2: Text and Math Buttons on the Toolbar
Figure 1.3: Accessing the Assistants from the Tools Menu
Figure 1.4: Accessing Tutors from the Tools Menu
Figure 1.5: Calculus - Single Variable → Differentiation Methods Tutor
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
Figure 1.8: Browse Tasks Dialog
Figure 1.9: Equation Label
Figure 1.10: Inserting an Equation Label
Figure 1.11: Controlling Equation Label Format
Figure 1.12: Label Reference
Figure 1.13: Document Block Markers
Figure 1.14: Expanded Document Block
Figure 1.15: Sample Help Page
Figure 2.1: Context Panel
Figure 2.2: Approximating the Value of a Fraction
Figure 2.3: Finding the Approximate Solution to an Equation
Figure 2.4: Units Palette
Figure 3.1: Calculus Palette
Figure 3.2: Integer Context Panel
Figure 3.3: ODE Analyzer Assistant
Figure 3.4: Task Browser
Figure 3.5: Insert Label Dialog
Figure 3.6: Format Labels Dialog: Adding a Prefix
Figure 4.1: Context Panel for an Integer
Figure 4.2: Context Panel for an Equation
Figure 4.3: ODE Analyzer Assistant
Figure 4.4: ODE Analyzer Assistant: Solve Numerically Dialog
Figure 4.5: ODE Analyzer Assistant: Solve Symbolically Dialog
Figure 4.6: Units Converter Assistant
Figure 4.7: Units Palette
Figure 5.1: Sorting a Polynomial Using the Context Panel
Figure 5.2: Matrix Palette
Figure 5.3: Matrix Palette: Choosing the Size
Figure 5.4: Insert Matrix or Insert Vector
Figure 5.5: Matrix Browser
Figure 5.6: Computing the Infinity Norm of a Matrix
Figure 5.7: Directional Derivative Tutor
Figure 5.8: Optimization Assistant
Figure 5.9: Optimization Assistant Plotter Window
Figure 5.10: Calculus 1 Derivatives Tutor
Figure 5.11: Calculus 1 Differentiation Methods Tutor
Figure 5.12: Multivariate Calculus Gradient Tutor
Figure 5.13: Multivariate Calculus Gradient Tutor Showing x-y Plane
Figure 5.14: Flowchart of solving a problem
Figure 5.15: Volume of Revolution Tutor
Figure 5.16: Inserted Task Template
Figure 5.17: Example Worksheet
Figure 6.1: Plot an Expression Using the Context Panel
Figure 7.1: Select Color Dialog
Figure 7.2: Character Style Dialog
Figure 7.3: Paragraph Style Dialog
Figure 7.4: Style Management Dialog
Figure 7.5: Defining a Character Style
Figure 7.6: Defining a Paragraph Style
Figure 7.7: Style Set Management Dialog
Figure 7.8: Header and Footer Dialog - Custom Header
Figure 7.9: Show Contents Dialog
Figure 7.10: Working with Document Blocks
Figure 7.11: Delete Table Contents Verification Dialog
Figure 7.12: Table Paste Mode Selection Dialog
Figure 7.13: Two Cells
Figure 7.14: Merged Cells
Figure 7.15: Drawing Tools and Canvas
Figure 7.16: Drawing Outline Color Icon
Figure 7.17: Drawing Properties Canvas Icon - Change the Gridline Color
Figure 7.18: Hyperlink Properties Dialog
Figure 7.19: Bookmark Indicator
Figure 7.20: Create Bookmark Dialog
Figure 7.21: Components Palette
Figure 7.22: Interactive Application Task Template
Figure 7.23: Spellcheck Dialog
Figure 8.1: Function Definition Palette Items
Figure 8.2: Evaluate at a Point
Figure 9.1: Code Edit Region
Figure 9.2: Collapsed Code Edit Region
Figure 9.3: Startup Code Editor
Figure 10.1: Components Palette
Figure 10.2: Label Properties Dialog
Figure 10.3: Slider Properties Dialog
Figure 10.4: The Inserted Components
Figure 10.5: DialComponent Action Code Editor
Figure 10.6: A Simple Maplet
Figure 10.7: Maplet Builder Interface
Figure 10.8: Image of the Maplet
Figure 10.9: Body Elements Used to Define This Maplet
Figure 11.1: Import Data Assistant
List of Tables
Table 1.1: Common Keystrokes for Entering Symbols and Formats
Table 1.2: Maple Toolbar Options
Table 1.3: Context Bar Tools
Table 1.4: Context Selector Options
Table 1.5: Text Mode vs. Math Mode
Table 1.6: Palette Categories
Table 1.7: Managing Palettes
Table 1.8: Complex Numbers using I
Table 1.9: Complex Numbers using i
Table 1.10: Help Page Icons
Table 3.1: Top Commands
Table 3.2: Top Packages
Table 4.1: Select Integer Commands
Table 4.2: Modular Arithmetic Operators
Table 4.3: Overview of Solution Methods for Important Equation Types
Table 4.4: Sample Dimensions
Table 4.5: Scientific Constants
Table 4.6: Restricting to Real Numbers
Table 5.1: Polynomial Arithmetic Operators
Table 5.2: Polynomial Coefficient and Degree Commands
Table 5.3: Select Other Polynomial Commands
Table 5.4: Additional Polynomial Help
Table 5.5: Matrix and Vector Arithmetic Operators
Table 5.6: Select Matrix and Vector Operators
Table 5.7: Select LinearAlgebra Package Commands
Table 5.8: Limits
Table 5.9: Optimization Package Commands
Table 5.10: Student and Instructor Resources
Table 6.1: The plot and plot3d Commands
Table 6.2: Common Plot Options
Table 6.3: Plot Context Bar Analysis Options
Table 6.4: The animate Command
Table 6.5: Animation Options
Table 9.1: Default Clause Values
Table 9.2: Iterative Commands
Table 9.3: The seq Command
Table 9.4: The add and mul Commands
Table 9.5: The select, remove, and selectremove Commands
Table 9.6: The map Command
Table 9.7: The zip Command
Table 10.1: Embedded Component Descriptions
Table 11.1: Summary of Content Translation When Exporting to Different Formats
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