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Appendix
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Section A1: The Working Environment
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The Standard Interface


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Maple's Standard Interface provides a host of easeofuse features, many requested by Maple users. It has two modes: the worksheet mode and the document mode. The document mode was designed for writing mathematical expositions as they would appear in a textbook. Its syntaxfree tools are designed to permit computing without having to master a set of Maple commands and the related syntax. Moreover, mathematical expressions are "live," and can be evaluated and updated if changes are made to other parts of the document. This functionality then lends itself to using the document mode as a scratch sheet, with interactive computations being entered and moved around the workspace with draganddrop techniques.

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But the two modes of worksheet and document are not mutually exclusive. In the midst of a document, a section that behaves like a worksheet can be entered, and in the midst of a worksheet, a section that functions like a document can be inserted.

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This ebook assumes the use of the Standard interface, supporting either the worksheet or document mode. It is written in document mode, with interactive calculations in document sections and commandbased calculations in worksheet sections. Our documents are written with the Marker column visible. This column of opposing triangles that delineate "document blocks," the building blocks of the document, appears to the left side of the work space, and is made visible by selecting "Markers" from the View menu. These delineating triangles are extremely useful when working interactively in Maple itself.

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The buildingblocks of the worksheet are the "execution groups" delineated by $\[\mathbf{\>}$, a bracket and a greaterthan symbol. In those sections where we illustrate working with commands, we insert an execution group, but do not display the bracket. An execution group can be inserted by clicking on the toolbar icon:
.

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Examples in this ebook are presented in both a document and a worksheet mode. Maple Solutions use the document mode to illustrate syntaxfree calculations, whereas Coded Solutions use the worksheet mode to illustrate commandbased calculations.

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Math Mode vs. Text Mode


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Input to Maple can be in math or text mode, or nonexecutable math mode. The current mode is indicated in the Context Bar at the top of the workspace, and you can change modes by clicking Text, Nonexecutable Math or Math in the Context Bar. (Function key F5 is a threeway toggle between these modes.)

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In math mode, "x^2" will appear as ${x}^{2}$, and for this reason such math is often called "2D" because it has both horizontal and vertical extension, just like handwritten notation. In text mode, math is linear and onedimensional; hence, it is often called "1D."

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Nonexecutable math is for math that you don't want to evaluate, and it generally used in the middle of a block of text. All math is live unless you've chosen to make it nonexecutable math.

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Either mode of entry can be used with either the document or the worksheet, as per Table A1.1.

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Math

Text

Document
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Document block: math, text, or both

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Math is "live" or nonexecutable

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Context Panel: Evaluate and Display Inline


$g\'\left(x\right)$
$\frac{\ⅆ}{\ⅆx}\phantom{\rule[0.0ex]{0.4em}{0.0ex}}g\left(x\right)$
$\mathrm{diff}\left(g\left(x\right)\,x\right)$

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No text input for commands.${}$


Worksheet
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Evaluate and Display Inline not available. Click Enter to evaluate.

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Text region: Click "T" in the Toolbar

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In a paragraph, math is live or nonexecutable. At an input prompt, math is live.


>

$g\prime \left(x\right)$

$\frac{{\ⅆ}}{{\ⅆ}{x}}\phantom{\rule[0.0ex]{0.4em}{0.0ex}}{g}{}\left({x}\right)$
>

$\frac{\ⅆ}{\ⅆ\phantom{\rule[0.0ex]{0.2em}{0.0ex}}x}g\left(x\right)$

$\frac{{\ⅆ}}{{\ⅆ}{x}}\phantom{\rule[0.0ex]{0.4em}{0.0ex}}{g}{}\left({x}\right)$
>

$\mathrm{diff}\left(g\left(x\right)\,x\right)$

$\frac{{\ⅆ}}{{\ⅆ}{x}}\phantom{\rule[0.0ex]{0.4em}{0.0ex}}{g}{}\left({x}\right)$

${2}{}{x}$

Table A1.1 Math vs. text mode in document and worksheet



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Math mode in a document block places a dotted rectangle around a slightly tilted cursor. The background while editing "live" math is blue, whereas the background for nonexecutable math is gray. Natural math notation can be entered using the keyboard and/or the palettes. Math so entered is understood by the Maple engine as the mathematics for which the notation stands. Maple commands can also be typed in math mode. Such mathematical notation can appear in the midst of a textual sentence, and it can be evaluated in place. To write such a sentence, switch to text mode where the cursor will be vertical, enter text, switch back to math mode, and enter math. This math can be evaluated via Context Panel: Evaluate and Display Inline, in which case an equal sign and the evaluation will appear inline with the math.

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Math mode entry needs no terminal punctuation, except for the colon (:) when output is to be suppressed.

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At a worksheet prompt, entry can be in either math or text modes. In math mode, the entry will be the same as it is in the document block, except that there is no dotted rectangle around the tilted cursor, and evaluation must be by pressing the Enter key (no inline evaluation). In text mode, commands are typed linearly. Text can only be entered in text regions. A text region is created by clicking the "T" icon in the toolbar.

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Math notation typed in math mode can be converted to text mode by

Context Panel: 2D Math≻Convert To≻1D Math Input
conversion in the opposite direction is by Context Panel: Convert To≻2D Math Input.
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The Structure of This Ebook


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The examples in this manual are presented with one or more of a Mathematical Solution, a Maple Solution  Interactive, and a Maple Solution  Coded. A Mathematical Solution appears as if it were in a textbook, with no reference to software tools; a Maple Solution  Interactive is a syntaxfree Maple solution; and a Maple Solution  Coded is a commandbased Maple solution. The Maple Solution  Interactive is deemed "syntaxfree" because it is implemented with easeofuse tools that require no commands. Some of these solutions use such builtin tools as Assistants, Tutors, and/or task templates; some can be implemented solely from the Context Panel, as described in Table A1.2, below. Thus, nearly all the examples in this manual can be worked without having to know a single Maple command.

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A Maple Solution  Coded requires knowledge and mastery of a suite of commands and their related syntax. This "learning curve" used to be a prerequisite for using Maple productively. But with the advent of the easeofuse features, this learning curve is significantly flattened by resorting to Maple's syntaxfree tools.

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Useful Features


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The Standard interface allowed Maple to acquire a number of useful features, the more important of which are listed in Table A1.2.

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Palettes

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The palettes along the left and right edges of the Maple window allow the insertion of templates for many mathematical constructions.

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The Tab and Shift+Tab keys are used to move between the fields in the template.

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Palettes are arranged by selecting the Palettes option in the View menu.


The Variable Manager

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The Variable Manager, implemented interactively in the Variables palette, automatically records variables to which a value has been assigned. These variables can be "unassigned" via the Variables palette itself, or via the Unassign option in the Context Panel.

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The Context Panel provides the Unassign option for the name of an assigned function.

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Both these unassign actions are the equivalent of invoking the unassign command.


The Math Editor
(Typeset Math)

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Natural mathematical notation is easily entered either from the keyboard or from the palettes. In document mode, this notation is understood by the Maple engine as the math for which the notation stands.

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See below in the section "Getting Help in Maple" for pointers to places in the Maple Help system where keyboard shortcuts are documented.


Atomic Variables

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An Atomic Variable is a group of characters that Maple sees as a single name. Any group of characters becomes such a name if set as, or converted to, an Atomic Variable.

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See Table A1.3 for ways to create an Atomic Variable.

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Atomic Variables appear in black, unless the View/Atomic Variables option is selected, in which case they appear in Magenta.


Literal Subscripts

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The literal subscript is a subscripted name combined as an Atomic Variable.

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See Table A1.4 for how the literal subscript on a single character can be set as an Atomic Variable.

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While the subscript is often a single integer such as 1, it can be more general, such as the word "one" or an expression such as $a\+b$.


Subscripts
(as Table Entries)

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A table whose name is, say, $x$, will have each of its entries denoted by a subscripted $x$. Each such subscripted $x$ is itself a Maple name to which a value may be assigned. These names are not Atomic Variables.

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See Table A1.4 for details on forming such table entries.

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Do not assign a value to the table name itself.


Exponents (superscripts)

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In math mode, exponents are set by first typing the caret (^) symbol: press Shift and the 6/^ key. This raises the cursor but does not display the caret.

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In text mode, type the caret, which will now be visible.


Context Sensitive Menus

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When a mathematical object is in focus, the Context Panel at the right edge of the worksheet provides a menu tailored to the mathematical object, and permits many calculations by simply selecting from the menu.


Assistants

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A collection of interactive popup tools, including the interactive Plot Builder for interactive graphing.

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Available in the Tools menu (as an Assistant) or through the Context Panel.


Tutors

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Some 50 interactive popups designed for pedagogical purposes, available in the Tools menu or through the Context Panel.


Task Templates

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Some 347 interactive tools designed to assist implementing specific tasks.

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Available from the Tools menu (Tools≻Tasks≻Browse) or from the Help system.


Equation Labels

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Maple outputs are automatically assigned an equation label (on the right of the screen) that stands for the item so labeled.

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This label can be used to reference the item by launching the Equation Label dialog via Ctrl+L (or its equivalent).


Command Completion

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Accessed either from the Tools menu, or the keyboard (Esc; or Ctrl+Space, or its equivalent), a popup list of all items in Maple that start with the letters typed.


Draganddrop

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Nearly all 2D math (either input/output) can be copied and pasted, the equivalent of which is selection and dragging while holding a special key.

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In Windows®, this key is Ctrl, so the phrase "Controldrag" is used. (The other popular operating systems support a similar feature.)

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Selection and dragging without holding the special key is the equivalent of cut/paste, an operation that is not used in this ebook.


Executable vs. NonExecutable
Typeset Math

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Typeset math (2D math) can be executable or nonexecutable. Executable math is set with a blue background; nonexecutable, with a gray.

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Details are available here.


Table A1.2 List of some useful interface features



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Table A1.3 lists three different ways to make a Maple name out of a group of typeset characters; the result is called an Atomic Variable. After selecting the characters, implement one of the methods in the table.
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Press the keys Ctrl+Shift+A


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Format Menu: Convert To≻Atomic Variable


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Context Panel: 2D math≻Convert To≻Atomic Variable


Table A1.3 Converting to an Atomic Variable



Table A1.4 details how (in Windows®) subscripting works under two different options in the Tools≻Options≻Interface dialog. The dropdown for "Underscore Entry" provides the two choices: "Inserts literal underscore" (which is the default) and "Inserts nonatomic subscript". This Study Guide has been written with a copy of Maple in which the alternate setting, namely, "Inserts nonatomic subscript", has been in use. The effect of this setting is to make it easier to enter subscripted names as table entries, rather than as Atomic Variables.
Setting

2D Math

1D Math

Alternate

Table Entry:

Shift Minus

${{x}}_{{1}}$

Atomic Variable:

See Table A1.3

$\mathrm{x\_\_y}$

Default

Table Entry:

Ctrl Shift Minus

${{x}}_{{1}}$

Atomic Variable:

Shift Minus Minus

$\mathrm{x\_\_y}$

Table A1.4 Simple subscripting under the two options for "Underscore Entry"



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In 1D math, with either setting, simple subscripts such as ${x}_{1}$ can be set as atomic variables by typing a double underscore. More complex expressions cannot easily be set as atomic variables in 1D math.

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In the default setting, using 2D (Typeset) math, the keystrokes that correspond to writing an underscore, actually write an underscore. In this mode, it takes two successive underscores to drop the cursor to the subscript position, and any name created in this way automatically becomes an Atomic Variable.

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In the default setting, using 2D (Typeset) math, the keystrokes Ctrl+Shift+Minus drop the cursor to the subscript position, and any name created in this way automatically becomes a table entry.

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In the alternate setting, using 2D (Typeset) math, the keystrokes that correspond to writing an underscore, lowers the cursor to the subscript position. Any name set in this way automatically becomes a table entry.

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In the alternate setting, using 2D (Typeset) math, the only way to obtain an Atomic Variable, is to use one of the three techniques detailed in Table A1.3.

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The numeric subscript on an Atomic Variable cannot be used as an index. That is why this ebook gives precedence to the subscripted variable as a table entry where a numeric subscript can be used as an index in operations such as summing and multiplying.

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Getting Help in Maple


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One of the best sources of help for Maple is the builtin Maple help system itself. This is accessed from the Help menu or from the circled questionmark in the toolbar.

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Help on a particular item can be found directly by typing a question mark before the item and pressing the Enter key. (For example, executing the command

$\?\mathrm{worksheet,documenting,2DMathShortcutKeys}$



launches a help page containing the most extensive summary of mathmode operations and usages.) Alternatively, launch the help page for an item by placing the cursor on the item, and pressing function key F2.
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Each help page in Maple has a set of examples at the bottom. These examples can be copied by selecting "Copy Examples" from the popup menu launched by secondary selection (rightclick with a twobutton mouse). Alternatively, if the toolbar icon that contains the letters "ws" (for "worksheet") is clicked, the help page will open as a worksheet where the examples can then be executed.

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A particularly useful section of the help system is the Student Portal, accessed by executing ?Student Portal, or by clicking the link Student Portal. The Student Portal is designed to answer nearly 150 questions of the form "How do I…?"

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Function key F1 accesses the Help system, and Ctrl+F2, a Quick Reference page. The Help menu option "Manuals, Resources, and more" provides the options: Maple Portal, Maple Resources, Plotting Guide, Tasks, Applications and Examples, Shortcut Keys, and Manuals. The Manuals option leads further to the builtin copy of the User Manual.

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Hence, the Maple Help system is generally the best place to obtain information on how to do something in Maple.

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Final Pointers for the Novice User


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Maple has been installed and launched, the Markers column is visible, the palettes have been organized, and it's time to do some Maple calculations. Here are a few additional tips for using Maple effectively.
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First, note that by default, autosave is enabled and set to save every three minutes. This can be changed via the Tools≻Options dialog, but nothing can be more frustrating than to lose work to a computer malfunction. It's probably best to leave some form of autosave active.

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Second, like most other software, Maple provides both a Save and a Save As option. In either case, be sure to save work often enough that important material won't be lost.

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Third, be wary of the assignments made to variables. When too many such assignments are made, it can be confusing to continue using these names in new problems. To unassign a specific variable, select Unassign from the Context Panel for that variable in the Variables palette, or use the unassign command. Alternatively, reset nearly everything in Maple to its initial state by clicking on the restart icon (the closed loop in the toolbar) or by executing the restart command.

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Fourth, if a Maple input is changed interactively, the effects of that change won't be cascaded down through the rest of any chain of calculations that are logically connected to that input. Something has to be done to cause such a change to ripple through the rest of the document. Select the items that need to be updated, and press the single exclamation mark in the toolbar. Of course, clicking on the triple exclamation icon in the toolbar will execute the whole document.

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Fifth, when a document has been saved, then recalled, what's on the screen isn't what's in Maple's memory. None of the assignments in the document are known to Maple. Assignments and calculations need to be reexecuted.

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Sixth, removing an assignment from the screen does not remove it from Maple's memory. Conversely, unassigning an assignment removes the connection in Maple's memory, but does not remove the assignment statement from the screen. So, it is possible to construct a completely unfathomable document by selectively assigning, and unassigning, deleting and inserting at any points in the document. It should be obvious to the reader that although possible, it's neither useful nor productive.

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