Maple Getting Started Guide
Contents
1. Commands Las or Package Commands Figure 37 Help Page Overview of the Optimization Package 76 3 Using Maple In general you can Review the calling sequence parameters and description Copy the examples into your worksheet From the help system Edit menu select Copy Examples Close or minimize the Help Navigator In your worksheet 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 linear programming definition is displayed Note The definition also contains a link to the associated Maple Optimiza tion package command LPSolve linear programming stack ofa tion ol ow is spt bue neto af oles paca operatic eel cora foo wy an eds lare see af gagnant wt amies eed See aleo rss sce eae eerie 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 32 Optimization Example 77 Optimization2. 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 mathematic ible and complete form That tool is provides a tool in an access ple 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 2 1 Introduction to Maple Digital Signal Processing lt d lt a i J Figure 1 1 Example Interactive Document in Maple 1 1 How Maple Helps You 3 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 icademic papers or books Insert hyperlinks to other files Web sites or email addres Insert images spreadsheets tables and symbols Embed graphical user interface compone
3. Products and Solutions for Students Maple Web site af Maple tutorials and help with classes student FAQs nstuctor pages applications by students the newest release of Maple and Maple books 1 Go to http wwwamaplesoft com In the menu of the main Web page click Product and Solutions and then For Stu 2 Maple Tools and Resources chapter japie Maple Help System iges and oiher resources Point and Click Interaction ious interfaces designed to help you solve problems quickly Commands Maple commands and Tar Worksheet Formani Formatting Working in Document Mode the blank sheet Maple Document environment quickly solving problems This guide was created using Maple 2 1 Starting Maple In this section arting the Standard Worksheet Interface The Maple Worksheet Basics 16 2 Maple Tools and Resources Starting the Standard Worksheet Interface To start the Standard Worksheet interface in Windows From the Start menu select Programs Maple Maple Alternatively Double click the Maple desktop icon Mudo Doubleclick the Maple application con i the Finder ora 7 Enter the ll path for example Fusr iocalimaple binixmaple Alternatively 1 Add your Maple directory for example usrlocal maple bin to your command search path P Enter xmaple The Maple Workshe
4. manipulate Matrices and Vectors and solve linear algebra problems LinearAlgebra routines operate on three principal data structures Matrices Vectors and scalars Naples Maglerappicaion is a graphical user interface comin ser point and click access to the power of Maple Users can perform x plot functions or display dialogs without using et interface works Maplets package contains commands and subpackages to create a Maplet application To create Maplet applications in a graphical interface environment use the Builder The Maplet Builder is available only in the Standard Worksheet interface From the Tools menu select Assistants and then Builder 79 80 4 The Next Step RealDomain The RealDomain package provides an environment in which he default Maple behavior of assuming that the basic underlying number system is the complex field is replaced by the assumption that the basie underlying number system is the field of real numbers SelentificConstants The SelentificConstants package provides access to the values of various physical constants for example the velocity of light and the atomic weight of sodium These values required to solve equa tions in fields such as chemistry and physics The SeientificCon stants package provides the units or each of the constant values allowing for greater understanding o
5. 2 18 I D Math Input Converted to 2 0 Math Input 50 2 Maple Tools and Resources 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 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 lect List of Commands 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 package 1 From the Help menu select Manuals Dictionary and more 2 Select List of Packages use a package command specify both the package and command names using the syntax packagelcommandYarguments If you are using number of commands in the package load the package using the with command To load a package Atthe Maple prompt enter the with command followed by the package name enclosed in parentheses and terminated with a semicolon 1 0 Math input Then press Enter 24 Commands 51 Using the with command to Toad the Optimization package A Tist of all commands in the package reris chi meae displayed To suppress the display of all command na
6. 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 3 1 Calculus Example 67 The command is inserted into your worksheet T Volume of Revolution T gt rot s Cage Val Von d aan 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 Help 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 Inthe 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 Caleulust 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 68 3 Using Maple 6 In your worksheet
7. Dictionary of Math and Engineering Terms Units and Tolerances J Education Assessment Maple OpenMaple H Maplets and MapleNet From the Help menu select Take a Tour of 141 How Maple Helps You 11 Tour and New User Roadmap Description New User Roadmap Find the most efficient path to solving a problem immediately or learning principles fand reviewing major features From the Help menu select Manuals Dictionary and more and then New User Roadmap 12 1 Introduction to Maple Site Resources Description Technical Support Online Maple Web site und resource for FAQs downloads and service packs links to discus sion groups and request technical support om 1 Go to http wwwamaplesott com 2 In the menu of the main Web page click Customer Support and then Support and Customer Service Application Center Maple Web site resource Tor fee 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 rwwimaplesoft com 2 In the menu of the main Web page click User Community and then Application Center Maple Web site resource for free complete course curricula and add on Maple packages and courses develop
8. L PSolve alinear program Calling Sequence constr b opt Parameters mma dene ciun pae opea qtii ofthe fm vu ahere opti of eum dept iaenralnmes ron sartor eur Sve temm T Descriplion command selves a ta sragram LF vich invokes computing the or minum of near tiec funcion sueco ear constans his pepe te ten teger ramen used o represant al forma af rteger program ger Programe are erect uana tne assume integervariabies or binaryvariables aptior See the folowing Integer Programming Options secton fer rare information Tis he page describes the ofthe LP Salve command when LP is specie fam summary cts fom pape LPSolve recagrizes protem in farm see e Sc Diss Form page Mathe furm eae t more efcirt computat is mare cole The fist parameter obj ie he obecvefurctin lich must be eresian The second promete consis opal and is a set or ist of relations of or inthe problem varables The problemn arces are ntetemates of type zarm urdi n nh Figure 39 Optimization LPSolve You can use one Maple command to solve the skating problem For inform ation on us
9. Maple Tools and Resources Basie Usage Description 2D Math Default setting Executable standard math nota tion Displayed in a format similar to that found in business and education documents P fax Access from the Insert 2 D Math menu switch between 1 D and 2 0 Math press the IFS key Tes Me When using 2 D Math the Math mode icon is highlighted in the toolbar Input 120 Math Executable Maple notation Usually an expres sion that Maple can evaluate factor x 2 2x 1 Access from the Insert Maple Input menu To switch between 1 0 and 2 D Math press the IFS key em When entering Maple Input or text in a ext region the Text mode icon is highlighted in the toolbar 24 Commands 43 2 D Math The default 2 D Math feature allows you to enter content in standard math notation gt restart gt facto 2x 1 rip Use the key that is x 2 to enter 2 Use the right arrow key to leave the exponent Basic Maple Functions The following are examples of basic Maple functions gt cos a sin a af a 43473 1 gt dim G Jim 44 2 Maple Tools and Resources Ein To use a palette with 2 D Math 1 Ensure the palette you require is visible If necessary from the View menu select Palettes and then Arrange Palettes 2 Ensure that you are in Math mode If nec
10. Shit underscore Square root and then com mand symbol comple tion shorteut key Arrow keys navigating the ex pressions 2 6 Working in Document Mode 61 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 Document Mode wing Maple Code i 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 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 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 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 Your company is designing a boule for its
11. T Tab icon 39 Tab key 39 table of contents help system 20 task menu access 7 volume of revolution 65 task template 31 technical support description 12 text right click 30 tools visualization 3 Tools menu assistants 22 tutors 26 Index 87 topic search 20 start Maple 16 tour 10 Worksheet mode 17 18 58 tutorials worksheets help system 20 running 41 tutors ws accessing 26 icon 20 curve analysis example 27 description 6 menu access 6 Tools menu 26 using 26 volume of revolution 64 Uu Units package description 81 Units Calculator 24 UNIX command complete 52 60 start Maple 16 VectorCalculus package description 81 View menu in help system 21 markers 57 using palettes 48 visualization commands tudent 26 volume of revolution example 64 Windows command complete 52 60 88 Index
12. and more gt Manuals gt Getting Started Guide lassie Worksheet Basie worksheet environment for older computers with limited memory Command line version Command line interface without graphical user inter faces features for solving very large complex problems lor batch processing with scripts Maplesofi Graphing Calculator Microsoft Windows only Graphical calculator interface to the Maple computational lengine Using it you can perform simple computations land create customizable zoomable graphs vi Preface Tnterface Description Graphical user interface containing windows textbox legions 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 worksheet or command line interfaces 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 for Interactive use through Maple commands which may offer advanced functio
13. f x gt sum afk x k k 0 m produet blj x j dr or To use a palette with 1 0 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 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 0 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 the next placeholder and not indent For details see Placeholders and the Tab Key page 39 Press Enter 24 Commands 49 Why Use Palettes in 1 D Math Using a palette that uses standard notation teaches you the related Maple command syntax You control the appearance of expressions the worksheet You convert 1 D Math to 2 D Math To convert 1 0 to 2 D math input 1 Enter an expression in 1 0 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 D m mg p Figure
14. from the Edit menu select Paste The examples are pasted into your worksheet 7 Run the examples and examine results Student Calculus1 J VolumeOfRevolution vole orersation af Calling Sequence a opts stah x a b opt a b opt tb a b ops Parameters p sehr grecs end points of the carve cose where cae of anis functnoptons fuxion2epoes oot revludaapuas vdmeopias soumedopdons vis ct Slt sec op epi Descpon command ems te vehe ote ore ValancORevihlonfi x u D cane rame vla sehn berate Genio feo ad le Boe oto By epson can spe ht the command rums a ht ortu ied atest Wie independent variable om be il tine Boa ops the ened wt be lods de ralig suc Figure 3 3 Student Package Help Page for VolumeOfRevolution Command To access an example worksheet 1 In the worksheet enter index examples The Example Worksheet Index opens 2 Expand the Calculus topic 3 1 Calculus Example 69 3 Click the CaleulusIntApps link The 1 Applications of Integ ration worksheet opens See Figure 3 4 4 Expand the Volume of Revolution topic 5 Examine and run the examples Calcu
15. indicate the boundaries of the document block Input prompts and execution groups are not displayed in document blocks 58 2 Maple Tools and Resources Em vere sco esaet For details on using document blocks see the Maple User Manual Bookmarks bookmark designates a location in active worksheet that can then accessed from other regions in your worksheet or by using hyperlinks in other worksheets Markers indicate the location of the bookmark Section 1 1 Section 1 2 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 Doc ent mode is described as follows A blank work area An input prompt or execution group is nor displayed although it can be inserted 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 2 6 Working in Document Mode 59 Pressing Ctrl Command displays results inline for Macintosh TI evaluates and Using the context menu ite Evaluate and Display Inline Pressing the Enter key This evaluates and displays results on the next line or if set in the Options dialog simply evaluates Using the context
16. menu item Evaluate 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 xy 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 60 2 Maple Tools and Resources 2 From the context menu select Evaluate and Display Inline The result is displayed with an sign day tay Common Key Strokes for Symbols and Formats Palettes are the quickest way to enter special formats however use the following key strokes you can also Ssmbol Formats Key Automatically Generated in Document emeret 2D FS 1 Es Example using fraction 1 versus 1 4 kommaniymbol Escape Macintosh ai completion Cui Space win dows ES Space UNIX action Forward slash 1 4 exponent super caret script Use right arrow key to leave superscript area subscript
17. new spring water product The boule must contain 18 ounces of water and the eight 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 You want to teach your students the concept Volume of Revol tion Specifically you want to plot and compute the volume of a solid of evolution generated by rotating f x x lt b about an axis line parallel to an axis 3 64 3 Using Maple Tutors Check for 7 Existing Took Templates Pages Problem p Check for 7 S Check for Sher Ready foe Se Resources Sher Check for Existing Tools Tutor Begin by examining the Tools menu for a Tutor graphical user interfa 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 Student Calculus VolumeOfRevotution Tutor The Volume of Revolution Tutor is displayed See Figure 3 1 The tutor a graphical user interface that allows you to enter a function and an interval w and manipulate the corresponding plot and view the full Ma
18. page Figure 2 2 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 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 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 Question mark icon indicates a help page WS icon indicates an example worksheet Example worksheets open ina new tab in the worksheet window D icon indicates a Definition TE icon indicates a Task template IM icon indicates a Manual Manuals open in new tab in the worksheet win 2 2 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 as worksh
19. various ways and support for stepping through important computations visualization commands are tools that create plots and animations showing the geometric interpretation of important concepts computation commands help you study the techniques of computa tion while solving problems For example using the Calculus 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 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 23 Point and Click Interaction 27 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 uc Cae Ame vo Figure 2 6 Tutor Example Calculus 1 Curve Analysis Context Menus Maple dynamically generates a context menu when you right click for Macintosh Control click an object or expression The actions available on the context menu depend on the properties of the object or expression For example you can manipulate and graph expressions enhance plots and format text 28 2 Maple Tools and Resources Example Context Menus nme E joan erin p semen
20. 3 The Assistants are graphical user interfa to various routines Back Solver a worksheet that allows you to take a mathematical for mula which involves multiple parameters enter values for all but one of the parameters and solve for the remaining one You can also produce a graph that shows the behavior of the formula as one of the parameters 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 Statisties 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 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 direct
21. 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 warning and information messages Tables images plots sketches or spreadsheets 24 Commands 55 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 fea Tc Figure 2 20 Inserting an Equation Label Ja ee ene Figure 2 21 Equation Label To apply equation labels 1 Enter an expression and press Enter Note that the equation label is dis played to the right of the answer in the worksheet 2 In a new execution group enter another expression that will reference output of the previous execution group 56 2 Maple Tools and Resources 3 From the Insert menu select Label Enter the label number in the Insert Label dialog and click OK Alternatively press Ctrl L CommandsL 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 Fo
22. Maple Getting Started Guide Copyright Maplesoft a division of Waterloo Maple Inc 2007 Maple Getting Started Guide Copyright Maples a division of Waterloo Maple Ic 2007 righi reserved electronic mechanical photocopying recording or otherwise Information document to change Contents Preface 1 Introduction to 1 1 How Maple Helps You Creating Interactive Documents Exploring or Visualizing Problems Computing Numeric and Symbolic Solutions Solving a Problem Accessing Resources 2 Maple Tools and Resources 2 1 Starting Maple tarting the Standard Worksheet Interface The Maple Worksheet 2 2 The Maple Help System Accessing the Help System Using the Help Navigator Viewing Help Pages as Worksheets Copying Examples 2 3 Point and Click Interaction Assistants Tutors Context Menus Task Templates Palettes Maplet Applications 24 Commands Maple Library Commands in the Worksheet Learning About Commands and Packages Using Examples to Learn about Commands Equation Labels 2 5 Worksheet Formatting Features Markers Document Blocks Bookmarks 40 50 53 54 57 57 57 58 iv Contents 2 6 Working in Document Mode Starting New Document Entering Math Common Key Strokes for Symbols and Formats Opening Documents Viewing Maple Code in Document Mode 3 Using Maple 3 1 Calculus Example Check for Existing Tools Tutor Check for Existing Tools Task Templa
23. Maple commands Packages contain related specialized 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 comer Enter Maple commands at this prompt for Maple to recognize your entry as Maple Input 1 0 Math or 2 D Math and execute the command 2 4 Commands Basic Usage Description gt Running the entire worksheet executing all commands e Tn the toolbar click the S icon From the Edit menu select Execute Worksheet Executing onc command Place the cursor in any Maple input region inthe execution group and press the Enter key Execuing scecsd area gt In the toolbar click the T icon From the Edit menu select Execute Selection Semicon separator Terminate 7 or ZD command with a semicolon ad output is displayed important 1 0 commands must terminate with a sentcolon or coton Catan Statement separator Terminate D ZD command with a colon and output is not displayed important 1 D commands must terminate with a semicolon or colon restarts restart command causes Maple clear is interna memory Alternatively in the toolbar click the restart icon e5 For specifie details refer to the Maple User Manual 42 2
24. Maple worksheet content such as 2 D Math embedded compon commands and plots that you can insert int your worksheet From the Tools menu select Tasks and then Browse Available for use as your Maple insala ion A convenient calculator interface using Maple technology Microsoft Windows only From the Start menu select Maple and then Maple Calculator 8 11 Introduction to Maple Online Help and Examples Description Help Pages The online help systern helps you find inform ation about a specifie topic command pack age or feature You can access help three ways gt From the Help menu select Maple Help In the toolbar click the Help icon gt Inthe worksheet enter For example type 2LinearAlgebra and then press Enter More than S000 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 ar expand alphabetical listing 1 How Maple Helps You 9 Online Help and Examples Description Applications and Example Worksheets Demonstration DC Motor Control Design Applications Sample applications demonstrate how Maple can be used to find and document a solution specifie problem Some applications all
25. access 6 examples 21 ODE Analyzer 23 corporate Optimization 23 72 Web site 11 13 83 84 Index curve analysis example 27 Curve Fitting Assistant 23 D D icon 20 Definition linear programming 76 document blocks 57 Document mode 58 documents running 41 Edit menu in help system 21 example calculus 63 optimization 71 example worksheets copy 21 description 9 menu access 9 examples index 53 exclamation point 41 execute command 41 execution group 41 expressions graph results 29 palettes 36 rights F Favorites palette 34 28 format labels 56 G government Web site 13 H Handwriting palette 34 Help Navigator using 20 help system accessing 19 description 8 dictionary 20 Edit menu 21 76 Help Navigator 19 icon 8 manuals 20 search 20 table of contents 20 tasks 20 search 20 tutorials 20 View menu 21 volume of revolution 67 1 icons 1 exclamation point 41 3 exclamation points 41 in help system 20 open as example worksheet 21 Tab 39 industry Web site 13 installation 15 Index 85 Installer Builder Ass interactive commands Student 27 interfaces list 16 tant 23 K key strokes 60 L library 40 library browser assistant 23 LinearAlgebra package description 79 LPSolve command 76 M M icon 20 Macintosh command complete 52 60 context menus 27 start Maple 16 manual command compl
26. e or Templates 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 TET Figure 2 1 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 22 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 Inthe 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 specific help
27. ed by experts in their fields to help users configure Maple for re search in specifie application areas 1 Go to bttpz wwwcmaplesoft com 2 In the menu of the main Web page click ser Community and then Application Center In the sidebar of the Web page click Re search Powertools or Education Powertools 1 1 How Maple Helps You 13 Web Site Resources Description Corporate and Government Maple Web site of productivity tools for en gineers und scientists online seminars and training subscription information on the Ex tended Maintenance Plan EMP and other 1 Go to http wwwamaplesoft com 2 In the menu of the main Web page click Site Resources Welcome Center and then the Corporate and Government lik in the body of Ihe Web page Maple Web site of productivity tools Tor en gineers scientists and applied mathem 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 maplesott com 2 In the menu of the main Web page click Site Resources Welcome Center and then the Corporate and Government link in the body of the Web page 3 In the sidebar of the Web page click the Industry and Government 14 1 Introduction to Maple Web Site Resources Description
28. eets that you can execute 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 P ae ee click the open current help page in work sheet window icon Copying Examples Instead of opening the entire page as a worksheet you can copy the Examples section to worksheet 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 Tun 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 wea 7 Porta Jona ii See pond Cite lei Coleone y E seca Figure 2 3 Accessing the Assistants from the Tools Menu 2 3 Point and Click Interaction 2
29. er te Arb apta errore n Pee Tee cr Cala Sg Vail og Apna ovde bn Figure 2 11 Browse Tasks Dialog Previewing Tasks Maple tasks can be previewed in three way 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 2 3 Point and Click Interaction 33 The tasks are sorted by subject to help you quickly find the desired task In the Browse Tasks dialog or Help Navigator you can view tasks without erting 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 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 wh
30. essary press FS to switch between 1 0 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 highlighted Enter your expression and if neces sary use the Tab key to move to the next placeholder Press Enter Why Use Palettes 2 D Math Ifyou are new Maple user palettes make entering expressions easier than entering syntax and reduce the possibility of introducing typing rors Your worksheet uses standard notation for mathematical content In the following figure compare the 2 D and 1 D Math input cmm Loe int rx row 24 Commands 45 You can control the appearance of expressions in the worksheet You 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 expres is displayed in 1 0 Math input notation 4 Press Enter to evaluate the expression gt F int sin x x gt faa gt b 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
31. et You can access the power of the Maple computation engine through a variety of user interfaces Standard Worksheet 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 2versions help page The first Maple session opens with the Startup dialog explaining the differ ence 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 2 1 Starting Maple 17 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 Basics Maple documents are saved as mw files They consist of files created in Worksheet or Document mode To start a Maple sessio 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 Mod
32. ether the task variables have as signed values in your worksheet If any task variable is assigned the Task Variables dialog opens to allow you to modify the names Maple uses the edited variable names for all variable instances in the inserted task By default the Task Variables dialog is displayed only if there is a naming t it to display every time you insert a task conflict You can s 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 Global is necessary 34 2 Maple Tools and Resources 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 collections of related items that you can insert by clicking or drag and dropping into a document Palettes contain Symbols like V Layouts like an item with a superscript and subscript Mathematical operations like a definite inte
33. etion 52 Maple Application Center solids of revolution 69 Maple Web site resources 12 Maplet Builder Assistant 23 create 39 top package 79 markers isplaying 57 math dictionary description 8 help system 20 mathematical palettes 37 numeric compute 4 ODE Analyzer Assistant 23 Optimization Assistant 23 72 example 71 LPSolve 77 Options dialog 45 auto command complete 51 command complete 51 P packages definition 40 top 79 palettes 1 D Math 48 2 D Math Input 44 accents 38 alphabetical 38 arrange 48 expression 36 favorites 34 mathematical 37 overview 34 symbol recognition 34 paste examples 21 Plot Builder Assistant 24 plots point and click 22 PowerTools 69 description 12 question mark icon 20 R RealDomain package description 80 resources access 6 diagram 5 in help system 20 right click expressions 28 graphic results 29 plots 30 text 30 running documents 41 worksheets 41 5 Scientific Constants 24 package description 80 ScientificErrorAnalysis package description 80 search help system 20 selection execute 41 semicolon usage 41 skates optimization example 71 solids of revolution example 64 solutions overview 4 Special Functions 24 Standard Worksheet 16 start Maple standard worksheet 16 statement separator 41 Student Center 14 package 26 top packages 80 symboli compute 4
34. f the equation The package also provides units matching for error checking of the solution The quantities available in the SeientificConstants package are di vided into two distinct categories Physical constants Properties of chemical elements and their isotopes ScicntiicErrorAma lysis ScientificErrorAnalysis package provides representation and construction of numerical quantities that have central value and an associated uncertainty or error which is a measure of the egre lof precision to which the quantity s value is known Various first order calculations of error analysis can be performed with these quantities Student Student package is a collection of subpackages designed to assist with the teaching and leaming of standard undergraduate mathemat cs Many commands display functions computations and theorems in various ways including stepping through important computations The Student package contains the following subpuckuges Calculusl single variable calculus LincarAlgebra linear algebra MultivariateCaleulus multivariate caleulus Precalculus precaleulus J VeetorCalculus multivariate vector calculus 42 op Commands 81 Units VectorCaleulus 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 a
35. gral with placeholders for the integrand variable of integration and endpoints of the interval of integration You can create a Favorites palette of the expressions and entities you use often The Handwriting 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 23 Point and Click Interaction 35 Figure 2 12 Handwriting Palette By default palettes are displayed when you launch Maple view palettes 1 From the View menu select Palettes 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 using palettes with Maple Input 1 0 Math and Standard Math 2 0 Math Input notation see Commands page 40 36 2 Maple Tools and Resources 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 ha
36. ing commands in packages see Maple Tools and Re sources page 15 gt with Optimization The same solution is returned using the LPSolve command 78 3 Using Maple een gt LPSolve 2 f 65 5 maximize constraints assume nonnegint 167 00000000000 s 10 f 11 6 The assume nonnegint and maximize options are described in the help page gt assume nonnegint Assume ill variables are non negativ teers maximize or maximize true Maximize the objective function By default that is if you exclude the maximize option the LPSolve command computes the minimum 4 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 Manu 1 From the Help menu select Manuals Dictionary and more 2 4 1 Top Packages Package Name Description t Manuals and then User Manual CodeGeneration The CodeGeneration package collection of commands and subpackages that enable the translation of Maple code to other pro eramming languages such as C Fortran Java MATLAB and Visual Basic LinearAlgebra The LinearAlgebra package contains commands to construct and
37. is displayed 3 Select the correct completion from the list gt reads 24 Commands 53 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 General Numerics General Symbolics Geometry Integration Integral Transforms Language and System Mathematical Visualizations 54 2 Maple Tools and Resources Elle Integration penile Y Complete Ellipic Integrals 955 Paar Figure 2 19 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 access Applications from the Help menu From the Help menu select Manuals Dictionary and more and then Applications and Examples The Applications and
38. lows you to move between placeholders For details about 2 0 Math see Commands page 40 Tab icon on Allows you to indent in the worksheet using the Tab Key E Maplet Applications Maplet application is 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 interfa The following simple Maplet contains a textbox region a button and a label prompting you to enter an equation ims CS Cx Figure 2 16 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 20 2 Maple Tools and Resources 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
39. lus 1 Applications of integration rincon jte 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 computer science statistics and data analysis finance communications graphics and more 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 User Community and then Application Center 3 In the sidebar click Education PowerTools 70 3 Using Maple 4 Click the Calculus II link and then the CalculusII Complete Set o Lessons link 5 Scroll to the Options area and click Download Maple Worksheet See Figure 3 5 6 Login in as a guest or Member 7 Download the file 8 Extract the L2 volumeRevolution mvs file 9 Run the worksheet and examine the results mouu Ir eenent ui Camps zz Figure 3 5 Maple Application Center PowerTools 3 2 Optimization Example 71 3 2 Optimization Example PROBLEM When sharpening ice skates figure skates speed skates and hockey skates cach must be processed by three machines The following table shows the time in hours required by each machine to process a pair of skates as well as the con
40. ly 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 interface to the solver commands in the Optimization package The Optimization package is a collection of commands for numerically solving optimization problems which involve 24 2 Maple Tools and Resources 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 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 plot of the objective function in the region of the solu tion or if 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 Scientific Constants an interface to the Maple database of scientific constants with over 20000 values of physical constants and pro
41. mes end the with Optimiz lation command with a colon 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 mand disable automatic command completion From the main menu select Tools gt Options gt Interface tab Clear the Automatic command completion check box 52 2 Maple Tools and Resources Manual Command Completion Manual command completion is always enabled use manual command completion 1 Begin entering a command in the worksheet 2 To list Maple packages commands and functions that match the entered text select Tools gt Complete Command or use short cut keys Escape Macintosh Ctrl Space Windows Ctrl Shift Space UNIX If there is unique completion it is inserted Otherwise a list of matches
42. nality 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 in introduction to the following Maple features This manual provides Worksheets and powerful interactive documents The help system 2 Point and click interaction with various interfaces to help you solve problems quickly Maple commands and standard math notation A road map for solving problem Preface vii For a complete list of manuals study guides toolboxes and other resources visit the Maplesoft Web site at http wwwmaplesoft 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 f Iback For suggestions and comments related to this and other manuals contact doc maplesoft com viii Preface 1 Introduction to Maple Don t worry about your difficulties in Mathematics I can assure you mine are still greater Albert Einstein
43. nd U S survey miles Maple also contains Units palettes that allow you to quickly enter the unt for an expression The VectorCalculus package is a collection of commands that form multivariate and vector calculus operations large set predefined orthogonal coordinate systems is available computa tions in the package can be performed in any of these coordinate systems I contains a facility for adding a custom coordinate system using that new coordinate system for your computations 4 2 Top Commands Command Name Description plor Create a two dimensional plot of functions solve Solve onc or more equations or inequalities Tor their unknowns Solve one or more equations using floating point arithmetic fevar Evaluate an expression at a given oin Numerically evaluate expressions Solve ordinary diferential equation ODES m Compute an indefinite or definite integral Compute an ordinary or partial derivative as the context dictate liit Calculate the Tinting value ora function sum For symbolic summation lis used 1o compute a closed form indefinite definite sum assumes Se variable properties and relationships between variables Similar functionality is provided by the assuming command assuming Compute the value of an expression under assumptions simplify Apply simplification sul to an expres
44. ns Solving a Problem When solving a problen 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 1 1 How Maple Helps You 5 morsu wea Attempting to solve a problem mm Sosane or prn Mery te rd Figure 1 2 A Selection of Maple Resources for Solving Problems 6 1 Introduction to Maple Accessing Resources Your work with the Maple program is supported by numerous resources Tutors Assistants Task Templates Description and Maple Calculator Tutors Over 40 interactive tutors help gain insight and understanding of topics in precal calculus multivariate calculus vector cal 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 Asians Assistants help you accomplish many tasks such g solving ODEs and ODE systems creating plots land matrices and supporting curve fitting From the Tools menu select Assistants and then one of the topic submenus 1 1 How Maple Helps You 7 Tutors Assistants Task Templates Description land Maple Calculator Task Templates Tasks show the steps required to salve a problem Each template is a collection of
45. nts Generate two and three dimensional plots and animations Sketch ideas in the worksheet 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 plications wssistants and Maplet ap Create plots and animations in two and three dimensions Right click Control click for Macintosh to export plot and more using context menus onvert manipulate 4 1 Introduction to Maple 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 lange equation sets Derive sophisticated equations Compute parametric solutions to problems Use precision control for maximum accuracy Include units measurement of error id tolerance management within an expression and perform calculations on this expression Process large datasets for industrial engineering and research applica tio
46. ols for constructing expressions Fenced palette of fenced symbols for constructing expressions Arrows a palette of arrow symbols for constructing expressions Constants and Symbols palette of constants and symbols for con structing express Punctuation a palette of various punctuation symbols such as the re gistered trademark and copyright symbols for inserting into text regions 38 2 Maple Tools and Resources Miscellaneous a palette of miscellaneous math and other symbols outside the above categories 1 gt Figure 2 14 Common Symbols Palette Alphabetical Palettes Roman Extended Upper Case Roman Extended Lower Case Diacritical Marks Greek Figure 2 15 Cyrillic Script Open Face and Fraktur Note Use the Roman Extended Upper Case and Lower Case palettes for accents such as grave or umlaut Figure 2 15 Greek Alphabet Palette 2 3 Point and Click Interaction 39 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 E Tab icon off Allows you to move between placeholders using the Tab key HET eons disabled when using D Math Math mode and as such the Tab key al
47. ow for input oF contain animations that you un however their primary use is as demon rations Topics include DC Motor Control Design Digital Filter Design Frequency Domain System Mentification Harmonie Oscillator l Mathematical Model to Simulation Code Mobile Robot Mobile Robot Modeling and Simulation Black Scholes Model M Signal Generation Example Worksheets lEmbedided executable worksheets covering hopies that demonstrate syntax or invoke IMaplet applications make complex problems easy to solve and visualize You can and modify the examples as needed Topics include Algebra Applications Fin lance Scientific Constants Scientific Error Analysis Calculus Connectivity Code Generation External Calling Differential Equations Discrete Mathematics General INumerics General Symbolies Geometry In Integral Transforms Language andl System and Mathematical Visualizations From the Help menu select Manuals Diction lary and more and then Applications and Examples 10 1 Introduction to Maple Tour and New User Roadmap Description Tour The Maple Tour consists of interactive se sions on the following topics J Ten Minute Tour Numeric and Symbolie Computations H Matrix Computations Differential Equations Special Functions Optimization P Statistics Programming and Code Generation
48. p pn Shorter Figure 2 7 Right click Control click Expressions 2 3 Point and Click Interaction gt 29 FS zu Figure 28 Right click Control click Expressions to Graph Results 30 2 Maple Tools and Resources Figure 29 Right click Control click Plots to Change Display Options rre following rest Figure 2 10 Right click Control click Text 2 3 Point and Click Interaction 31 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 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 32 2 Maple Tools and Resources Tamasa Dren noenten slsppreximate Definite Integrat ofa Function Description eum Ld Ec E E a E am
49. perties of chemical elements All of these constants come with the corresponding unit and if applicable with the uncertainty or error that is how precisely we know the value of this constant Special Functions an interface to the Maple database of the properties of over 200 special functions including the Hypergeometric Bessel Mathieu Heun and Legendre families of functions Units Calculator a worksheet that allows you to convert between 500 units of measurement 2 3 Point and Click Interaction 25 Figure 2 4 Assistant Example Curve Fitting 26 2 Maple Tools and Resources Tutors Using the Tools 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 EET p Tusc y coetui gt 2 9 ET UE rudes Compta Parens coram Sims Figure 2 5 Accessing Tutors from the Tools Menu The Tutors are also accessed through the Student package For definition of the term package see Commands page 40 The Student package is a collection of subpackages designed to assist wit the teaching and learning of standard undergraduate mathematics The sub packages contain many commands for displaying functions computations and theorems in
50. ple com mand associated with your entries and selections 3 1 Calculus Example 65 n ep cn regem Figure 3 1 Volume of Revolution Tutor 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 Tasks 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 66 3 Using Maple 3 From the displayed list select Volume of Revolution The Volume of Revolution task is displayed in the right pane of the Browse Tasks dialog See Figure 3 2 7 i is axa o e Cette Leen pre esee recien Volume of Revol v Description P fiction an repere gt coos 1 Fem M a mardi SESS e cog n 5 amas scm fe e Mere cee a a ae From te Toa mens er Tea Callas Variable zl Volumes of Revolution Cice oss Volumes of Herohtion bo gt enin inde Figure 3 2 Task Template for Volume of Revolution 4 Select the Insert into New Worksheet check box
51. rmat menu select Labels and then Label Display In the Format Labels dialog select one of the numbering schemes Optionally enter an appropriate numbering prefix jaa a femataes 9 Ps ro Figure 2 22 Format Labels Dialog Adding a Prefix 2 5 Worksheet Formatting Features 57 The Format Labels Label Reference menu item allows you to switch between the label name and its reference content acra Figure 2 23 Label Reference 2 5 Worksheet Formatting Features Markers Maple displays markers for formatting features in a vertical bar along the left pane of the worksheet These markers icons indicate the presence of hidden attributes in the worksheet such as Document block boundaries cution groups marked for autoexecute annotations bookmarks and numeric formatting To activate markers From the View menu select Markers Document Blocks In Worksheet mode 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 presentation where for example the Maple programming language is not essential to the concept and only output such as a plot the final answer explanatory text must be displayed Markers
52. s specific layout such as expressions with one or more superscripts and subscripts Components a palette that allows you to embed simple graphical inter face components for example a button into your worksheet You can associate actions with components for exampie a command that is ex when a button is clicked Handwriting 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 SD 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 23 Point and Click Interaction 37 Figure 2 13 Matrix Palette Mathematical Palettes Common Symbols palette of common symbols for constructing ex pressions using sums products and x among other things See Figure 245 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 Large Operators a palette of large operators for constructing expres sions Negated palette of negation symb
53. sion expand Diseibute products over sums 82 4 The Next Step Normalize a rational expression Conven an expression to a different type 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 clas group of expressions that share some common properties These classes or groups are known las pes series Generalized series expansion Apply a procedure to each operand of an expression meli mem 22 automatic com ind completion 51 Symbols d B icon 41 bookmark 58 m bottle icon 41 volume of revolution 63 1 D Math 46 using palettes 48 2 2 Math Input 43 calculus example 63 using palettes 44 Classic Worksheet 16 CodeGeneration help page icon 20 package description 79 help topic 8 19 colon usage 41 A command completion accents 38 automatic 51 alphabetical manual 52 palettes 38 command line interface 16 Application Center commands description 12 LPSolve 77 applications 54 Optimization 75 Help menu 54 restart 41 Assistants top 81 Back Solver 23 VolumeOfRevolution 64 CurveFitting 23 computation commands Data Analysis 23 Student 26 description 6 context menus Import Data 23 using 27 Installer Builder 23 convert Library Browser 23 LD to 2 D 49 Maplet Builder 23 copy menu
54. straints maximum time in hours day each machine can operate Figure Speed Hockey Maximum skates skates skates operation Machine AT 1 E MahieB Machine C 14 T The profit on sharpening figure skates is 87 per pair speed skates is 6 pair and hockey skates is 5 per pair How many pairs of each should be sharpened per day to obtain maximum profit What is the profit PROCESS Formulate the Problem number of figure skates per day 8 umber of speed skates per day h number of hockey skates per day Objective function is 7 amp s Sh 72 3 Using Maple Constraints are Obtain Resources Check for exi ing tools 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 3 2 Optimization Example 73 po quse Oum reete reset per ren Figure 3 6 Optimization Assistant with Values Entered 74 3 Using Maple 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 en
55. te Check for Instructions Help Page and Example Worksheet Other Ready To Use Resources 3 2 Optimization Example Check for Existing Tools Assistant Check for Instructions Help Page 4 The Next Step 4 1 Top Packages 4 2 Top Commands Index 58 59 59 60 61 61 63 63 65 67 69 72 75 79 79 81 83 Preface The Maple Software The Maple 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 Interface Description Standard Worksheet 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 lut 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 lard Worksheet interface to Maple An interactive version of this manual is available in the Standard Worksheet interface From the Help menu select Manuals Diction lary
56. ter 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 Constraint field Enter f 1 2 s h lt 22 Click Add Enter f 1 3 h lt 23 Click Add Enter L f h lt 21 Click Add gt 5 In the Add Bound group box click Assume variables nonnegat ive 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 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 75 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 Navigutor 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 descrip See Figure 3 7 Overview of the Optimization Package Bescon ur VS Sato XO Ee S VA TUTTA nerd he Ong Te gt Acessng Opinion
57. 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 afier the current execution group 46 2 Maple Tools and Resources option v Dome s ber 2 C tmien ainera p p pr p p Enact Evatt Decent Bets Figure 2 17 Options Dialog Input Display Maple Input 1 D Math Important With Maple Input you must terminate commands with a semi colon or colon gt restart Enter the Maple input followed by a semicolon If the input ends with semicolon the result is usually displayed as seen below gt factor x 2 2 x 1 24 Commands 47 1 However if the input ends with a colon the result is computed but the result is not displayed gt faetor x 2 2 x 1 Define custom functions gt gt 2 gt 13 6 gt 1 2y42 Basic Comput The following are examples of basic computations using Maple Input 1 0 Math gt cos alpha 2 sin alpha 2 cos a sin a ax bx 48 2 Maple Tools and Resources gt a intiexpisqrt 2 x gt restart gt limit f x x infinity Jim
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