INFORMATION SYSTEMS SERVICES Getting Started with Maple 9.5 This document is an introduction to the Maple 9.5 for Windows computer algebra system. AUTHOR: Information Systems Services University of Leeds DATE: November 2004 EDITION: 2.0 TUT 38 UNIVERSITY OF LEEDS
Contents 1 Introduction... 2 1.1 Aim of this Document... 2 2 The Maple Worksheet Interfaces... 3 2.1 Starting Maple for Windows... 3 2.2 Standard Interface Menus... 4 2.3 Toolbar... 7 2.4 Context Bar... 8 2.5 The Status Bar... 9 2.6 The Classic Interface... 9 2.7 Input Display Notation... 10 3 The Maple Help System...11 3.1 New Users Tours... 11 3.2 Basic How To... 12 3.3 Example Worksheets... 12 3.4 Dictionary of Definitions in Maths... 12 3.5 Help from the Tools Menu... 13 3.6 Maple on the Web... 13 4 Maple Organisation...14 4.1 The Maple Library... 14 5 Entering Expressions in Maple...15 5.1 Numeric Computation... 18 5.2 Symbolic Computation... 19 5.3 Plots... 20 Format Conventions In this document the following format conventions are used: Menu items are given in a Bold, Arial font. Keys that you press are enclosed in angle brackets. Windows Applications <Enter> Feedback If you notice any mistakes in this document please contact the Information Officer. Email should be sent to the address info-officer@leeds.ac.uk Copyright This document is copyright University of Leeds. Permission to use material in this document should be obtained from the Information Officer (email should be sent to the address info-officer@leeds.ac.uk) Print Record This document was printed on 8-Dec-04. 1
1 Introduction Maple 9.5 is a mathematical application for exploring, teaching, and applying mathematics. It provides an interactive problem-solving environment, complete with procedures for performing symbolic, numeric and graphical computations. Examples of its use include the solution of partial differential equations, encryption of messages, error analyses on lab data and visualisation of complex mathematical information. Maple 9.5 contains thousands of mathematical procedures, and custom procedures can be created using the Maple programming language. Writing code in this language does not require expert programming skills, as Maple contains a large library of routines which can be used as building blocks. This programming language can also be used to automate long or repetitive sets of instructions. Once a Maple application has been created, tools are available within the package for publishing it and exporting results to other software applications. Worksheets can be exported in the formats: HTML, HTML with MathML, LATEX, Maple Text, Plain Text, RTF and XML. Graphics can be exported in the formats: DXF, EPS, GIF, JPEG/JPG, POV, Windows BMP, or WMF. 1.1 Aim of this Document This document is intended as an introduction to the Maple 9.5 interface. From the information in this document, you should be able to open Maple 9.5, familiarise yourself with the interface and use the HELP system. You should also be able to open create, save and print files, and carry out simple operations. It is assumed that you know how to log on to the network and perform basic MS Windows operations with a mouse. No prior knowledge of Maple is assumed Several Maple worksheets are used in this introduction. Before you begin, download the zip file provided for use with this document. Open a web browser such as Internet Explorer and go to URL: www.leeds.ac.uk/iss/documentation/tut/examples/index.html Scroll down to TUT38 and right click on the zip file. Select Save Link As (or Save Target As). When the Save As dialog box appears, select a suitable directory and click Save. Open Windows Explorer and double click the zip file. Click File > Extract All to unzip the Maple worksheets. 2
2 The Maple Worksheet Interfaces Maple 9.5 provides users with two worksheet interfaces. Both have access to the full mathematical engine of the product and take advantage of the new functionality in Maple 9.5. A worksheet is a flexible document for exploring mathematical ideas and for creating sophisticated technical reports. Worksheets can contain sections, text regions, hyperlinks, symbolic spreadsheets, sketch regions, and more. Context-sensitive menus and palettes provide alternative methods of entering input. By default, worksheets open in the enhanced and more modern Standard Worksheet. The Classic Worksheet, available on Windows and UNIX platforms, has the traditional Maple worksheet look and uses less memory. In Windows, you can change the Maple worksheet file association using the Worksheet File Association Selector application from the Tools folder of the Maple 9.5 Start menu. If your system has less than the recommended amount of physical memory, it is suggested that you use the Classic Worksheet version of Maple 9.5. 2.1 Starting Maple for Windows To use Maple you need to be logged on to the network, and running Windows XP. To run the program, open the Start Menu, select Miscellaneous and then Maple 9.5. Several options will be available on the submenu. Choose Maple 9.5 from the list to select the Standard Worksheet interface. Maple may take a minute or two to load, and when it opens, a Tip of the Day window may appear. If it does, close this window and the screen should look like the one below. Figure 1 The Maple Standard Interface The Maple interface follows many standard MS Windows conventions that users of other MS Windows programs will be familiar with. It contains a title bar, a collection of menus, toolbars and a status bar. 3
2.2 Standard Interface Menus There are eight main menus available. The menus follow the standard Windows format of having the File and Edit menus to the left-hand side of the screen and the Window and Help menus on the right. Some of the options on these menus may be greyed out in the illustrations below because they are not applicable at the moment. For example, unless a selection has been made on the worksheet, the Cut, Copy and Paste options will not be appropriate, and so they will not be available on the Edit menu. File The File menu deals with all the filehandling functions in Maple. Commands are available to create a new file, open an existing file, save an existing file, export the contents of a file in a different format, and print the contents of the current file. Note that there are alternatives to using the mouse to select items, e.g. a file can be closed using the shortcut Ctrl+F4. Note also that some items have submenus. An example of this is the Recent Documents item. Pointing to this with a mouse will open a submenu which will list the most recent documents (if any) that have been used. Edit This menu contains commands for undoing or redoing the last actions, cut, copy and paste. It also allows for the selection of the whole worksheet or sections of it, as well as containing a Find function. The facility to insert hyperlinks is also provided, bookmarks can be inserted, edited or deleted and sections of the input can be split or combined. The Execute option will allow execution of the whole of the worksheet, or just the selected section. Figure 2 The File Menu Figure 3 The Edit Menu 4
View The view menu allows the user to choose whether or not to display the Toolbar, Context Bar and Status Bar. These options can be modified by clicking on the required item. Several palettes are available and they can be displayed on the worksheet permanently, or hidden from view. The Zoom factor can be selected in one of six ways, ranging from 50% to 400%. Other options allow the user to move backwards or forwards through the worksheet, show or hide the contents and expand or collapse sections of the worksheet. These will be explained in more detail later in the document. Insert The insert menu allows insertion of text, or other instructions which may be written either in standard mathematical notation, or in Maple notation. Non-text input will be described in detail later. In addition, new sections, graphs and other objects may be inserted in a Maple worksheet. Figure 4 The View Menu Format This allows the user to apply formatting features to characters, sections or page numbers, to indent or outdent sections and to convert from one input type to another. Figure 5 The Insert Menu Figure 6 The Format Menu 5
Tools The Tools menu allows access to further help in the form of Assistants and Tutors. It also contains a spellchecking facility, and a facility to complete automatically a command which has been partially entered by the user. The Options section allows the user to customise the interface. Window If the user has more than one worksheet open (as in this screenshot), a list of the open windows will be displayed in the lower half of the window, and the user will have the option to display the windows using one of the four options shown. Help Maple offers an extremely comprehensive Help facility. This will be dealt with in the Section 3. Figure 7 The Tools Menu Figure 8 The Window Menu Figure 9 The Help Menu 6
2.3 Toolbar Underneath the menu bar is a toolbar that contains shortcut buttons to common commands. If the mouse is pointed at a button on the toolbar and left for a few seconds, the function of that button will be displayed. Figure 10 The Maple Toolbar File Buttons The first five buttons carry out the most common commands from the File Menu: Create New File, Open Existing File, Save File, Print File and Print Preview File respectively. Edit Buttons These allow the operations of Cut, Copy and Paste to be carried out. Undo / Redo These allow the user to undo or redo the previous action. Text Insert text after the current paragraph. Executable Maple Insert executable Maple after the current paragraph. Create / Remove Section These allow the user to create a section containing the current selection, or remove a section containing the current selection. Hyperlink Navigation Clicking on one of these allows the user to step backwards or forwards in the hyperlink history. 7
Control Execution The user can interrupt the current operation, debug the current operation or restart the Maple server. Zoom Controls The zoom can be set to 100%, 200% or 250%. Help This allows the user to search for help on a given topic. 2.4 Context Bar Figure 11 The Maple Context Bar Toggle Input Toggle between Standard Maths and Maple input. Executable / Non-executable Toggle between executable and non-executable expression. Input Type The user can select the type of input by clicking on the down arrow at the right hand side of this button and then choosing from the list of available options. Selection of font type and font size. Font Controls Formatting These buttons allow the formatting features Bold, Italic and Underline to be applied to the selected input. 8
Font Colour The font colour can be changed by clicking this button and then making a selection from the colour palette. Highlight Colour The highlight colour can be changed by clicking this button and then making a selection from the colour palette. Alignment These alignment buttons allow left, centre and right alignment features to be applied. Execute Sheet This executes the whole of the worksheet. Execute Selection This executes only the code that is currently selected. 2.5 The Status Bar The status bar is situated at the bottom of the Maple window, and indicates the processor status, execution time and the amount of memory taken. 2.6 The Classic Interface To use the Classic Interface, close Maple down and then select Start > Programs > Miscellaneous > Maple 9.5 > Classic Worksheet Maple 9.5 Figure 12 Program Menu 9
2.7 Input Display Notation There are two Input Display notations. Maple Notation displays input in Maple syntax. Standard Maths Notation displays input in a typeset similar to that found in textbooks. By default, any new worksheet will open with a prompt in Maple notation. There are four palettes available in the worksheet: Symbol, Expression, Vector and Matrix. To display a palette, click on the View menu and select it. To display all the palettes, click View > Palette > Show All. In the first illustration, the Expression palette is selected. To display one of the others, click on the appropriate button. Figure 13 Maple Palettes 10
3 The Maple Help System Maple has a comprehensive Help system which can be accessed by clicking on the Help item on the menu bar. Context-sensitive help can be obtained by highlighting the term required and then pressing the F1 function key. Figure 14 The Help Menu 3.1 New Users Tours The Quick New User's Tour is designed to provide a general overview of the Maple computer algebra system. This tour introduces some of the common routines and easy-to-use tools to get the user started with Maple. The Full Tour presents the fundamental Maple commands. The following list shows the topics covered in the Full Tour: Numerical Calculations Algebraic Computations 2-D Graphics 3-D Graphics Calculus Vector Calculus Differential Equations Linear Algebra Programming Programming the Maple Graphical User Interface Help System Summary 11
3.2 Basic How To This reference page covers the most basic system knowledge required to use Maple, as well as providing the syntax for the most common commands. A section of this page is reproduced below: Figure 15 Extract From Maple Basic How To 3.3 Example Worksheets Example worksheets are available for each of the following topics: Language and System, Connectivity, Calculus, Maplet applications, Algebra, Geometry, Discrete Mathematics, Integration, Integral Transforms, Differential Equations, General Symbolics, General Numerics, Mathematical Visualization and Applications. 3.4 Dictionary of Definitions in Maths The Maple Math Dictionary provides over 5000 mathematical definitions. These definitions can be accessed as help pages: From the alphabetical listing in the Dictionary Contents tab of the Maple Help Navigator Through hyperlinks in a worksheet or help page Using the? command Using the topic index or search facilities To access a list of dictionary entries: From the Help menu, select Math Dictionary. The Maple Help Navigator opens with the Dictionary Contents tab active. Definitions are organized alphabetically. 12
3.5 Help from the Tools Menu Further Help can be accessed via the Tools menu item. Figure 16 The Tools Menu From the Assistants sub-menu, the following tools are available: curve fitting, library browser, matrix builder, ODE analyser, optimisation, plot builder and unit converter. Through the Tutors sub-menu, help can be obtained in the areas of precalculus, single variable calculus, multivariable calculus and linear algebra. A spellchecker is available, and this can also be invoked using the function key F7. Maple will automatically complete commands. When the full command is offered, pressing the <Return> key will insert it 3.6 Maple on the Web Extensive help is offered by Maple via the web: The Maple Application Centre at www.mapleapps.com offers over 1000 free downloadable Maple applications including exhibits of mathematical graphical art, visual effects and animations. An on-line tour is available at www.mapleapps.com/app_center_tour/ and various tutorials for new Maple users can be found at www.mapleapps.com/tutorial.shtml. The Maple PowerTools suite of free courses and packages at www.mapleapps.com/powertools/ provides lecturers with free course materials, and researchers with add-on Maple packages for specialised fields. Over 35 PowerTools are available to be downloaded free of charge. The Maple Student Centre at www.maple4students.com helps students who are using Maple in undergraduate courses. This site contains Maple tutorials, Maple materials for specific courses and Maple applications written by students. MaplePrimes at www.mapleprimes.com is a controlled access website that provides exclusive use to users who subscribe to the Extended Maintenance Plan. Useful information can be downloaded free of charge for users who are eligible. To obtain a password for access to this site, contact the University of Leeds Help Desk on extension 33333. Product and Company information is available at www.maplesoft.com/main.shtml Technical support is available from www.maplesoft.com/support/index.shtml and the product can be registered at http://register.maplesoft.com/ 13
4 Maple Organisation Calculations in Maple are performed by a computational engine called the Maple kernel. The kernel consists of C code and is approximately 10% of the system s total size. It contains the Maple language interpreter, algorithms for basic numerical calculation and routines to display results and perform other I/O operations. The kernel also saves the values for worksheet variables. When working with several worksheets in the same Maple session, Maple can be run in three different kernel modes: shared, parallel, and mixed. The default is parallel kernel mode. Kernel mode must be set at the beginning of a session. In shared mode, variable assignments defined in one worksheet apply to all open worksheets. In parallel mode, variable assignments defined in one worksheet work independently of those defined in other open worksheets. In mixed mode, the user is prompted to specify the kernel connection for each worksheet window when a new worksheet is opened. Those worksheets that share a kernel share variable assignments. Those worksheets using parallel kernels have independent variable assignments. The kernel mode can be changed using the Options tab on the Tools menu. 4.1 The Maple Library The Maple library is divided into two parts: Main Packages The main library consists of the most frequently used Maple commands and each package contains a group of commands for related calculations. For example, the LinearAlgebra package contains commands for the manipulation of matrices. For a complete list of packages, see the Help system. A command from a package can be used in one of three ways: 1. Use the complete name of the package and the command name package[cmd]( ) If the package has a sub-command, use the complete name of the package, the complete name of the subpackage and then the command name. package[subpackage][cmd]( ) 2. Activate the short form of the names for all the commands in the package using the with command with(package) If the package has a sub-package, use with(package[subpackage]) and then use the short form of the command cmd( ) 3. Activate the short name for a single command from a package with(package, cmd) If the package has a sub-package, use with(package[subpackage], cmd) and then use the short form of the command cmd( ) 14
5 Entering Expressions in Maple Expressions can be entered at the prompt, or by using the keyboard and the palettes. The palettes enable the user to enter a command without knowing its syntax. The following task will demonstrate the entering and evaluation of the following expression: Task 1 Definite Integral (Standard Math Notation) Activity 1.1 If Maple is not running, follow the instructions in Section 2.1 to begin. Note that the prompt is showing the default Maple Input Prompt (> sign in red type). Activity 1.2 Switch to Standard Math Notation using one of the following methods: Ctrl + G Insert > Standard Math Notation Click on the leftmost icon on the context bar A question mark will now appear after the prompt. If the Expression Palette is not currently displayed, select View > Palette > Expression to display it. On the expression palette, select the definite integral button which is second from the left on the top row. The integration sign will appear, with question mark placeholders for the required values. Figure 17 Standard Math Input 15
Activity 1.3 Type in 0 for the lower limit, then use the <Tab> key to move the cursor to the upper limit. From the Symbol Palette click on π, or type Pi. (N.B. Maple is case sensitive so take care to type the P using upper case and the i using lower case.) Click the <Tab> key to move the cursor to the function position. Select cos from the Expression Palette and type x then <Tab>. The cursor will now move to its final position. Type x and then <Tab> followed by <Return>. Figure 18 Maple Input and Output (a) The screenshot above shows the default colours for Maple input, output and text. The Format menu can be used to modify styles or create new styles 16
Task 2 Definite Integral (Maple Notation) Activity 2.1 Switch to Maple Notation using one of the following methods: Ctrl + M Insert > Maple Input On the expression palette, select the definite integral button. The following expression will appear, with placeholders for the required values. Figure 19 Maple Notation Activity 2.2 Select cos from the Expression Palette and then type x followed by the <Tab> key. Type x <Tab> then 0 <Tab> and then Pi, followed by <Return>. Note that Maple will automatically append a semicolon at the end of the input. Once the expressions are known they can be typed directly into the worksheet. Each expression must end in a semicolon, or Maple will report a syntax error. Figure 20 Maple Input and Output (b) 17
5.1 Numeric Computation The most basic computations in Maple are numeric, and it can function as a calculator with integers or floating point numbers. Maple computes exact calculations with rational numbers. To Maple, the rational number 5/2 and the floating point approximation 2.5 are distinct objects. Any thing typed after a hash symbol is ignored, so documentation can be inserted without using Insert > Text. Figure 21 Calculations with Rational and Floating Point Numbers Maple can work with arbitrarily large integers. It can calculate large integers, count the number of digits in a number, factor integers and test for primes. Examples of operations on integers are shown below: Figure 22 Operations on Integers Maple can also work with complex numbers, and it recognises standard mathematical constants such as π and e, the base of natural logarithms. (Note that π must be entered as Pi.) Figure 23 Example evalf Function All the standard mathematical functions are available. Type? functions to see a list. 18
5.2 Symbolic Computation Maple can work with mathematical unknowns and expressions which contain them. Names can be assigned to expressions, and they can include any alphanumeric characters and the underscore character. They must not begin with a number, and since Maple starts internal variables with the underscore character, it is unwise to use this as the first character in a name. The assignment operator is := For example, eqn1:=3*x + 1 Functions can also be defined using the arrow notation, e.g. f:=x->3*x + 1 The first example of f in the illustration below defines an expression f, and the second defines a function f. Figure 24 Comparison of Equation and Function Maple has several basic types of objects: Expression sequences Lists Sets Arrays Tables Strings. Operations are available for these object types, e.g. union and intersection of sets, concatenation operation for strings and selection of a single element from an array. 19
Figure 25 Maple Object Types Set & String Note that the commands can be combined into a single execution group. To do this, highlight all the commands and then use Edit > Split or Join > Join Execution Group. 5.3 Plots Maple can produce several forms of graphs. It accepts explicit, implicit and parametric forms and recognises several coordinate systems. When a graph has been produced, many of its features may be edited. Clicking on a graph, and then right clicking the mouse will open a context-sensitive menu. Figure 26 Graph Editing Menu 20
The arrows at the right-hand side indicate that for some options, a sub-menu exists. For example, the arrow to the right of the Export option opens a sub-menu which lists the graphics formats for Maple plots: Drawing Exchange Format (DXF) Encapsulated Postscript (EPS) Graphics Interchange Format (GIF) JPEG File Interchange Format (JPG) Persistence of Vision (POV) Windows Bitmap (BMP) Windows Metafile (WMF) Figure 27 Export Formats for Graphs Some of the plotting functions (e.g. plot and plot3d) are contained within the main Maple library, and these can be called at any time during a Maple session. Many additional features are contained in the plots and plottools packages referred to in Section 4.1. For further information on these, type?plots and?plottools. When graphing in two dimensions, the plot function should be used. In order to plot an explicit function, Maple requires the name of the function and its domain. Figure 28 Plot Command 21
It is also possible to plot a user-defined function: Figure 29 Plot3d Command with User-Defined Function This 3d plot can be rotated by dragging it in the plot region. 22
Task 3 Numeric Computation Activity 3.1 Open the example file section1.mws (this file, like the others in this document has been downloaded from the Maple Centre. Section 3.6 gives the URL required to access similar resources). Figure 30 Maple Tutorial Worksheet. Activity 3.2 When the worksheet opens, its sections are collapsed. To expand the first section, click on the plus sign to the left of the heading Doing Exact Arithmetic with Maple. Figure 31 Expanded Section of Maple Worksheet Activity 3.3 Follow the instructions to view a series of examples. At the end of each section, complete the series of exercises. 23
Task 4 Symbolic Computation Activity 4.1 Open the worksheet section2.mws and execute the example commands before completing the exercises at the end of the section. Task 5 Plots Activity 5.1 Open the worksheet section3.mws and execute the example commands before completing the exercises at the end of the section. Task 6 Using the Assistant Activity 6.1 Select Tools > Assistants > Curve Fitting. Complete the dialog box as shown below. Figure 32 Curve Fitting Assistant Activity 6.2 Click the Next Page button and insert the x values 4,5,6,7 and the f(x) values 22,23,24,25 Click Fit Curve. 24
Activity 6.3 When the next dialog box appears, click the Plot button in the Least Squares Panel to see the regression line. Figure 33 Straight Line Fit Activity 6.4 Select the Plot Points button to remove the straight line, and modify the expression in the Least Squares Panel. Figure 34 Quadratic Expression in Least Squares Panel Click on the Plot button again to view the new curve and then click on the Close button to leave the Curve Fitting Assistant dialog box. Figure 35 Quadratic Fit 25
Task 7 Quitting Maple You should always quit any computer program when you have finished your session. Never switch off the computer without closing down Windows. Do not leave a computer whilst you are still logged on to it as others may use your account and could damage your files. Activity 7.1 Before leaving Maple make sure you have saved your work. To leave Maple choose File > Exit or click on the Close box in the top right-hand corner of the Maple window. Activity 7.2 After leaving Maple, choose Start > Logout. You must always logout before leaving your computer. 26