Maple Getting Started Guide
Contents
1. 57 Bookmarks 57 iii 2 6 Working in Document Mode 58 Starting a New Document 59 Entering Math 59 Common Key Strokes for Symbols and Formats 60 Opening Documents 60 Viewing Maple Code in Document Mode 61 3 Using Maple 63 3 1 Calculus Example 63 Check for Existing Tools Tutor 64 Check for Existing Tools Task Template 65 Check for Instructions Help Page and Example Worksheet 67 Other Ready To Use Resources 69 3 2 Optimization Example 70 Check for Existing Tools Assistant 72 Check for Instructions Help Page2. 74 4 The Next Step 79 4 1 Top Packages 79 4 2 Top Commands 81 Index 83 iv Contents Preface The Maple Software The MapleTM software is a powerful system that you can use to solve complex mathematical problems You can also create professional quality documents presentations and custom interactive computational tools in the Maple en vironment You can access the power of the Maple computational engine through a variety of interfaces Description Interface 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 res ults The advanced formatting features help you create the customized document you need Because the docu ments are live you can edit the parameters and with the click of a button compute the new results The Getting Started Guide was created using the Stand ard Worksheet interface to Maple An interactive version of th
3. 31 Figure 2 12 Browse Tasks Dialog Previewing Tasks Maple tasks can be previewed in three ways From the Tools menu select Tasks and then Browse The Browse Tasks dialog opens and displays the list of tasks From the Help menu select Manuals Dictionary and more and then Tasks The Help Navigator opens In the left pane click the Tasks folder to displays the list of tasks From the File menu select New and then Templates The Browse Tasks dialog opens and displays the list of tasks 32 2 Maple Tools and Resources The tasks are sorted by subject to help you quickly find the desired task In the Browser Task dialog or Help Navigator you can view tasks without inserting them into your worksheet Inserting a Task into the Worksheet From both the Browse Tasks dialog and the Help Navigator you can insert a task into a worksheet 1 Select the Insert into New Worksheet check box 2 Click Insert Default Content or Insert Minimal Content Default content includes the task title and description Minimal content inserts only the major components commands and buttons 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 as signed values in your worksheet If any task variable is assigne
4. Precalculus precalculus VectorCalculus multivariate vector calculus Student 80 4 The Next Step The Units package accepts approximately 300 distinct unit names for example meters and grams and over 550 units with various contexts for example standard miles and U S survey miles Maple also contains Units palettes that allow you to quickly enter the unit for an expression Units The VectorCalculus package is a collection of commands that per form multivariate and vector calculus operations A large set of predefined orthogonal coordinate systems is available All computa tions in the package can be performed in any of these coordinate systems It contains a facility for adding a custom coordinate system and using that new coordinate system for your computations VectorCalculus 4 2 Top Commands Description Command Name Create a two dimensional plot of functions plot Solve one or more equations or inequalities for their unknowns solve Solve one or more equations using floating point arithmetic fsolve Evaluate an expression at a given point eval Numerically evaluate expressions evalf Solve ordinary differential equations ODEs dsolve Compute an indefinite or definite integral int Compute an ordinary or partial derivative as the context dictates diff Calculate the limiting value of a function limit For symbolic summation It is used to compute a closed fo
5. Maplets and MapleNet From the Help menu select Take a Tour of Maple Tour 10 1 Introduction to Maple Description Tour and New User Roadmap Find the most efficient path to solving a problem immediately or learning principles and reviewing major features From the Help menu select Manuals Dictionary and more and then New User Roadmap New User Roadmap 1 1 How Maple Helps You 11 Description Web Site Resources Maple Web site and resource for FAQs downloads and service packs links to discus sion groups and request technical support form Telephone technical support numbers in Contact Customer Service link 1 Go to http www maplesoft com 2 In the menu of the main Web page click Support and then Technical Support Technical Support Online Maple Web site resource for free applications related to mathematics education science engineering computer science statistics and data analysis finance communications graphics Many applications are available in translation French Spanish and German 1 Go to http www maplesoft com 2 In the menu of the main Web page click Resources and then Application Center Application Center Maple Web site resource for free complete course curricula and add on Maple packages and courses developed by experts in their fields to help users configure Maple for re search in specific application areas 1 Go t
6. Command line version Classic Worksheet Custom built Maplet applications Calculator interface Windows only In this guide references to the graphical Maple interface refer to the Standard Worksheet interface For more information on the various interface options refer to the versions help page 16 2 Maple Tools and Resources The first Maple session opens with the Startup dialog Figure 2 1 explaining the difference between Document mode and Worksheet mode The dialog contains links to items such as various document options help resources including updates and other introductory help pages and application resources on the Web Subsequent sessions display Tip of the Day information Document mode allows you to start solving problems right away without needing syntax or Maple commands Worksheet mode is the most familiar mode to users of previous versions of Maple You enter commands at an input prompt to get results Figure 2 1 Startup Dialog 2 1 Starting Maple 17 Basics Maple documents are saved as mw files They consist of files created in Worksheet or Document mode To start a Maple session In the Startup dialog select one of the document options Blank Docu ment Blank Worksheet Template or Open a File or 1 Close the Startup dialog 2 From the File menu select New and then one of the following Worksheet Mode Document Mode or T
7. command symbol completion forward slash fraction Use right arrow key to leave superscript area caret exponent super script _ Shift underscore subscript sqrt and then com mand symbol comple tion shortcut key square root Arrow keys navigating the ex pressions Opening Documents Like in Worksheet mode in Document mode documents are saved as mw files Files saved in Document mode open automatically in Document mode and not in Worksheet mode 60 2 Maple Tools and Resources Viewing Maple Code in Document Mode In Document mode documents are created as a series of document blocks As such you can expand document blocks to view hidden code To view code in Document mode 1 Ensure that the Markers feature is activated From the View menu select Markers Document block markers are displayed in the left side bar 2 Insert the cursor in a document block to be expanded 3 From the View menu select Expand Document Block 4 To hide the code again from the View menu select Collapse Document Block For more information on document blocks see the Maple User Manual 2 6 Working in Document Mode 61 62 2 Maple Tools and Resources 3 Using Maple Maple is a powerful application with many resources to guide you The fol lowing examples provide you with scenarios to learn about using Maple re sources and the Maple program When using
8. Important With Maple Input you must terminate commands with a semi colon or colon restart gt Enter the Maple input followed by a semicolon If the input ends with a semicolon the result is usually displayed as seen below factor x 2 2 x 1 gt 46 2 Maple Tools and Resources However if the input ends with a colon the result is computed but the result is not displayed factor x 2 2 x 1 gt Define custom functions f x gt x 2 gt f 3 gt f y 1 gt Basic Computations The following are examples of basic computations using Maple Input 1 D Math cos alpha 2 sin alpha 2 gt a x 2 b x c gt 2 4 Commands 47 a int exp sqrt 2 x x gt restart gt limit f x x infinity gt sum a k x k k 0 m product b j x j j 0 n gt To use a palette with 1 D Math Input 1 Ensure the palette you require is visible If necessary from the View menu select Arrange Palettes 2 Ensure that you are in Text mode If necessary press F5 to switch between 1 D Math Text mode and 2 D Math Math mode 3 With your mouse click a palette expression The expression is displayed in 1 D Math notation in the execution group of the worksheet 4 The first placeholder is highlighted Enter your expression and if necessary use the Tab key to move to the next placeholder Important Ensure that your Tab key is set to move to th
9. bottle volume of revolution 63 C calculus example 63 Classic Worksheet 16 CodeGeneration package description 79 colon usage 41 command completion automatic 51 manual 52 command line interface 16 commands LPSolve 76 Optimization 74 restart 42 top 81 VolumeOfRevolution 64 computation commands Student 26 context menus using 27 convert 1 D to 2 D 49 copy examples 22 corporate Web site 11 13 83 curve analysis example 27 Curve Fitting Assistant 24 D D icon 21 Definition linear programming 75 document blocks 57 Document mode 58 documents running 41 E Edit menu in help system 22 example calculus 63 optimization 70 examples index 53 example worksheets copy 22 description 9 menu access 9 exclamation point 41 execute command 41 execution group 41 expressions graph results 29 palettes 36 right click 28 F format labels 56 G government Web site 13 H Help Navigator using 21 help system accessing 20 description 8 dictionary 21 Edit menu 22 75 Help Navigator 20 icon 8 manuals 21 search 21 table of contents 21 tasks 21 topic search 21 tutorials 21 View menu 22 volume of revolution 67 I icons 1 exclamation point 41 3 exclamation points 41 in help system 21 open as example worksheet 22 Tab 39 industry Web site 13 installation 15 Installer Builder Assistant 24 interactive commands 84 Index Student 27
10. User Manual 4 1 Top Packages Description Package Name The CodeGeneration package is a collection of commands and subpackages that enable the translation of Maple code to other pro gramming languages such as C Fortran Java MATLAB and Visual Basic CodeGeneration The LinearAlgebra package contains commands to construct and manipulate Matrices and Vectors and solve linear algebra problems LinearAlgebra routines operate on three principal data structures Matrices Vectors and scalars LinearAlgebra A Maplet application is a graphical user interface containing win dows textbox regions and other visual interfaces which gives a user point and click access to the power of Maple Users can perform calculations plot functions or display dialogs without using the worksheet interface The Maplets package contains commands and subpackages to create a Maplet application To create Maplet applications in a graphical user interface environment use the Maplet Builder The Maplet Builder is available only in the Standard Worksheet interface From the Tools menu select Assistants and then Maplet Builder Maplets 79 The RealDomain package provides an environment in which the default Maple behavior of assuming that the basic underlying number system is the complex field is replaced by the assumption that the basic underlying number system is the field of real numbers RealDomain The ScientificConstants package provide
11. example 70 solids of revolution example 64 solutions overview 4 Standard Worksheet 16 start Maple standard worksheet 16 statement separator 41 Student Center 14 package 26 top packages 80 symbolic compute 4 Symbol Recognition palette 34 T Tab icon 39 Tab key 39 table of contents help system 21 task menu access 6 volume of revolution 65 task template 31 technical support description 12 text right click 30 tools visualization 3 Tools menu assistants 23 tutors 26 topic search 21 tour 10 tutor 86 Index volume of revolution 64 tutorials help system 21 tutors accessing 26 curve analysis example 27 description 6 menu access 6 Tools menu 26 using 26 U Unit Converter Assistant 25 Units package description 81 UNIX command complete 52 60 start Maple 16 V VectorCalculus package description 81 View menu in help system 22 markers 57 using palettes 48 visualization commands Student 26 volume of revolution example 64 W Windows command complete 52 60 start Maple 16 Worksheet mode 18 19 58 worksheets running 41 WS icon 21 Index 87 88 Index
12. 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 introduction to the following Maple features Worksheets and powerful interactive documents The help system Point and click interaction with various interfaces to help you solve problems quickly Maple commands and standard math notation A road map for solving problems vi Preface 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 first time Maple users 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 doc maplesoft com Preface vii viii Preface 1 Introdu
13. from the Tools Menu The Tutors are also accessed through the Student package For a definition of the term package see Commands page 40 The Student package is a collection of subpackages designed to assist with the teaching and learning of standard undergraduate mathematics The sub packages contain many commands for displaying functions computations and theorems in various ways and support for stepping through important computations The visualization commands are tools that create plots and animations showing the geometric interpretation of important concepts The computation commands help you study the techniques of computa tion while solving problems For example using the Calculus1 package you can differentiate a function one step at a time specifying the differ entiation rule applied at each step At any time during a single step 26 2 Maple Tools and Resources computation you can request a hint about the next step which you can then apply to the problem or proceed directly to the final answer The interactive commands use Maplet technology to help you explore concepts and solve problems using a point and click interface These commands launch tutors that provide a graphical interface to visualization and computation commands Figure 2 7 Tutor Example Calculus 1 Curve Analysis Context Menus Maple dynamically generates a context menu when you right click for Macintosh Control c
14. graphical user interface components Generate two and three dimensional plots and animations Sketch ideas in the worksheet Copy cut and paste information Bookmark specific areas Insert symbols from over 20 palettes Easily update revise and distribute your documents Exploring or Visualizing Problems Maple has many tools to help you examine and demonstrate concepts You can Solve problems using point and click tutors assistants and Maplet ap plications Create plots and animations in two and three dimensions Right click Control click for Macintosh to export convert manipulate plot and more using context menus 1 1 How Maple Helps You 3 Computing Numeric and Symbolic Solutions Maple is an analytic computation system It performs mathematical compu tations and manipulations to solve problems from various technical discip lines Maple computes both numeric and symbolic solutions to mathemat ical problems For example Maple performs computations on expressions that contain symbols such as and returns exact symbolic results You can Instantly simplify large equation sets Derive sophisticated equations Compute parametric solutions to problems Use precision control for maximum accuracy Include units measurement of error and tolerance management within an expression and perform calculations on this expressio
15. integration The Symbol Recognition palette provides an efficient way to find and insert the desired symbol You draw the symbol with your mouse and then Maple matches your input against symbols available in the system 34 2 Maple Tools and Resources Figure 2 13 Symbol Recognition Palette By default palettes are displayed when you launch Maple To view palettes 1 From the View menu select Palettes 2 Select Expand Docks 3 Right click Control click for Macintosh the palette dock From the context menu select Show All Palettes Alternatively from the main menu select View gt Palettes gt Arrange Palettes to display specific palettes Important This section provides an overview of the palettes For instructions on using palettes with Maple Input 1 D Math and Standard Math 2 D Math Input notation see Commands page 40 2 3 Point and Click Interaction 35 Expression Palettes Expression a palette for constructing expressions such as integrals and derivatives Matrix a palette consisting of a dialog that allows you to enter the number of rows and columns required designate type such as zero filled and designate shape such as diagonal See Figure 2 14 Layout a palette that allows you to add math content that has specific layout such as expressions with one or more superscripts and subscripts Components a palette that allows you to embed simple gr
16. interface to the solver commands in the Optimization package The Optimization package is a collection of commands for numerically solving optimization problems which involve finding the minimum or maximum of an objective function possibly subject to constraints You can select one of the methods shown in the interface to obtain a minimum or maximum of an objective function under the given constraints When you click the Solve button the problem the objective function constraints bounds and options is solved using 24 2 Maple Tools and Resources the indicated method and the solution is provided in the Solution area of the Maplet application When a solution is obtained clicking the Plot button displays a plot of the objective function in the region of the solu tion or if the problem is bounded a plot of the objective function over the search region Plot Builder a graphical user interface for creating plots animations and interactive plots with sliders in two and three dimensions Unit Converter a graphical user interface for performing unit conver sions in the worksheet Figure 2 5 Assistant Example Unit Converter 2 3 Point and Click Interaction 25 Tutors Using the Tools gt Tutors menu you can access over 40 interactive tutors that aid in the learning of precalculus calculus multivariate calculus vector calculus and linear algebra concepts Figure 2 6 Accessing Tutors
17. interfaces list 16 K key strokes 60 L library 40 library browser assistant 24 LinearAlgebra package description 79 LPSolve command 75 M M icon 21 Macintosh command complete 52 60 context menus 27 start Maple 16 manual command completion 52 Maple Application Center solids of revolution 69 Maplet Builder Assistant 24 Maplets create 39 top package 79 Maple Web site resources 12 markers displaying 57 math dictionary description 8 help system 21 mathematical palettes 37 N numeric compute 4 O ODE Analyzer Assistant 24 Optimization Assistant 24 72 example 70 LPSolve 76 Options dialog 45 auto command complete 51 command complete 51 P packages definition 41 top 79 palettes 1 D Math 48 2 D Math Input 44 accents 38 alphabetical 38 arrange 48 expression 36 mathematical 37 overview 34 symbol recognition 34 paste examples 22 Plot Builder Assistant 25 plots right click 30 point and click 23 PowerTools 69 Index 85 description 12 Q question mark icon 21 R RealDomain package description 80 resources access 6 diagram 5 in help system 21 right click expressions 28 graphic results 29 plots 30 text 30 running documents 41 worksheets 41 S ScientificConstants package description 80 ScientificErrorAnalysis package description 80 search help system 21 selection execute 41 semicolon usage 41 skates optimization
18. mand To disable automatic command completion From the main menu select Tools gt Options gt Interface tab Clear the Automatic command completion check box 2 4 Commands 51 Manual Command Completion Manual command completion is always enabled To use manual command completion 1 Begin entering a command in the worksheet 2 To list all Maple packages commands and functions that match the entered text select Tools gt Complete Command or use short cut keys Command Shift Space Macintosh Ctrl Space Windows Ctrl Shift Space UNIX If there is a unique completion it is inserted Otherwise a list of matches is displayed 3 Select the correct completion from the list 52 2 Maple Tools and Resources Using Examples to Learn about Commands Most help pages contain examples you can copy and run in the worksheet However some topics also provide example worksheets that demonstrate the power of Maple commands You can use the example worksheets to learn how commands and options behave To access example worksheets In the worksheet enter examples index The Index to Example Worksheets opens Topics presented include Algebra Applications finance scientific constants scientific error analysis Calculus Connectivity code generation external calling Differential Equations Discrete Mathematics
19. menu select Manuals Dictionary and more 2 Select List of Packages To use a package command specify both the package and command names using the syntax package command arguments If you are using a number of commands in the package load the package using the with command To load a package At the Maple prompt enter the with command followed by the package name enclosed in parentheses and terminated with a semicolon 1 D Math input Then press Enter 50 2 Maple Tools and Resources Using the with command to load the Optimization package A list of all commands in the package is displayed To suppress the display of all command names end the with Optimiz ation command with a colon gt with Optimization After loading a package you can use the short form names that is the command names without the package name gt LSSolve x 2 x 6 x 9 Automatic Command Completion By default automatic command completion is enabled If it is not enabled from the main menu select Tools gt Options gt Interface tab Select the Automatic command completion check box 1 Begin entering a command in the worksheet Maple compares your entry with Maple packages commands functions and other assigned names If the entered text has a unique completion a tool tip containing the matching command name is displayed above the entry 2 You can continue typing the command or press Enter to insert the com
20. menu select Tasks and then Browse Task Templates 6 1 Introduction to Maple Description Tutors Assistants Task Templates and Maple Calculator Available for use as part of your Maple installa tion A convenient calculator interface using Maple technology Microsoft Windows only From the Start menu select Maple10 and then Maple Calculator Maplesoft Graphing Calculator 1 1 How Maple Helps You 7 Description Online Help and Examples The online help system helps you find inform ation about a specific topic command pack age or feature You can access help three ways From the Help menu select Maple Help In the toolbar click the Help icon In the worksheet enter topicname For example type LinearAlgebra and then press Enter Help Pages More than 5000 mathematical and engineering terms and over 300 figures and plots 1 From the Help menu select Maple Help 2 In Resources drop down list select Defin ition 3 Enter search word or expand alphabetical listing Dictionary 8 1 Introduction to Maple Description Online Help and Examples Applications 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 as demon strations Topics include DC Motor Control De
21. to Maple 2 Maple Tools and Resources In this chapter Launching the program and the user interface Note For installation and licensing instructions refer to the Install htm file on your Maple Installation CD Starting Maple Accessing help pages and other resources Maple Help System Accessing various interfaces designed to help you solve problems quickly Point and Click Interaction Using Maple commands and language Commands Interpreting formatting features Worksheet Formatting Fea tures Using the blank sheet Maple Document environment for quickly solving problems Working in Document Mode This guide was created using Maple 2 1 Starting Maple In this section Starting the Standard Worksheet Interface The Maple Worksheet Basics 15 Starting the Standard Worksheet Interface To start the Standard Worksheet interface in From the Start menu select Programs Maple 10 Maple 10 Alternatively Double click the Maple 10 desktop icon Windows Double click the Maple 10 application icon in the Finder Macintosh Enter the full path for example usr local maple bin xmaple Alternatively 1 Add your Maple 10 directory for example usr local maple bin to your command search path 2 Enter xmaple UNIX The Maple Worksheet You can access the power of the Maple computation engine through a variety of user interfaces Standard Worksheet
22. 64 3 Using Maple Figure 3 1 Volume of Revolution Tutor Accessed from Tools Menu After you Close the tutor the plot is inserted into your worksheet Check for Existing Tools Task Template To access a task template for the volume of revolution 1 From the Tools menu select Task and then Browse The Browse Task dialog opens displaying a list of tasks The tasks are sorted by subject to help you quickly find the desired task 2 Expand the Calculus folder 3 From the displayed list select Volume of Revolution The Volume of Revolution task is displayed in the right pane of the Browse Task dialog See Figure 3 2 3 1 Calculus Example 65 Figure 3 2 Task Template for Volume of Revolution 4 Select the Insert into New Worksheet check box 5 Click Insert Default Content Before inserting a task Maple checks whether the task variables have assigned values in your worksheet If any task variable is assigned the Task Variables dialog opens allowing you to modify the names Maple uses the edited variable names for all variable in stances in the inserted task The command is inserted into your worksheet 66 3 Using Maple Parameters are marked as placeholders Update the parameter values as required To navigate between placeholders in the worksheet press the Tab key 6 After updating any parameters run the command by pressing Enter Check for Instructions Hel
23. General Numerics General Symbolics Geometry Integration Integral Transforms Language and System Mathematical Visualizations 2 4 Commands 53 Figure 2 20 Example Worksheet Note You can also use the Help menu to access Applications sample applications that demonstrate how Maple can be used to find and document a solution to a specific problem To access Applications from the Help menu From the Help menu select Manuals Dictionary and more and then Applications and Examples The Applications and Examples help page opens Equation Labels Equation labeling allows you to reference Maple output in text and math of your worksheet The label is associated with all output within an execution group You cannot apply equation labels to the following Error warning and information messages Tables images plots sketches or spreadsheets 54 2 Maple Tools and Resources By default equation labels are displayed If equation labels are not displayed verify the following 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 Labels Ensure that Worksheet is selec ted Figure 2 21 Inserting an Equation Label Figure 2 22 Equation Label To apply equation labels 1 Enter an expression and press Enter Note that the equation labe
24. Maple Getting Started Guide Copyright Maplesoft a division of Waterloo Maple Inc 2005 Maple Getting Started Guide Copyright Maplesoft Maple Maple Application Center Maple Student Center and Maplet are all trademarks of Waterloo Maple Inc Maplesoft a division of Waterloo Maple Inc 2005 All rights reserved No part of this book may be reproduced stored in a retrieval system or transcribed in any form or by any means electronic mechanical photocopying recording or otherwise Information in this document is subject to change without notice and does not represent a commitment on the part of the vendor The software described in this document is furnished under a license agreement and may be used or copied only in accordance with the agreement It is against the law to copy the software on any medium except as specifically allowed in the agreement Windows is a registered trademark of Microsoft Corporation Java and all Java based marks are trademarks or registered trademarks of Sun Microsystems Inc in the United States and other countries Maplesoft is independent of Sun Microsystems Inc 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 74 3 Contents Preface v 1 Introduction to M
25. Maple to solve a problem consider the following process 1 Formulate your problem 2 Obtain Maple resources that allow you to solve it 3 1 Calculus Example Problem Scenario A Your company is designing a bottle for its new spring water product The bottle must contain 18 ounces of water and the height is fixed The design includes an undulating curved surface You know the amplitude and equation of the curve but you must find the radius You require the Volume of Revolution Scenario B You want to teach your students the concept of a Volume of Revolu tion Specifically you want to plot and compute the volume of a solid of revolution generated by rotating f x a x b about an axis or a line parallel to an axis 63 Check for Existing Tools Tutor Begin by examining the Tools menu for a Tutor graphical user interface to a Volume of Revolution problem To access a Tutor for the Volume of Revolution 1 From the Tools menu select Tutors and then Calculus Single Variable Notice that a Volume of Revolution tutor exists 2 Click the Volume of Revolution menu item The worksheet is populated with the following Maple command gt The Volume of Revolution Tutor is displayed See Figure 3 1 The tutor is a graphical user interface that allows you to enter a function and an interval view and manipulate the corresponding plot and view the full Maple com mand associated with your entries and selections
26. What is the profit PROCESS Formulate the Problem f number of figure skates per day s number of speed skates per day h number of hockey skates per day Objective function is Constraints are Obtain Resources Check for existing tools 3 2 Optimization Example 71 Follow instructions Consider ready to use resources Check for Existing Tools Assistant To access an Assistant graphical user interface to the optimization functionality From the Tools menu select Assistants and then Optimization See Figure 3 6 Figure 3 6 Optimization Assistant with Values Entered 72 3 Using Maple To enter values for the problem Enter the objective function and constraints 1 In the Problem group box click Edit in the Objective Function group box 2 In the dialog that returns enter 7 f 6 s 5 h Click Done 3 Click Edit in the Constraints and Bounds group box The Constraints dialog opens 4 In the Add Bound group box click Assume all variables nonnegative 5 In the Add Constraint field Enter f 1 2 s h lt 22 Click Add Enter f s 1 3 h lt 23 Click Add Enter 1 4 f s h lt 21 Click Add 6 Click Done to return to the Optimization Assistant dialog 7 In the Solver group box select Linear 8 Click Variable Types In the Variable Types dialog select the Integer check boxes for all variables 9 In
27. ab icon on Allows you to indent in the worksheet using the Tab key Maplet Applications A Maplet application is a 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 plot functions or display dialogs without using the worksheet interface 2 3 Point and Click Interaction 39 The following simple Maplet contains a textbox region a button and a label prompting you to enter an equation Figure 2 17 Maplet Application Example You can create custom Maplets using the Maplets package syntax based or the Maplet Builder a graphical user interface tool For details refer to the Maple User Manual 2 4 Commands Maple is powerful flexible and customizable In addition to the point and click features Maple contains a set of commands and a programming lan guage In this section The Maple Library Commands in the Worksheet 2 D Math Input Maple Input 1 D Math Input Learning about Commands and Packages Using Examples to Learn About Commands Equation Labels 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 40 2 Maple Tools and Resources Packages contain related spe
28. aphical inter face components for example a button into your worksheet You can associate actions with components for example a command that is ex ecuted when a button is clicked Symbol Recognition a palette that provides an efficient way to find and insert the desired symbol Draw the symbol with your mouse and Maple matches your input against symbols available in the system Units SI a palette that inserts a unit from the International System of Units SI or any general unit For details refer to the Units SI help page Units FPS a palette that inserts a unit from the Foot Pound Second System FPS or any general unit For details refer to the Units FPS help page 36 2 Maple Tools and Resources Figure 2 14 Matrix Palette Mathematical Palettes Common Symbols a palette of common symbols for constructing ex pressions using sums products and among other things See Figure 2 15 Relation Standard a palette of standard relational operator symbols for constructing expressions Operators a palette of operators for constructing expressions Relational Round a palette of round relational operator symbols for constructing expressions Large Operators a palette of large operators for constructing expres sions Negated a palette of negation symbols for constructing expressions Fenced a palette of fenced symbols for constructi
29. aple 1 1 1 How Maple Helps You 1 Creating Interactive Documents 3 Exploring or Visualizing Problems 3 Computing Numeric and Symbolic Solutions 4 Solving a Problem 4 Accessing Resources 6 2 Maple Tools and Resources 15 2 1 Starting Maple 15 Starting the Standard Worksheet Interface 16 The Maple Worksheet 16 2 2 The Maple Help System 19 Accessing the Help System 20 Using the Help Navigator 21 Viewing Help Pages as Worksheets 22 Copying Examples 22 2 3 Poi
30. ar programming definition is displayed Note The definition also contains a link to the associated Maple Optimiza tion package command LPSolve Figure 3 8 Definition of Linear Programming 2 Click the Optimization LPSolve link in either the definition or overview help page See Figure 3 9 3 2 Optimization Example 75 Figure 3 9 Optimization LPSolve You can use one Maple command to solve the skating problem For inform ation on using commands in packages see Maple Tools and Re sources page 15 gt The same solution is returned using the LPSolve command 76 3 Using Maple gt gt The assume nonnegint and maximize options are described in the help page assume nonnegint Assume all variables are non negative integers maximize or maximize true Maximize the objective function By default that is if you exclude the maximize option the LPSolve command computes the minimum 3 2 Optimization Example 77 78 3 Using Maple 4 The Next Step After you have reviewed the contents of the first three chapters you can scan the top Maple packages topics and commands Additionally for detailed information about features you have reviewed in this book and other advanced features refer to the Maple User Manual To access the Maple User Manual 1 From the Help menu select Manuals Dictionary and more 2 Select Manuals and then
31. as worksheets 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 window opens Alternatively in the help system toolbar click the open current help page in a work sheet window icon Copying Examples Instead of opening the entire page as a worksheet you can copy the Examples section to a worksheet To copy examples 1 With the help page displayed in the right pane of the help system from the Edit menu select Copy Examples 2 Close or minimize the Help Navigator and return to your worksheet 3 In your worksheet place the cursor at the location where the examples are to be pasted 4 From the Edit menu select Paste The Examples section of the help page is now executable content in your worksheet 22 2 Maple Tools and Resources 2 3 Point and Click Interaction Maple contains many built in features that allow you to solve problems quickly without learning new commands In this section Assistants Tutors Context Menus Task Templates Palettes Maplet Applications Assistants Using the Tools gt Assistants menu you can access tools to help you accom plish various tasks Figure 2 4 Accessing the Assistants from the Tools Menu 2 3 Point and Click Interaction 23 The Assistants are graphica
32. cialized commands for performing tasks from disciplines such as Student Calculus Statistics or General Relativity Theory Commands in the Worksheet In Worksheet mode a new worksheet opens with a Maple prompt in the upper left hand corner Enter Maple commands at this prompt for Maple to recognize your entry as Maple Input 1 D Math or 2 D Math and execute the command Description Basic Usage gt Maple prompt In the toolbar click the icon From the Edit menu select Execute gt Worksheet Running the entire worksheet executing all commands Place the cursor in any Maple input region in the execution group and press the Enter key Executing one command In the toolbar click the icon From the Edit menu select Execute gt Selection Executing selected area Statement separator Terminate a 1 D or 2 D command with a semicolon and output is displayed Important All 1 D commands must terminate with a semicolon or colon Semicolon Statement separator Terminate a 1 D or 2 D command with a colon and output is not displayed Important All 1 D commands must terminate with a semicolon or colon Colon 2 4 Commands 41 Description Basic Usage The restart command causes Maple to clear its internal memory Alternatively in the toolbar click the restart icon For specific details refer to the Maple User Manual restart Default setting Executable standard
33. cific help page Figure 2 3 Example Help Page 20 2 Maple Tools and Resources Using the Help Navigator The Help Navigator contains a field for topic or text based searches Topic searches reveal a list of matching topics sorted by exactness of match Text searches reveal a list of topics based on keyword frequency You can search all or specific Resources such as Help Pages Tasks definitions in the Maple Math and Engineering Dictionary Tutorials and Manuals 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 A folder icon in the Table of Contents tab indicates that a topic can be expanded into subtopics Clicking a topic preceded by a question mark icon displays the associated help page in the right pane To display potential matches in the right pane click a topic preceded by an icon Question mark icon indicates a help page WS icon indicates an example worksheet Example worksheets open in a new tab in the worksheet window D icon indicates a Definition T icon indicates a Task template M icon indicates a Manual Manuals open in a new tab in the worksheet win dow 2 2 The Maple Help System 21 Viewing Help Pages as Worksheets In help pages examples are not executable The Maple help system allows you to open help pages
34. ction to Maple Don t worry about your difficulties in Mathematics I can assure you mine are still greater Albert Einstein 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 access ible complete and error free form That tool is Maple 1 1 How Maple Helps You With Maple 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 easy to modify example worksheets You can also devise custom solutions using the Maple program ming language While you work you can document your process providing text descriptions 1 Figure 1 1 Example Interactive Document in Maple 2 1 Introduction to Maple Creating Interactive Documents Maple allows you to create powerful documents for use as business and education tools technical reports presentations assignments and handouts You can Include instructions and equations beside your computations Integrate calculations spreadsheets and equations Format text for reports academic papers or books Insert hyperlinks to other files Web sites or email addresses Insert images spreadsheets tables and symbols Embed
35. d 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 1 From the Tools menu select Options 2 Click the Display tab 3 In the Show task variables on insert drop down list select Always 4 Click Apply to Session or Apply Globally as necessary 2 3 Point and Click Interaction 33 Updating Parameters and Running the Commands In tasks parameters are marked as placeholders or specified using sliders or other embedded components Update the parameter values as required Note To navigate between placeholders in the worksheet press the Tab key After updating any parameters perform the task by running the commands or by clicking buttons Palettes The Maple worksheet environment provides access to over 20 palettes Palettes are collections of related items that you can insert by clicking or drag and dropping into a document Palettes contain Symbols like Layouts like an item with a superscript and subscript Mathematical operations like a definite integral with placeholders for the integrand variable of integration and endpoints of the interval of
36. e next placeholder and not indent For details see Placeholders and the Tab Key page 39 5 Press Enter 48 2 Maple Tools and Resources Why Use Palettes in 1 D Math Using a palette that uses standard notation teaches you the related Maple command syntax You can control the appearance of expressions in the worksheet You can convert 1 D Math to 2 D Math To convert 1 D to 2 D math input 1 Enter an expression in 1 D Math notation 2 Select the expression and then right click Control click Macintosh to open the context menu 3 Select Convert To and then 2 D Math Input The expression is displayed in 2 D Math input notation 4 Press Enter to evaluate the expression Figure 2 19 1 D Math Input Converted to 2 D Math Input 2 4 Commands 49 Learning About Commands and Packages Each help page contains the correct syntax for a command calling sequences parameters and description of use Examples and links to related subjects are provided at the bottom of each help page Many topics include more ex amples which are presented in example worksheets To view a list of top level commands 1 From the Help menu select Manuals Dictionary and more 2 Select List of Commands A Maple package is a group of related commands For example the Optim ization package contains commands for numerically solving optimization problems To view a list of packages 1 From the Help
37. emplates This guide discusses features common to Worksheet and Document mode For information on Templates see Task Templates page 31 In structions for using Document mode are provided in the last section Working in Document Mode page 58 In subsequent sessions Maple starts in Document mode Every time you open a Document Maple displays a Quick Help pop up list of important shortcut keys To invoke Quick Help at any time press the F1 key Important This guide was created using Maple 18 2 Maple Tools and Resources Figure 2 2 The Maple Standard Worksheet Interface in Worksheet Mode 2 2 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 determ ining the syntax of Maple commands and for learning about Maple features In this section Accessing the Help System Using the Help Navigator Viewing Help Pages as Worksheets Copying Examples 2 2 The Maple Help System 19 Accessing the Help System To access the Maple help system From the Help menu in your worksheet select Maple Help or In the worksheet enter HelpOverview The Maple help system opens in a separate window The window has two panes The left pane contains the Help Navigator where you initiate searches and the right pane displays the final search result such as a spe
38. es and displays results on the next line or if set in the Options dialog simply evaluates Using the context menu item Evaluate 58 2 Maple Tools and Resources Command completion is supported For specific platform shortcut keys see Common Key Strokes for Symbols and Formats page 60 Starting a New Document To start a new document in Document mode From the File menu select New and then Document Mode Note By default Maple opens in Document mode Entering Math Review the following example Entering the expression 1 Enter x 2 Press the key The cursor moves to superscript position Enter 2 3 Press the right arrow key The cursor moves right Enter the symbol and then enter y 4 Press the symbol The cursor moves to superscript position Enter 2 Evaluating the expression 1 Right click Control click for Macintosh the expression 2 From the context menu select Evaluate and Display Inline The result is displayed with an sign 2 6 Working in Document Mode 59 Common Key Strokes for Symbols and Formats Palettes are the quickest way to enter special formats however you can also use the following key strokes Automatically Generated in Document Key Symbol Formats Example using fraction versus 1 4 F5 enter exit 2 D Math Command Shift Space Macintosh Ctrl Space Win dows Ctrl Shift Space UNIX
39. highlighted Enter your expression and if neces sary use the Tab key to move to the next placeholder 5 Press Enter Why Use Palettes in 2 D Math If you are a new Maple user palettes make entering expressions easier than entering syntax and reduce the possibility of introducing typing er rors Your worksheet uses standard notation for mathematical content In the following figure compare the 2 D and 1 D Math input 44 2 Maple Tools and Resources You can control the appearance of expressions in the worksheet You can convert 2 D Math to 1 D Math 1 Enter an expression in 2 D Math notation 2 Select the expression and then right click Control click Macintosh to open the context menu 3 Select 2 D Math Convert To and then 1 D Math Input The expression is displayed in 1 D Math input notation 4 Press Enter to evaluate the expression You can change the default math input notation for your Maple session for future use To change math input notation for a session or globally 1 From the Tools menu select Options The Options Dialog opens 2 Click the Display tab 3 In the Input Display drop down list select 2 D Math Notation 4 Click the Apply to Session or Apply Globally button Important The selected input display becomes available after the current execution group 2 4 Commands 45 Figure 2 18 Options Dialog Input Display Maple Input 1 D Math
40. ing language is not essential to the concept and only output such as a plot the final answer or explanatory text must be displayed Markers indicate the boundaries of the document block Warning messages input prompts and execution groups are not displayed in document blocks For details on using document blocks see the Maple User Manual Bookmarks A bookmark designates a location in an active worksheet that can then be accessed from other regions in your worksheet or by using hyperlinks in other worksheets Markers indicate the location of the bookmark 2 5 Worksheet Formatting Features 57 Figure 2 24 Bookmarks 2 6 Working in Document Mode Document mode allows you start solving problems right away free of the syntax of the worksheet environment Document mode is described as follows A blank work area An input prompt or execution group is not displayed although it can be inserted Warning messages are not displayed You can combine text and math in the same line As with Worksheet mode you can insert images plots tables sketches and Maple spreadsheets All math is entered as 2 D Math You execute 2 D Math in Document mode by using any of the following methods Pressing Ctrl Command for Macintosh This evaluates and displays results inline Using the context menu item Evaluate and Display Inline Pressing the Enter key This evaluat
41. is manual is available in the Standard Worksheet interface From the Help menu select Manuals Diction ary and more gt Manuals gt Getting Started Guide Standard Worksheet Basic worksheet environment for older computers with limited memory Classic Worksheet Command line interface without graphical user inter faces features for solving very large complex problems or batch processing with scripts Command line version Graphical calculator interface to the Maple computational engine Using it you can perform simple computations and create customizable zoomable graphs MaplesoftTM Graphing Calculator Microsoft Windows only v Description Interface 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 MapletTM Applications This manual describes how to use the Standard Worksheet interface Not all features are available in the Classic Worksheet interface and Command line version The Standard Worksheet interface has two modes Document mode and Worksheet mode Document Mode Using the Document mode you can perform quick cal culations You can enter a mathematical expression and then evaluate ma nipulate solve or plot with a few keystrokes or mouse clicks Worksheet Mode The Worksheet mode is designed
42. l is dis played to the right of the answer in the worksheet 2 4 Commands 55 2 In a new execution group enter another expression that will reference the output of the previous execution group 3 From the Insert menu select Label Enter the label number in the Insert Label dialog and click OK Alternatively press Ctrl L Command L Macintosh to open the Insert Label dialog 4 The item is now a label Press Enter to obtain the result You can change the formatting of equation labels From the Format menu select Labels and then Label Display In the Format Labels dialog select one of the numbering schemes Optionally enter an appropriate numbering prefix Figure 2 23 Format Labels Dialog Adding a Prefix 56 2 Maple Tools and Resources 2 5 Worksheet Formatting Features Markers Maple displays markers for formatting features in a vertical bar along the left pane of the worksheet Icons beside associated text or input represent document blocks and hyperlink bookmarks To activate markers From the View menu select Markers Document Blocks Document blocks allow you to hide input or output 1 D and 2 D content within a specified area You can combine text and 2 D content in the same line Document blocks can be collapsed to hide input or output or expanded to reveal Maple code This feature is useful when creating a presentation where for example the Maple programm
43. l user interfaces to various routines Curve Fitting a graphical user interface to commands in the CurveFit ting package Data points can be entered as independent and dependent values Data Analysis a graphical user interface to the data analysis commands in the Statistics package Import Data a graphical user interface to read data from an external file into Maple Output is a Maple Matrix Installer Builder a graphical user interface to the InstallerBuilder package in which you can create installers for your Maple toolboxes For information on toolboxes go to http www maplesoft com Library Browser a graphical user interface to manipulate the libraries in a specified directory Maplet Builder a graphical user interface to the Maplets package The Maplets package contains commands for creating and displaying Maplet applications point and click interfaces For a definition of Maplets see Maplet Applications page 39 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 only in the Standard Worksheet interface ODE Analyzer a graphical user interface to obtain numeric or symbolic solutions to a single ODE or a system of ODEs You can also plot the solution Optimization a graphical user
44. lick an object or expression The actions available on the context menu depend on the properties of the object or expression For 2 3 Point and Click Interaction 27 example you can manipulate and graph expressions enhance plots and format text Example Context Menus Figure 2 8 Right click Control click Expressions 28 2 Maple Tools and Resources Figure 2 9 Right click Control click Expressions to Graph Results 2 3 Point and Click Interaction 29 Figure 2 10 Right click Control click Plots to Change Display Options Figure 2 11 Right click Control click Text 30 2 Maple Tools and Resources Task Templates Task templates help you perform a specific task in Maple such as Performing a mathematical computation for example solving an equation symbolically or numerically or determining the Taylor approximation of a function of one variable Constructing a Maple object for example a function Creating a document for example an application The tasks are organized in the help system by subject to help you quickly find the appropriate task Each task is a collection of Maple worksheet con tent such as 2 D mathematics commands embedded components for ex ample buttons and plots that you can directly insert into your worksheet You specify the parameters of your problem and then run the worksheet 2 3 Point and Click Interaction
45. math nota tion Displayed in a format similar to that found in business and education documents gt Access from the Insert gt 2 D Math menu To switch between 1 D and 2 D Math press the F5 key When using 2 D Math the Math mode icon is highlighted in the toolbar 2 D Math Executable Maple notation Usually an expres sion that Maple can evaluate gt factor x 2 2 x 1 Access from the Insert gt Maple Input menu To switch between 1 D and 2 D Math press the F5 key When entering Maple Input or text in a text region the Text mode icon is highlighted in the toolbar Maple Input 1 D Math 42 2 Maple Tools and Resources 2 D Math The default 2 D Math feature allows you to enter content in standard math notation gt gt Tip Use the key that is x 2 to enter Use the right arrow key to leave the exponent Basic Maple Functions The following are examples of basic Maple functions gt gt gt 2 4 Commands 43 gt To use a palette with 2 D Math 1 Ensure the palette you require is visible If necessary from the View menu select Arrange Palettes 2 Ensure that you are in Math mode If necessary press F5 to switch between 1 D Math Text mode and 2 D Math Math mode 3 With your mouse click a palette expression The expression is displayed in 2 D Math notation in the execution group of the worksheet 4 The first placeholder is
46. n Process large datasets for industrial engineering and research applica tions Solving a Problem When solving a problem you can Select the best resource to quickly find the solution or the right guidelines to a step by step process Document the solution as you work through the problem 4 1 Introduction to Maple Figure 1 2 A Selection of Maple Resources for Solving Problems 1 1 How Maple Helps You 5 Accessing Resources Your work with the Maple program is supported by numerous resources Description Tutors Assistants Task Templates and Maple Calculator Over 40 interactive tutors help beginner users gain insight and understanding of topics in precal culus calculus multivariate calculus vector cal culus and linear algebra courses Some tutors help you work through a problem step by step From the Tools menu select Tutors and then one of the topic submenus Tutors Assistants help you accomplish many tasks such as solving ODEs and ODE systems creating plots and matrices supporting curve fitting and per forming unit conversions From the Tools menu select Assistants and then one of the topic submenus Assistants Tasks show the steps required to solve a problem Each template is a collection of Maple worksheet content such as 2 D Math embedded compon ents commands and plots that you can insert into your worksheet From the Tools
47. ng expressions Arrows a palette of arrow symbols for constructing expressions Constants and Symbols a palette of constants and symbols for con structing expressions 2 3 Point and Click Interaction 37 Punctuation a palette of various punctuation symbols such as the re gistered trademark and copyright symbols for inserting into text regions Miscellaneous a palette of miscellaneous math and other symbols outside the above categories Figure 2 15 Common Symbols Palette Alphabetical Palettes Roman Extended Upper Case Roman Extended Lower Case Diacritical Marks Greek Figure 2 16 Cyrillic Script Open Face and Fraktur Note Use the Roman Extended Upper Case and Lower Case palettes for accents such as grave or umlaut 38 2 Maple Tools and Resources Figure 2 16 Greek Alphabet Palette Placeholders and the Tab Key As an illustration click the exponent button in the Expression palette The expression is displayed with the first placeholder highlighted To move to the next placeholder use the Tab key The Tab icon in the toolbar allows you to set the Tab key to move between placeholders or to indent Tab icon off Allows you to move between placeholders using the Tab key The Tab icon is disabled when using 2 D Math Math mode and as such the Tab key allows you to move between placeholders For details about 2 D Math see Commands page 40 T
48. nt and Click Interaction 23 Assistants 23 Tutors 26 Context Menus 27 Task Templates 31 Palettes 34 Maplet Applications 39 2 4 Commands 40 The Maple Library 40 Commands in the Worksheet 41 Learning About Commands and Packages 50 Using Examples to Learn about Commands 53 Equation Labels 54 2 5 Worksheet Formatting Features 57 Markers 57 Document Blocks
49. o http www maplesoft com 2 In the menu of the main Web page click Resources and then Research Powertools or Education Powertools PowerTools 12 1 Introduction to Maple Description Web Site Resources Maple Web site of productivity tools for en gineers and scientists online seminars and training subscription information on the Ex tended Maintenance Plan EMP and other resources 1 Go to http www maplesoft com 2 In the menu of the main Web page click Resources Welcome Center and then the Corporate and Government link Corporate and Government Maple Web site of productivity tools for en gineers scientists and applied mathem aticians Covers the following application areas finance signal processing and commu nication optimization electronics chemical and mechanical systems control systems design and biotech and pharmaceutical fields 1 Go to http www maplesoft com 2 In the menu of the main Web page click Industry and select one of the topics Industry and Government 1 1 How Maple Helps You 13 Description Web Site Resources Maple Web site of Maple tutorials and graphics help with classes student FAQs instructor pages applications by students the newest release of Maple and Maple books 1 Go to http www maplesoft com 2 In the menu of the main Web page click Academic and then Student Center Student Center 14 1 Introduction
50. p Page and Example Worksheet The help system provides command syntax information To access a help page 1 From the Help menu select Maple Help The Help Navigator opens 2 In the search field enter volume of revolution and click Search The search results include the command help page the dictionary definition and the associated tutor help page 3 Review the calling sequence parameters and description in the Stu dent Calculus1 Volume of Revolution help page See Figure 3 3 4 Copy the examples into your worksheet From the help system Edit menu select Copy Examples 5 Close the Help Navigator 3 1 Calculus Example 67 6 In your worksheet from the Edit menu select Paste The examples are pasted into your worksheet 7 Run the examples and examine results Figure 3 3 Student Package Help Page for VolumeOfRevolution Command To access an example worksheet 1 In the worksheet enter index examples The Index to Example Worksheets opens 2 Expand the Calculus topic 68 3 Using Maple 3 Click the Calculus1IntApps link The Calculus1 Applications of Integ ration worksheet opens See Figure 3 4 4 Expand the Volume of Revolution topic 5 Examine and run the examples Figure 3 4 Example Worksheet Other Ready To Use Resources The Maple Application Center contains free user contributed applications related to mathematics education science engineering compute
51. r science statistics and data analysis finance communications graphics and more To access a free application for volume of revolution 1 Go to the Maplesoft Web site http www maplesoft com 2 In the menu of the main Web page click Resources and then Education PowerTools 3 Click the Calculus II link and then the CalculusII Complete Set of Lessons link 3 1 Calculus Example 69 4 Scroll to the Options area and click Download Maple Worksheet See Figure 3 5 5 Login in as a guest or Maplesoft Member 6 Download the zip file 7 Extract the L2 volumeRevolution mws file 8 Run the worksheet and examine the results Figure 3 5 Maple Application Center Powertools 3 2 Optimization Example PROBLEM When sharpening ice skates figure skates speed skates and hockey skates each must be processed by three machines 70 3 Using Maple The following table shows the time in hours required by each machine to process a pair of skates as well as the constraints maximum time in hours per day each machine can operate Maximum operation Hockey skates Speed skates Figure skates 22 1 1 2 1 Machine A 23 1 3 1 1 Machine B 21 1 1 1 4 Machine C The profit on sharpening figure skates is 7 per pair speed skates is 6 per pair and hockey skates is 5 per pair How many pairs of each should be sharpened per day to obtain maximum profit
52. rm for an indefinite or definite sum sum Set variable properties and relationships between variables Similar functionality is provided by the assuming command assume is Compute the value of an expression under assumptions assuming Apply simplification rules to an expression simplify Distribute products over sums expand 4 2 Top Commands 81 Normalize a rational expression normal Convert an expression to a different type convert Type checking command In many contexts it is not necessary to know the exact value of an expression it suffices to know that an expression belongs to a broad class or group of expressions that share some common properties These classes or groups are known as types type Generalized series expansion series Apply a procedure to each operand of an expression map 82 4 The Next Step Index Symbols icon 41 icon 41 help page icon 21 help topic 8 20 1 D Math 46 using palettes 48 2 D Math Input 43 using palettes 44 A accents 38 alphabetical palettes 38 Application Center description 12 applications 54 Help menu 54 Assistants CurveFitting 24 Data Analysis 24 description 6 Import Data 24 Installer Builder 24 Library Browser 24 Maplet Builder 24 menu access 6 ODE Analyzer 24 Optimization 24 72 Plot Builder 25 Tools menu 23 Unit Converter 25 automatic command completion 51 B bookmark 57
53. s access to the values of various physical constants for example the velocity of light and the atomic weight of sodium These values are required to solve equa tions in fields such as chemistry and physics The ScientificCon stants package provides the units for each of the constant values allowing for greater understanding of the equation The package also provides units matching for error checking of the solution The quantities available in the ScientificConstants package are di vided into two distinct categories Physical constants Properties of chemical elements and their isotopes ScientificConstants The ScientificErrorAnalysis package provides representation and construction of numerical quantities that have a central value and an associated uncertainty or error which is a measure of the degree of precision to which the quantity s value is known Various first order calculations of error analysis can be performed with these quantities ScientificErrorAna lysis The Student package is a collection of subpackages designed to assist with the teaching and learning of standard undergraduate mathemat ics Many commands display functions computations and theorems in various ways including stepping through important computations The Student package contains the following subpackages Calculus1 single variable calculus LinearAlgebra linear algebra MultivariateCalculus multivariate calculus
54. sign Digital Filter Design Frequency Domain System Identification Harmonic Oscillator Mathematical Model to Simulation Code Mobile Robot Mobile Robot Modeling and Simulation Black Scholes Model Example Worksheets Embedded executable worksheets covering topics that demonstrate syntax or invoke Maplet applications make complex problems easy to solve and visualize You can copy and modify the examples as needed Topics include Algebra Applications Fin ance Scientific Constants Scientific Error Analysis Calculus Connectivity Code Generation External Calling Differential Equations Discrete Mathematics General Numerics General Symbolics Geometry In tegration Integral Transforms Language and System and Mathematical Visualizations From the Help menu select Manuals Dictionary and more and then Applica tions and Examples Applications and Example Worksheets 1 1 How Maple Helps You 9 Description Tour and New User Roadmap The Maple Tour consists of interactive ses sions on the following topics Ten Minute Tour Numeric and Symbolic Computations Matrix Computations Differential Equations Special Functions Optimization Statistics Programming and Code Generation Dictionary of Math and Engineering Terms Units and Tolerances Education Assessment Maple T A OpenMaple
55. the Options group box select Maximize 10 Click Solve 11 Click Done to return to the Optimization Assistant 12 Click Quit to return the solution 167 and the values for f s and h to the Maple document 3 2 Optimization Example 73 Check for Instructions Help Page The help system provides command syntax information To access a help page 1 From the Help menu select Maple Help The Help Navigator opens 2 In the search field enter Optimization and click Search 3 The search results include the Overview of the Optimization Package help page dictionary definitions and example worksheets 4 With the Overview page displayed in the right pane review the description See Figure 3 7 Figure 3 7 Help Page Overview of the Optimization Package In general you can Review the calling sequence parameters and description 74 3 Using Maple Copy the examples into your worksheet From the help system Edit menu select Copy Examples Close the Help Navigator In your work sheet from the Edit menu select Paste The examples are pasted into your worksheet Run the examples and examine results In this case you can also open the many dictionary definitions and additional help pages 1 In the Overview of the Optimization Package help page click the linear programs link See Figure 3 8 The dictionary link is indicated by one of the arrows in the figure The line
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