command the brilliance of a thousand mathematicians
Getting Started Guide
M-0027-00-E Printed in Canada
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2002 Waterloo Maple Inc,Maple is a registered trademark of Waterloo Maple Inc,
Maple 8
Getting Started Guide
2002 by Waterloo Maple Inc.
ii
Waterloo Maple Inc.
57 Erb Street West
Waterloo,ON N2L 6C2
Canada
Maple and Maple V are registered trademarks of Waterloo Maple Inc.
Maplets is a trademark of Waterloo Maple Inc.
2002,2001 by Waterloo Maple Inc,All rights reserved.
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All other trademarks are property of their respective owners.
Printed in Canada
ISBN 1-894511-25-5
1 Chapter 1,Introduction to Maple,...............................................,1
1.1 Installing Maple,...............................................................................,1
1.2 Starting Maple,.................................................................................,1
1.3 The Maple Window,..........................................................................,2
1.4 Accessing Help Pages........................................................................,4
1.5 Entering Expressions in Maple........................................................,5
2 Chapter 2,Solving a Problem,....................................................,9
2.1 Scenario,............................................................................................,9
2.2 Commands in Packages,...................................................................,9
2.3 Math and Visualization,.................................................................,10
Plotting the hill,............................................................................,11
Finding the maximum point of the surface,................................,12
Finding the skier’s starting point,...............................................,13
Finding the path down,................................................................,14
2.4 Using a For Loop—Finding the Path.............................................,15
Performing the initialization,......................................................,15
Specifying the For Loop,...............................................................,16
2.5 Visualization Revisited...................................................................,17
2.6 Documenting Your Work,...............................................................,19
Adding text,...................................................................................,19
Structuring the worksheet with sections,...................................,21
Contents
iii
Adding numbers,..........................................................................,22
2.7 Exporting to HTML.........................................................................,23
3 Chapter 3,Getting More Information,......................................,25
3.1 The Help System.............................................................................,25
Maple help pages,.........................................................................,25
Help page toolbar,.........................................................................,26
Getting help,.................................................................................,27
Help command,........................................................................,27
Help Browser,..........................................................................,27
iv?Contents
Topic search,............................................................................,27
Full text search,.......................................................................,28
3.2 Manual Set,.....................................................................................,28
3.3 New User’s Tour..............................................................................,29
3.4 Example Worksheets,.....................................................................,29
3.5 Web Sites,........................................................................................,29
Index,.................................................................................................,31
1 Introduction to Maple
Chapter 1,Introduction to MapleMaple is an analytic computation system,It performs mathematical
computations and manipulations for solving problems from various technical
disciplines,Most significantly,Maple computes both numerical as well as
symbolic solutions to mathematical expressions,This means that Maple
performs computations on expressions that contain symbols,such as π or x,
without performing numerical approximations,For example,Maple
determines that the derivative of G86G76G81G11G91G12 is G70G82G86G11G91G12,even when G91 has not been
assigned a value,Maple provides exact solutions to many technical problems,
In addition,Maple has visualization tools that contribute to the problem-
solving process,
1.1 Installing Maple
For installation and licensing instructions,refer to the G44G81G86G87G68G79G79G17G75G87G80 file on
your Maple CD.
1.2 Starting Maple
You can run the Maple program with either a graphical user interface or a
command-line interface,In the graphical user interface,you can enter Maple
commands at the prompt,or you can use palettes,context-sensitive menus,
and other features to construct commands,The worksheet is your Maple
document,and in it you can format and document your commands,
In the command-line interface,you enter Maple commands at the prompt,
While you cannot access the graphical interface features,the command-line
1
2 Chapter 1,Introduction to Maple
interface uses less memory than the worksheet interface,It is therefore useful
in solving very large or complex problems on computers with limited memory.
This guide covers the standard interface,For more information on the
command-line interface,look in your Maple folder for the G70G80G71G79G76G81G72G17G87G91G87G3file
(for Macintosh,refer to the G38G82G80G80G68G81G71G3G47G76G81G72G3G53G72G68G71G80G72 file).
To start the standard interface in Windows:
From the Start menu,choose Programs,Maple 8,then Maple 8.
To start the standard interface on a Macintosh computer:
1,Double-click the Maple 8 application icon on the Macintosh hard drive.
2,If prompted,enter your User ID in the Maple 8 Multiple User Logon
dialog box,and click Log On,If you have entered a new ID,you have to
confirm its creation.
To start the standard interface in UNIX or Linux:
Enter the full path,for example,
G18G88G86G85G18G79G82G70G68G79G18G80G68G83G79G72G18G69G76G81G18G91G80G68G83G79G72
Or,
1,Add your Maple 8 directory (for example,G18G88G86G85G18G79G82G70G68G79G18G80G68G83G79G72G18G69G76G81) to your
command search path.
2,Enter G91G80G68G83G79G72.
On all operating systems,the first Maple worksheet session opens with the
Introduction to Maple 8 page that points you to the New User’s Tour,updates,
and other introductory help pages,Subsequent worksheet sessions start with
a new,blank worksheet.
1.3 The Maple Window
The Maple window resembles that of a typical application program,The main
features are shown in Figure 1-A on page 3,
1.3 The Maple Window 3
Figure 1-A Maple window features
A
Toolbar
A toolbar containing shortcut buttons.
B
Context bar
A toolbar containing context-sensitive shortcut buttons,(This means that the
buttons change based on the cursor location or selection.) It can also contain a
field for editing and entering text.
C
Section heading
The name or title of a section.
D
Maple input
A mathematical expression that Maple evaluates,By default,input commands
are entered at the prompt,“>”,and are displayed in red type,The resulting
output is displayed beneath.
A
B
E
C
D
F
G
H
I
J
L
M
N
K
4 Chapter 1,Introduction to Maple
1.4 Accessing Help Pages
The commands and features in Maple are documented in online help pages,To
view help pages,at the prompt,enter a question mark (G34) followed by the
name of the command or subject on which you want help,Do not enter any
spaces,For example,to refer to the help page on natural logarithms,enter
G34G79G81,For information on different ways to get help,see The Help System on
page 25.
E
Maple output
The result of an executed Maple input command,By default,Maple output is
displayed in blue type in Standard Math Notation.
F
Execution group
A set of Maple input with its corresponding output.
G
Worksheet
A Maple document.
H
Section
A grouping of worksheet elements.
I
Section range bracket
A line that,brackets” the elements of a section.
J
Prompt
By default,the Maple prompt is a greater-than symbol that indicates where to
enter Maple input.
K
Symbol palette
A collection of buttons for entering mathematical symbols in Maple.
L
Expression palette
A collection of templates for entering mathematical expressions in Maple.
M
Matrix palette
A collection of templates for entering matrices in Maple.
N
Vector palette
A collection of buttons for entering vectors in Maple.
1.5 Entering Expressions in Maple 5
1.5 Entering Expressions in Maple
To enter expressions at the prompt,use the keyboard,the palettes,or both,
Using the keyboard is the most direct method,but the palettes enable you to
enter a command without knowing its syntax.
There are two types of input display,Use Maple Notation to display input as
Maple syntax,Maple Notation is the default,Use Standard Math Notation
to display input in typeset notation as it appears in a textbook.
These examples step you through entering in various ways.
To enter the integral in Standard Math Notation by using the palettes:
1,Display the palettes,if necessary,From the View menu,choose Palettes,
then Show All Palettes,The Symbol,Expression,Matrix,and Vector
palettes are displayed,Move the palettes to the side of the worksheet,if
necessary.
2,If required,change the input to Standard Math Notation,(If there is a
question mark (?) after the prompt,the input is already set to Standard
Math Notation.) At the prompt,right-click,The context-sensitive menu is
displayed,Choose Standard Math.
3,On the Expression palette,click,The integral symbol appears,and
the question mark placeholder is selected.
4,On the Expression palette,click,The function sin appears,with
another placeholder,
5,Enter G91 (on the keyboard),and press TAB to go to the next placeholder.
6,Repeat step 5.
7,Enter G19 (zero),and press TAB.
8,On the Symbol palette,click,(It is in the bottom row.)
9,Press ENTER,
Your worksheet should resemble that of Figure 1-B on page 6,
x()sin xd
0
π
∫
6 Chapter 1,Introduction to Maple
Figure 1-B Integral input in Standard Math Notation
The next example shows you how you can use the palettes to enter the
expression and learn the Maple command syntax at the same time.
To enter the integral in Maple Notation by using the palettes:
1,On the Expression palette,click,The integral command appears,
and the %? placeholder is selected.
2,On the Expression palette,click,The function sin appears,with
another placeholder,
3,Enter G91 (on the keyboard),and press TAB to go to the next placeholder.
4,Repeat step 5.
5,Enter G19 (zero),and press TAB.
6,On the Symbol palette,click,(It is in the bottom row.)
7,Press ENTER,
Note,Maple appends a semicolon to the end of the command,This signifies the
end of the statement.
1.5 Entering Expressions in Maple 7
Your worksheet should look similar to the one in Figure 1-C.
Figure 1-C Integral input in Maple Notation
Now that you know the correct notation,you could enter the expression at the
prompt,For more information on entering expressions,see the examples in
the next chapter and refer to G34G90G82G85G78G86G75G72G72G87G15G72G91G83G85G72G86G86G76G82G81G86G15G72G81G87G72G85G76G81G74 (Enter
Expressions in Maple),For more information on using palettes,refer to
G34G90G82G85G78G86G75G72G72G87G15G72G91G83G85G72G86G86G76G82G81G86G15G83G68G79G72G87G87G72G86 (Overview of Palettes).
For the rest of this guide,it is assumed that you are entering expressions in
Maple Notation.
8 Chapter 1,Introduction to Maple
2 Solving a Problem
Chapter 2,Solving a ProblemThis chapter presents a mathematical problem with its solution,The
discussion of the problem and its solution introduces you to key features of the
Maple program,Do not worry too much about the mathematics,The purpose
of this problem is to show you Maple; the mathematics is secondary.
Note,When entering Maple commands,please keep in mind that they are case-
sensitive.
2.1 Scenario
A skier has made her way to the top of a mountain,She wants to take the
steepest path down,which she can find by performing the calculations
outlined in this chapter,Start by opening a new worksheet for this problem.
To open a new worksheet:
From the File menu,choose New.
2.2 Commands in Packages
Some of the commands used in the discussion are found in packages,A
package is a group of routines related to a particular area of mathematics,You
can always access commands in packages by using the long form,that is,
specifying both package and function name,G83G68G70G78G68G74G72G62G73G88G81G70G87G76G82G81G64G11G17G17G12,but to
be able to use the short form,that is,specify only the function name,use the
G90G76G87G75 command first.
9
10 Chapter 2,Solving a Problem
To access commands in the G83G79G82G87G86 package:
At the prompt,enter the following and press ENTER.
G90G76G87G75G11G83G79G82G87G86G12G30
After executing the command,Maple lists any warnings,followed by all of the
commands that are included in the package,For the G83G79G82G87G86 package,a
warning indicates that the name of one of the commands in the package,
G70G75G68G81G74G72G70G82G82G85G71G86G15G3is the same as a global name that is already defined,After
executing the G90G76G87G75 command,the original meaning of the command is not
available until you restart Maple,
For other methods of accessing commands in packages,refer to Section 3.7,
“The Organization of Maple,” in the Maple Learning Guide,For a list of all the
packages in Maple,refer to G34G76G81G71G72G91G15G83G68G70G78G68G74G72G86 (Index of descriptions for
packages of library functions).
2.3 Math and Visualization
Use some mathematical and visualization commands to determine basic
properties of the hill,If you want more information on any of the commands
used here,enter a question mark,followed by the name of the command,For
example,to find help on the exponential command,enter G34G72G91G83 (The
Expontential Function).
Suppose that the height at a point G11G91G15G92G12 of the hill is given by G73,in thousands
of feet.
To enter the expression in Maple:
At the prompt,enter the following and press ENTER:
G73G3G29G32G3G22G18G11G20G14G91G65G21G14G92G65G21G12G18G11G20G18G23G14G20G18G21G13G11G91G14G20G12G65G21G14G20G18G21G13G11G92G14G21G12G65G21G12G30
The expression for the shape of the hill is assigned to the name G73 by means of
the assignment operator,:=” so that it can be referred to in subsequent
calculations,For more information about assignments,refer to G34G29G32 (The
f
3
1 x
2
y
2
++()
1
4
---
x 1+()
2
2
-------------------
y 2+()
2
2
-------------------++
---------------------------------------------------------------------------------------------=
2.3 Math and Visualization 11
assignment statement),and for more information about names,refer to G34G81G68G80G72G86
(Names).
Plotting the hill
Before solving the problem,it would be helpful to get an idea of what the hill
looks like (and an idea of what the answer should be),
To plot the expression:
1,Right-click the output of the expression (for Macintosh,option-click),The
context-sensitive menu is displayed.
2,Choose Plots,3-D Plot,then x,y,Maple inserts the plot into the
worksheet.
Note,The content of context-sensitive menus varies depending on the cursor
location or selected expression,For more information,refer to
G34G90G82G85G78G86G75G72G72G87G15G72G91G83G85G72G86G86G76G82G81G86G15G80G68G81G76G83G88G79G68G87G72G70G86G80 (Use Context-Sensitive Menus
to Manipulate Expressions).
To add axes:
Right-click the plot (for Macintosh,option-click),choose Axes,then
Boxed.
To modify the axes ranges:
1,Right-click the plot (for Macintosh,option-click),choose Axes,then
Ranges.
2,In the Axis Range dialog box:
a.Under X Axis,click the button beside the top range box,Enter?G23 in
the top box,then enter G22 in the bottom box.
b.Similarly,change the Y Axis to range from?G23 to G22.
c.Click OK.
The visualization tools in Maple enable you to see the surface from more than
one angle.
To rotate the surface:
1,Click the plot to select it.
2,Place the pointer on the plot,but not directly on the surface of the hill.
3,Drag the plot in any direction,The surface rotates.
12 Chapter 2,Solving a Problem
Depending on how you rotated the plot,it may look similar to Figure 2-A.
Figure 2-A Plot of the hill
While you could look at the surface and guess what the highest point is,you
can obtain a more precise answer by using calculus.
Finding the maximum point of the surface
Determine the location of the top of the hill by taking partial derivatives,
setting them to G19,and solving for G91 and G92.
To find the partial derivative of G73 with respect to G91:
At the prompt,enter the following and press ENTER,
G73G91G3G29G32G3G71G76G73G73G11G73G15G91G12G30
2.3 Math and Visualization 13
To find the partial derivative of G73 with respect to G92:
At the prompt,enter the following and press ENTER.
G73G92G3G29G32G3G71G76G73G73G11G73G15G92G12G30
Since you are interested in the real solution,use the G73G86G82G79G89G72 command instead
of the more general G86G82G79G89G72 command.
To solve the system of equations G94G73G91G32G19G15G3G73G92G32G19G96:
At the prompt,enter the following and press ENTER.
G87G82G83G66G91G92G3G29G32G3G73G86G82G79G89G72G11G94G73G91G32G19G15G73G92G32G19G96G15G94G91G15G92G96G15G94G91G32G16G22G17G17G19G15G92G32G16G22G17G17G19G96G12G30
The top of the hill is therefore at approximately G94G91G3G32G3?G17G28G19G21G25G20G19G19G20G28G28G15
G92G3G32G3G16G20G17G27G19G24G21G21G19G19G23G19G96.
Note,Sets do not preserve order,so you may instead obtain the equivalent set,
{ G92G3G32G3?G20G17G27G19G24G21G21G19G19G23G19G15G3G91G3G32?G17G28G19G21G25G20G19G19G20G28G28G96.
Finding the skier’s starting point
Assume that the skier does not start at the peak but slightly to the side,To
approximate this location,add a small factor,say G19G17G19G24,to the G91G16 and G92G16
values,Assign these values to the variables G91 and G92 and then add the
approximating factor.
To assign the values to the variables:
At the prompt,enter the following and press ENTER.
G68G86G86G76G74G81G11G8G12G30
The ditto operator (%) refers to the result of the previous computation,For
more information,refer to G34G8 (The ditto operators).
To define the starting G91G16 and G92G16values,G91G20G3andG3G92G20,G3respectively:
At the prompt,enter the following and press ENTER.
G91G20G29G32G91G14G19G17G19G24G30
G92G20G29G32G92G14G19G17G19G24G30
The names G91 and G92 have values assigned to them,Since G91 and G92G3are used as
variables in future calculations,they must be unassigned before proceeding.
To unassign G91 and G92:
At the prompt,enter the following and press ENTER.
G91G29G32G183G91G183G30
G92G29G32G183G92G183G30
14 Chapter 2,Solving a Problem
To find the G93-coordinate of the starting point:
Evaluate the function representing the hill at the G91G16 and G92G16values
representing the starting point (G91G20G15G92G20),At the prompt,enter the following
and press ENTER.
G93G20G29G32G72G89G68G79G11G73G15G94G91G32G91G20G15G92G32G92G20G96G12G30
The numerical result {G91G20G3G32G16G17G27G24G21G25G20G19G19G20G28G28G3G15G3G92G20G3G32G3G16G20G17G26G24G24G21G21G19G19G23G19G15G3G93G20G3G32G3
G21G17G20G23G24G25G22G20G23G24G22G96 is an approximation of the skier’s starting point.
Finding the path down
Before you find the path,take a look at the level curves of the hill to get an
idea of the skier’s path.
To plot the level curves:
The G70G82G81G87G82G88G85G83G79G82G87 command with five contours suggests an interesting
shape,as shown in Figure 2-B,At the prompt,enter the following
command and press ENTER.
G70G82G81G87G82G88G85G83G79G82G87G11G73G15G3G91G32?G21G17G17G20G15G3G92G32?G22G17G17G20G15G3G70G82G81G87G82G88G85G86G32G24G15G3G73G76G79G79G72G71G32G87G85G88G72G12G30
Figure 2-B Level curves of the hill
2.4 Using a For Loop—Finding the Path 15
2.4 Using a For Loop—Finding the Path
Next,construct and plot the path on the surface of the hill that the skier
should take,The negative of the gradient (G73G11G91G15G92G12G3G82G85G3?G74G85G68G71G11G73G11G91G15G92G12) in the
Maple language),gives the G91 and G92G3components of the direction of steepest
descent,At each point G11G91G15G92G15G93G12 on the surface,the skier should travel in the
direction ofG73G11G91G15G92G12,while staying on the surface,SinceG73G11G91G15G92G12 changes
from point to point,you can break the process into steps,building an
approximation of the path of steepest descent,If the step size is too large,the
path may leave the surface of the hill,If the step size is too small,you derive
no benefit from the increased number of calculations.
Performing the initialization
Assume that the skier is currently at the starting point (G91G20G15G92G20G15G93G20),Use a
timestep of 0.1 and find 25 points along the path,Use the arrays G83G82G76G81G87G22G71 and
G85G82G88G87G72G22G71 to store the values of the computed points and the direction taken,
respectively,To simplify the calculation of the points and route,define vector
representations of the expressions for the hill and the derivatives with respect
to both G91 and G92.
To define vector representations of the expressions:
At the prompt,enter the following and press ENTER.
G74G29G32G72G89G68G79G11G73G15G94G91G32G51G62G20G64G15G92G32G51G62G21G64G96G12G30
G74G91G29G32G72G89G68G79G11G73G91G15G94G91G32G51G62G20G64G15G92G32G51G62G21G64G96G12G30
G74G92G29G32G72G89G68G79G11G73G92G15G94G91G32G51G62G20G64G15G92G32G51G62G21G64G96G12G30
To declare the arrays for storing the values at each timestep:
At the prompt,enter the following and press ENTER.
G83G82G76G81G87G22G71G29G32G36G85G85G68G92G11G20G17G17G21G24G12G30
G85G82G88G87G72G22G71G29G32G36G85G85G68G92G11G20G17G17G21G24G12G30
To define the initialization:
At the prompt,enter the following and press ENTER.
G87G76G80G72G86G87G72G83G29G32G19G17G20G30
G83G82G76G81G87G22G71G62G20G64G29G32G31G91G20G15G92G20G15G93G20G33G30
Note,The notation G31G91G20G15G92G20G15G93G20G33 defines a Vector while P[i] accesses the i
th
element of the list P,For more information about Vectors,refer to G34G57G72G70G87G82G85
(Vector - construct a Vector),For more information about lists,refer to G34G79G76G86G87G86
(Sets and Lists).
16 Chapter 2,Solving a Problem
Specifying the For Loop
To obtain the additional 24 points,use a G73G82G85 loop,A G73G82G85 loop repeatedly
executes a sequence of Maple commands entered between the G73G82G85 and G72G81G71G3
commands of the loop,that is,in the loop body,It executes the commands as
the value of a numeric variable,called an index,varies from its specified
initial value to its specified final value,The value of the index is incremented
after each execution of the commands in the body of the loop,The iteration
stops when the value of the index is greater than the specified final value,For
information on other programming structures in Maple,refer to the Maple
Introductory Programming Guide.
To start the G73G82G85 loop:
At the prompt,enter the following and press ENTER.
G73G82G85G3G76G3G73G85G82G80G3G20G3G87G82G3G21G23G3G71G82
Note,After you press ENTER,Maple returns the message:,Warning,premature
end of input.” It is simply reminding you that the G73G82G85 statement is not complete,To
continue entering your input without receiving this warning,use SHIFT+ENTER to
go to the next line.
The next commands comprise the body of the G73G82G85 loop,These commands find
the skier’s position at the end of each time step.
To construct the 3-D normalized negative of the gradient vectors:
At the prompt,enter the following and press ENTER.
G85G82G88G87G72G22G71G62G76G64G3G29G32G3G47G76G81G72G68G85G36G79G74G72G69G85G68G62G49G82G85G80G68G79G76G93G72G64G11G72G89G68G79G11G31G16G74G91G15G16G74G92G15G19G33G15G3
G51G32G83G82G76G81G87G22G71G62G76G64G12G12G30
To find the next point in the skier’s path:
At the prompt,enter the following and press ENTER.
G83G82G76G81G87G22G71G62G76G14G20G64G3G29G32G3
G72G89G68G79G11G31G51G62G20G64G15G51G62G21G64G15G74G33G15G51G32G83G82G76G81G87G22G71G62G76G64G14G87G76G80G72G86G87G72G83G13G85G82G88G87G72G22G71G62G76G64G12G30
To complete the G73G82G85 loop:
At the prompt,enter the following and press ENTER,Remember to end the
line with a colon to suppress the output.
G72G81G71G3G71G82G29
This command ends the G73G82G85 loop,After you press ENTER,the five commands in
the loop body are repeated 24 times,At the end of each iteration,the value of G76
is increased by 1,That is,for the first iteration,the value of G76 is its initial
value 1,for the second 2,and so on,For the last iteration the value of G76 is 24,
Maple exits at the end of the 24th iteration once G76 is set to 25 (since 25 is
outside of the bounds of the loop).
2.5 Visualization Revisited 17
To graph the path,you must convert the points representing the path of the
skier,which are stored in the G83G82G76G81G87G22G71 array,to a list.
To convert the G83G82G76G81G87G22G71 array to a list:
At the prompt,enter the following and press ENTER.
G79G76G86G87G83G82G76G81G87G86G22G71G3G29G32G3G62G86G72G84G11G3G70G82G81G89G72G85G87G11G3G83G82G76G81G87G22G71G62G76G64G15G3G79G76G86G87G3G12G15G3G76G32G20G17G17G21G24G3G12G64G29
You will use these lists in the next section.
2.5 Visualization Revisited
The visualization tools in Maple enable you to create different kinds of two-
and three-dimensional plots in a number of coordinate systems,In addition,
you can plot more than one element on a single set of axes,First assign the
individual plots to names,then plot them together by using the G71G76G86G83G79G68G92
command.
To plot the hill and assign it to the name G80G82G88G81G87G68G76G81:
At the prompt,enter the following and press ENTER,Remember to end the
line with a colon to suppress the output.
G80G82G88G81G87G68G76G81G3G29G32G3G83G79G82G87G22G71G11G73G15G3G91G32?G22G17G17G22G15G3G92G32?G23G17G17G23G15G3G68G91G72G86G32G69G82G91G72G71G12G29
To plot the set of points on the path as a straight line and assign it to
G83G68G87G75G22G71:
At the prompt,enter the following and press ENTER.
G83G68G87G75G22G71G3G29G32G3G83G82G76G81G87G83G79G82G87G22G71G11G79G76G86G87G83G82G76G81G87G86G22G71G15G3G86G87G92G79G72G32G79G76G81G72G15G3G70G82G79G82G85G32G85G72G71G12G29
To plot the starting point of the skier and assign it to G86G78G76G72G85:
At the prompt,enter the following and press ENTER.
G86G78G76G72G85G3G29G32G3G83G82G76G81G87G83G79G82G87G22G71G11G70G82G81G89G72G85G87G11G83G82G76G81G87G22G71G62G20G64G15G79G76G86G87G12G15G3G86G92G80G69G82G79G32G70G85G82G86G86G15G3
G86G92G80G69G82G79G86G76G93G72G32G24G19G15G70G82G79G82G85G32G92G72G79G79G82G90G12G29
To view all three elements at once,
At the prompt,enter the following and press ENTER.
G71G76G86G83G79G68G92G11G80G82G88G81G87G68G76G81G15G3G86G78G76G72G85G15G3G83G68G87G75G22G71G12G30
To rotate the surface of the plot to see the path:
1,Click the plot to select it.
2,Place the pointer on the plot,but not directly on the surface of the hill.
3,Drag the plot in any direction,The surface rotates.
18 Chapter 2,Solving a Problem
Your plot should look similar to that of Figure 2-C,For a list of all the
different types of plots,refer to G34G83G79G82G87G86G3(Introduction to the plots package),For
overview information on plots,refer to G34G90G82G85G78G86G75G72G72G87G15G83G79G82G87G76G81G87G72G85G73G68G70G72 (Overview
of Plotting),For information on different plot options,refer to G34G83G79G82G87G15G82G83G87G76G82G81G86G3
(plot[options]) and G34G83G79G82G87G22G71G15G82G83G87G76G82G81 (plot3d[option]).
Figure 2-C The skier’s starting position,the path,and the hill
Similarly,you could display a contour plot with the skier’s path.
2.6 Documenting Your Work 19
2.6 Documenting Your Work
You can document the steps you took to solve a problem by adding some text
to your worksheet,You can then format the text by using different predefined
styles,or you can define your own styles,In addition,you can insert formatted
mathematics in your text.
Adding text
Add a title to your worksheet,and add some text to describe the problem that
you are solving,You can also add text in other locations in the worksheet to
describe how you are solving the problem,
To add a title to your worksheet:
1,Insert a new execution group at the top of the worksheet,place the
insertion point on the top line,and from the Insert menu,choose
Execution Group,then Before Cursor,
2,Click to add text rather than a Maple command.
3,Enter the following text.
G55G75G72G3G54G78G76G72G85G183G86G3G51G68G87G75
4,From the style box (indicated in Figure 2-D),select Title.
5,Press ENTER,and enter your name,It is automatically formatted in the
Author style,
Figure 2-D Worksheet with a title; context bar for text
Style box
Choose styles for the text in your
worksheet.
Text insert button
Insert text in your worksheet.
20 Chapter 2,Solving a Problem
It is possible to redefine the styles (their alignment,font,underlining,and so
on),For more information,refer to G34G90G82G85G78G86G75G72G72G87G15G71G82G70G88G80G72G81G87G76G81G74G15G86G87G92G79G72G86
(Overview of Maple Text Styles).
To add a text description to the worksheet:
1,Place the insertion point on the first input command (the G90G76G87G75 command).
2,From the Insert menu,choose Execution Group,then Before Cursor,
A new prompt appears.
3,Click to add text.
4,Enter the following sentences:
G36G3G86G78G76G72G85G3G75G68G86G3G80G68G71G72G3G75G72G85G3G90G68G92G3G87G82G3G87G75G72G3G87G82G83G3G82G73G3G68G3G80G82G88G81G87G68G76G81G17G3G54G75G72G3G90G68G81G87G86G3G87G82G3
G87G68G78G72G3G87G75G72G3G86G87G72G72G83G72G86G87G3G83G68G87G75G3G71G82G90G81G15G3G90G75G76G70G75G3G86G75G72G3G70G68G81G3G73G76G81G71G3G69G92G3G83G72G85G73G82G85G80G76G81G74G3
G87G75G72G3G70G68G79G70G88G79G68G87G76G82G81G86G3G82G88G87G79G76G81G72G71G3G76G81G3G87G75G76G86G3G90G82G85G78G86G75G72G72G87G17
To add formatted math to the text:
1,To add another paragraph and an extra space to the worksheet,press
ENTER twice,
2,Enter the following text.
G54G88G83G83G82G86G72G3G87G75G68G87G3G87G75G72G3G75G72G76G74G75G87G3G68G87G3G68G3G83G82G76G81G87G3G11G91G15G92G12G3G82G73G3G87G75G72G3G75G76G79G79G3G76G86G3G74G76G89G72G81G3G69G92G3
G73G32G22G18G11G20G14G91G65G21G14G92G65G21G12G18G11G20G18G23G14G20G18G21G13G11G91G14G20G12G65G21G14G20G18G21G13G11G92G14G21G12G65G21G12G15G3G76G81G3G87G75G82G88G86G68G81G71G86G3G82G73G3
G73G72G72G87G17
3,Highlight the equation,
4,From the Format menu,choose Convert to,then Standard Math,The
equation appears in standard math notation.
Your worksheet should look like that in Figure 2-E on page 21.
2.6 Documenting Your Work 21
Figure 2-E Text description with formatted math
Structuring the worksheet with sections
You can add sections to your worksheet to group various elements,When you
enclose elements in a section (or indent them),Maple automatically inserts a
place for a section title,
To add and title a section:
1,Select the first two paragraphs in the worksheet,(They begin with,A
skier …” and end with,… in thousands of feet.”)
2,Click (Indent) on the toolbar,A large range bracket topped by a little
square appears to the left of the two paragraphs you selected.
3,Click next to the box,and enter the title of the section:
G51G85G82G69G79G72G80G3G39G72G86G70G85G76G83G87G76G82G81
Compare your worksheet to Figure 2-F on page 22,You can continue to
document each step in the problem,For more information about sections,refer
22 Chapter 2,Solving a Problem
to G34G90G82G85G78G86G75G72G72G87G15G71G82G70G88G80G72G81G87G76G81G74G15G86G87G85G88G70G87G88G85G76G81G74G21 (Structure Worksheets With
Sections).
Figure 2-F Worksheet with a titled section
Adding numbers
If you plan to print your worksheet,you may find it useful to add page
numbers to the bottom of the page.
To add page numbers (centered at the bottom of the page):
1,From the Format menu,choose Page Numbers.
2,In the Page Number dialog box,
a.Select the Show Page Numbers check box.
b.Under Vertical location,leave the default selection at Bottom.
c.Under Horizontal location,click Center.
d.Click OK.
For more information about the page number options,refer to
G34G90G82G85G78G86G75G72G72G87G15G71G82G70G88G80G72G81G87G76G81G74G15G83G68G74G72G81G88G80G69G72G85G86G3(Page Numbers).
2.7 Exporting to HTML 23
To save your worksheet:
From the File menu,choose Save,If you have not saved it previously,you
are prompted for a file location and name that ends with,mws (for Maple
worksheet).
2.7 Exporting to HTML
You can export your worksheet as an HTML file,(Maple worksheets can also
be exported to HTML with MathML,LaTeX,Maple text,plain text,Rich Text
Format (RTF),and Extensible Markup Language (XML),For more
information,refer to G34G90G82G85G78G86G75G72G72G87G15G80G68G81G68G74G76G81G74G15G72G91G83G82G85G87 (Export a Worksheet).)
To export a worksheet as HTML:
1,With the worksheet you want to export open,from the File menu,select
Export As,then HTML.
2,In the Save As dialog box,enter the name of the file,and click Save.
3,In the HTML Options dialog box,enter the name of the folder for the
images (plots and formatted math) in your worksheet.
4,The resulting HTML page will include the worksheet filename and all of
its sections as links,If you want these links to appear in a left frame,
select the Use Frames check box,If you prefer that the links be at the top
of the page,separated by a horizontal rule,clear the Use Frames check
box.
5,Click OK.
The HTML file is created,You can then open it in your Web browser.
For more information on how to export worksheets,refer to G34G90G82G85G78G86G75G72G72G87G15
G80G68G81G68G74G76G81G74G15G72G91G83G82G85G87G43G55G48G47 (Export as HTML),For information on how Maple
translates the worksheet to HTML,refer to
G34G90G82G85G78G86G75G72G72G87G15G80G68G81G68G74G76G81G74G15G72G91G83G82G85G87G87G82G43G55G48G47 (Translation of Maple Worksheets to
HTML).
24 Chapter 2,Solving a Problem
3 Getting More Information
Chapter 3,Getting More InformationThis guide is a brief introduction to the Maple program,Maple has many
other features,such as spreadsheets,an Excel link,and a MATLAB link,To
learn more,you can use the Maple help system,read the Maple 8 manuals,
and access other online resources.
3.1 The Help System
Maple provides a custom online help system consisting of over 3000 reference
pages,The help system is a convenient resource for determining the syntax of
Maple commands and for learning about the features of the Maple program.
Maple help pages
When you invoke a particular help page in Maple,it is displayed in a new
window,with the Help Browser at the top,Most help pages in Maple are
command reference pages,such as the one in Figure 3-A on page 26.
25
26 Chapter 3,Getting More Information
Figure 3-A Sample Help page
Help page toolbar
The help page toolbar provides commands that make it easier for you to use
the help system,Some of the commands are shown in Figure 3-B on page 27.
Help page name
Full name of the help page.
Help Browser
Tool for perusing
help file topics,Click
on a topic to display
either its subtopics or
its help page,A topic
has subtopics if the
topic name is
followed by an
ellipsis (…).
Name and
description
Statement of the name
and a brief description
of the Maple
command.
Examples
Sample Maple
commands,To copy
all the examples on a
help page,from the
Edit menu,choose
Copy Examples,You
can then paste these
examples into a Maple
worksheet and
execute them.
See Also
Section that contains
hyperlinks to related
topics.
3.1 The Help System 27
Figure 3-B Help toolbar
Getting help
Maple provides many ways of accessing the information in the help system.
The help command displays the help page of a specified command or topic.
The Help Browser lists the help pages in a hierarchy organized by topic,
Topic search finds a help page that matches a specific topic name.
Full text search finds help pages that contain a particular word or phrase.
Help command If you know,or can guess,the name of a help page,you can
access it by using the help command,It is the most direct method of obtaining
help,To use the help command,at the prompt,enter a question mark followed
by the command or topic on which you want help and press ENTER,Note that
you do not have to terminate a help command with either a semicolon or a
colon,For more information,refer to G34G75G72G79G83 (help).
Help Browser The Help Browser is a five-column table of contents that lists
the help pages by topic,Some topics are listed in more than one location,to
help you more easily find the information you need,For more information,
refer to G34G90G82G85G78G86G75G72G72G87G15G85G72G73G72G85G72G81G70G72G15G69G85G82G90G86G72 (Use the Help Browser).
Topic search Topic Search finds the help page that has the specified topic
name (for example,“ithprime”),It may find a help page that lists the specified
topic name as a synonym or an alternate spelling instead,Note that Topic
Search is not case-sensitive,To use Topic Search,from the Help menu,choose
Topic Search,Enter your Topic word and click Search,For more
information,refer to G34G90G82G85G78G86G75G72G72G87G15G75G72G79G83G15G87G82G83G76G70G86G72G68G85G70G75 (Perform a Topic
Search).
Back
Display the previously
viewed help page.
Forward
Display the subsequently
viewed help page.
Alpha forward
Display the help page that is next
alphabetically in the help system
hierarchy,
Alpha back
Display the help page that is
previous alphabetically in the
help system hierarchy,
Parent
Display the parent help
page.
Introduction
Display the Introduction to
Maple 8 page.
28 Chapter 3,Getting More Information
Full text search Full Text Search searches all the help pages and returns
results based on the frequency with which the text occurs,With this search,
you can search on more than one word,However,the results may include
pages that contain only one of the words listed in the Topic box,and not all of
them,Note that Full Text Search is not case-sensitive,To use Full Text
Search,from the Help menu,choose Full Text Search,Enter your word or
words,and click Search,For more information,refer to
G34G90G82G85G78G86G75G72G72G87G15G75G72G79G83G15G73G88G79G79G87G72G91G87G86G72G68G85G70G75 (Perform a Full Text Search).
3.2 Manual Set
The Maple software comes with the following manuals.
Title Content
Maple 8 Getting Started
Guide
This guide contains an introduction to the
graphical user interface and a tutorial that
outlines using Maple to solve mathematical
problems and create technical documents,In it,
there is additional information for new users about
the online help system,New User’s Tour,example
worksheets,and Waterloo Maple Inc,Web site.
Maple 8 Learning Guide This guide explains how Maple and the Maple
language work,It describes the most important
commands and uses them to solve technical
problems.User hints for Maplets are also described
in this guide.
Maple 8 Introductory
Programming Guide
1
1,The Student Edition does not include the Maple 8 Introductory Programming Guide
and the Maple 8 Advanced Programming Guide,These programming guides can be
purchased from school and specialty bookstores or directly from Waterloo Maple Inc.
This guide introduces the basic Maple
programming concepts,such as expressions,data
structures,looping and decision mechanisms,
procedures,input and output,debugging,and
Maplets.
Maple 8 Advanced
Programming Guide
1
This guide extends the basic Maple programming
concepts to more advanced topics,such as modules,
input and output,numerical programming,
graphics programming,and compiled code.
3.3 New User’s Tour 29
3.3 New User’s Tour
The New User’s Tour is a set of interactive worksheets that you can use to
learn about Maple,The worksheets present commands that every user should
know,The tour covers many areas of Maple,such as the worksheet
environment,numerical calculations,algebraic computations,graphics,
calculus,differential equations,linear algebra,finance and statistics,
programming,and online help,The New User’s Tour is easy to follow and a
single topic only takes 10 to 15 minutes to complete.
To access the New User’s Tour:
From the Help menu,choose New User’s Tour.
3.4 Example Worksheets
The example worksheets (there are about 80) contain examples from the
Maple programming language and from ten different areas of mathematics,
such as algebra,geometry,discrete mathematics,integration,integral
transforms,differential equations,general symbolics,general numerics,and
mathematical visualization.
To see the contents of the set of example worksheets:
At the prompt,enter G34G72G91G68G80G83G79G72G86G15G76G81G71G72G91 and press ENTER.
3.5 Web Sites
Waterloo Maple’s Web site has,among other things,information on products,
support,and services,
To visit Waterloo Maple’s Web site:
In your Web browser,enter this URL:
G90G90G90G17G80G68G83G79G72G86G82G73G87G17G70G82G80,or
From the Help menu in your Maple 8 session,select Maple on the Web,
and Maple Home Page.
The Maple Application Center,includes a forum for sharing solutions,
demonstrations of Maple PowerTools,and an online tutorial.
30 Chapter 3,Getting More Information
To visit The Maple Application Center Web site:
In your Web browser,enter this URL:
G90G90G90G17G80G68G83G79G72G68G83G83G86G17G70G82G80,or
From the Help menu in your Maple 8 session,select Maple on the Web,
and Application Center.
The Student Center,includes course help,Maple tutorials,and Maple
graphics.
To visit The Student Center Web site:
In your Web browser,enter this URL:
G90G90G90G17G80G68G83G79G72G23G86G87G88G71G72G81G87G86G17G70G82G80,or
From the Help menu in your Maple 8 session,select Maple on the Web,
and Student Center.
Symbols
c8 operator,13
:= operator,10; terminator,6
c34 command,4,27
A
address of Application Center Web
site,30
address of Web site,29
Advanced Programming Guide,28
Application Center,29
arrays
converting to a list,17
c68c86c86c76c74c81c3command,13
assigning names,10
Author text style,19
axes of plots,11
B
Back help button,27
bar,See toolbar
bracket,4
browser,See Help Browser
in packages,9
reference pages,25–26
computations,numeric and symbolic,1
contents of help,27
context bar,3,19
context-sensitive menus,11
c70c82c81c87c82c88c85c83c79c82c87 command,14
c70c82c81c89c72c85c87 command,17
copying help examples,26
D
derivatives,partial,12
c71c76c73c73 command,12
c71c76c86c83c79c68c92 command,17
ditto operator,13
document,See worksheets
E
equations,solving,13
c72c89c68c79c3command,16
examples in help,26
example worksheets,29
execution group,4,19–20
exporting worksheets,23
Expression palette,4–6
Index
31
buttons
in help toolbar,27
Indent,21
short cuts,3
Text insert,19
C
case-sensitive commands,9,27
centering page numbers,22
Command Line Maple,1–2
commands
case-sensitivity,9
help,4,27
how to enter,5
expressions
entering,5,7
referring to,10
F
finding help topics,27–28
floating toolbars,See palette
c73c82c85 loops,16
formatted math,20–21
formatting text,19
Forward help button,27
frames in HTML export,23
full text search,28
Index 32
G
Getting Started Guide,28
guides,28
H
headings
sections,21
worksheets,19
Help,26
Help Browser,25–27
help command,4,27
help pages,4,25–26
HTML export,23
I
images in HTML export,23
indenting worksheet elements,21
installing Maple,1
integrals,entering,5
Introduction page,2,27
Introductory Programming Guide,28
K
keyboard commands,5
L
LaTeX,23
launching Maple,1–2
Learning Guide,28
licensing Maple,1
list,17
M
manuals,28
Maple Advanced Programming
Guide,28
Maple Application Center,29
Maple Getting Started Guide,28
Maple help,25–28
Maple input,3
Maple Introductory Programming
Guide,28
Maple Learning Guide,10,28
Maple Notation,6
Maple output,4
Maplets,28
Maple window,2–3
Maple worksheets,See worksheets
mathematical expressions
entering,5,7
referring to,10
mathematics in text regions,20–21
MathML,23
Matrix palette,4
memory usage,2
menus,context-sensitive,11
N
names
assigning,11
help pages,26
new execution group,19–20
New User’s Tour,2,29
new worksheet,9
numbering pages,22
numerical solutions,1
O
online help,4,25–28
options
page numbers,22
plot,17–18
P
packages,9
page numbers,22
palette
Expression,4–6
general information,5–7
Matrix,4
Symbol,4–6
Vector,4
partial derivatives,12
plots
adding axes,11
contour,14
entering,11
name assignments,17
options,17–18
rotating,11,17
c83c79c82c87c86 package,10
positioning page numbers,22
Programming Guides
Advanced,28
Introductory,28
prompt,4,19–20
Q
question mark (c34) command,4,27
R
range brackets,4
range of plot axes,11
33 Index
reference pages,25–26
related help pages,26
right-click menus,11
rotating plots,11,17
RTF,23
S
saving worksheets,23
searching help system,27–28
section
heading,3
in a worksheet,4,21–22
range bracket,4
semicolon (c30) terminator,6
sets,13
shortcut buttons,See buttons
shortcut menus,11
Standard Math Notation,4–6
starting Maple,1–2
Student Center,30
styles for text,19
symbolic solutions,1
Symbol palette,4–6
syntax of commands,5
system of equations,solving,13
T
table of contents,help,27
text entry,19–21
titles
sections,21
worksheets,19
Title text style,19
toolbar
help page,26–27
main window,3,19
topic search,27
tutorial,See New User’s Tour
U
URL of Application Center Web site,30
URL of Web site,29
user interface elements,2–4
V
Vector palette,4
W
Web site address,29
window features,2–3
c90c76c87c75c3command,9–10,20
word processing,See text entry
worksheets
adding text,19
adding title,19
creating new,9
example,29
exporting to HTML,23
main window,1,4
numbering pages,22
saving,23
sections,4,21–22
X
x and y plot axes,11
XML,23
Index 34
command the brilliance of a thousand mathematicians
Advanced Programming Guide
Printed in Canada
Waterloo Maple Inc.
57 Erb Street West
Waterloo,Ontario | Canada N2L 6C2
tel,1.519.747.2373 | fax,1.519.747.5284
info@maplesoft.com | www.maplesoft.com
North American Sales,1.800.267.6583
2002 Waterloo Maple Inc,Maple is a registered trademark of Waterloo Maple Inc,
Advanced Programming Guide
Getting Started Guide
M-0027-00-E Printed in Canada
Waterloo Maple Inc.
57 Erb Street West
Waterloo,Ontario | Canada N2L 6C2
tel,1.519.747.2373 | fax,1.519.747.5284
info@maplesoft.com | www.maplesoft.com
North American Sales,1.800.267.6583
2002 Waterloo Maple Inc,Maple is a registered trademark of Waterloo Maple Inc,
Maple 8
Getting Started Guide
2002 by Waterloo Maple Inc.
ii
Waterloo Maple Inc.
57 Erb Street West
Waterloo,ON N2L 6C2
Canada
Maple and Maple V are registered trademarks of Waterloo Maple Inc.
Maplets is a trademark of Waterloo Maple Inc.
2002,2001 by Waterloo Maple Inc,All rights reserved.
The electronic version (PDF) of this book may be downloaded and printed for personal
use or stored as a copy on a personal machine,The electronic version (PDF) of this book
may not be distributed,Information in this document is subject to change without notice
and does not represent a commitment on the part of the vendor,The software described in
this document is furnished under a license agreement and may be used or copied only in
accordance with the agreement,It is against the law to copy the software on any medium
except as specifically allowed in the agreement.
The use of general descriptive names,trade names,trademarks,etc.,in this publication,
even if the former are not especially identified,is not to be taken as a sign that such names,
as understood by the Trade Marks and Merchandise Marks Act,may accordingly be used
freely by anyone.
Windows is a registered trademark of Mircosoft Corporation.
All other trademarks are property of their respective owners.
Printed in Canada
ISBN 1-894511-25-5
1 Chapter 1,Introduction to Maple,...............................................,1
1.1 Installing Maple,...............................................................................,1
1.2 Starting Maple,.................................................................................,1
1.3 The Maple Window,..........................................................................,2
1.4 Accessing Help Pages........................................................................,4
1.5 Entering Expressions in Maple........................................................,5
2 Chapter 2,Solving a Problem,....................................................,9
2.1 Scenario,............................................................................................,9
2.2 Commands in Packages,...................................................................,9
2.3 Math and Visualization,.................................................................,10
Plotting the hill,............................................................................,11
Finding the maximum point of the surface,................................,12
Finding the skier’s starting point,...............................................,13
Finding the path down,................................................................,14
2.4 Using a For Loop—Finding the Path.............................................,15
Performing the initialization,......................................................,15
Specifying the For Loop,...............................................................,16
2.5 Visualization Revisited...................................................................,17
2.6 Documenting Your Work,...............................................................,19
Adding text,...................................................................................,19
Structuring the worksheet with sections,...................................,21
Contents
iii
Adding numbers,..........................................................................,22
2.7 Exporting to HTML.........................................................................,23
3 Chapter 3,Getting More Information,......................................,25
3.1 The Help System.............................................................................,25
Maple help pages,.........................................................................,25
Help page toolbar,.........................................................................,26
Getting help,.................................................................................,27
Help command,........................................................................,27
Help Browser,..........................................................................,27
iv?Contents
Topic search,............................................................................,27
Full text search,.......................................................................,28
3.2 Manual Set,.....................................................................................,28
3.3 New User’s Tour..............................................................................,29
3.4 Example Worksheets,.....................................................................,29
3.5 Web Sites,........................................................................................,29
Index,.................................................................................................,31
1 Introduction to Maple
Chapter 1,Introduction to MapleMaple is an analytic computation system,It performs mathematical
computations and manipulations for solving problems from various technical
disciplines,Most significantly,Maple computes both numerical as well as
symbolic solutions to mathematical expressions,This means that Maple
performs computations on expressions that contain symbols,such as π or x,
without performing numerical approximations,For example,Maple
determines that the derivative of G86G76G81G11G91G12 is G70G82G86G11G91G12,even when G91 has not been
assigned a value,Maple provides exact solutions to many technical problems,
In addition,Maple has visualization tools that contribute to the problem-
solving process,
1.1 Installing Maple
For installation and licensing instructions,refer to the G44G81G86G87G68G79G79G17G75G87G80 file on
your Maple CD.
1.2 Starting Maple
You can run the Maple program with either a graphical user interface or a
command-line interface,In the graphical user interface,you can enter Maple
commands at the prompt,or you can use palettes,context-sensitive menus,
and other features to construct commands,The worksheet is your Maple
document,and in it you can format and document your commands,
In the command-line interface,you enter Maple commands at the prompt,
While you cannot access the graphical interface features,the command-line
1
2 Chapter 1,Introduction to Maple
interface uses less memory than the worksheet interface,It is therefore useful
in solving very large or complex problems on computers with limited memory.
This guide covers the standard interface,For more information on the
command-line interface,look in your Maple folder for the G70G80G71G79G76G81G72G17G87G91G87G3file
(for Macintosh,refer to the G38G82G80G80G68G81G71G3G47G76G81G72G3G53G72G68G71G80G72 file).
To start the standard interface in Windows:
From the Start menu,choose Programs,Maple 8,then Maple 8.
To start the standard interface on a Macintosh computer:
1,Double-click the Maple 8 application icon on the Macintosh hard drive.
2,If prompted,enter your User ID in the Maple 8 Multiple User Logon
dialog box,and click Log On,If you have entered a new ID,you have to
confirm its creation.
To start the standard interface in UNIX or Linux:
Enter the full path,for example,
G18G88G86G85G18G79G82G70G68G79G18G80G68G83G79G72G18G69G76G81G18G91G80G68G83G79G72
Or,
1,Add your Maple 8 directory (for example,G18G88G86G85G18G79G82G70G68G79G18G80G68G83G79G72G18G69G76G81) to your
command search path.
2,Enter G91G80G68G83G79G72.
On all operating systems,the first Maple worksheet session opens with the
Introduction to Maple 8 page that points you to the New User’s Tour,updates,
and other introductory help pages,Subsequent worksheet sessions start with
a new,blank worksheet.
1.3 The Maple Window
The Maple window resembles that of a typical application program,The main
features are shown in Figure 1-A on page 3,
1.3 The Maple Window 3
Figure 1-A Maple window features
A
Toolbar
A toolbar containing shortcut buttons.
B
Context bar
A toolbar containing context-sensitive shortcut buttons,(This means that the
buttons change based on the cursor location or selection.) It can also contain a
field for editing and entering text.
C
Section heading
The name or title of a section.
D
Maple input
A mathematical expression that Maple evaluates,By default,input commands
are entered at the prompt,“>”,and are displayed in red type,The resulting
output is displayed beneath.
A
B
E
C
D
F
G
H
I
J
L
M
N
K
4 Chapter 1,Introduction to Maple
1.4 Accessing Help Pages
The commands and features in Maple are documented in online help pages,To
view help pages,at the prompt,enter a question mark (G34) followed by the
name of the command or subject on which you want help,Do not enter any
spaces,For example,to refer to the help page on natural logarithms,enter
G34G79G81,For information on different ways to get help,see The Help System on
page 25.
E
Maple output
The result of an executed Maple input command,By default,Maple output is
displayed in blue type in Standard Math Notation.
F
Execution group
A set of Maple input with its corresponding output.
G
Worksheet
A Maple document.
H
Section
A grouping of worksheet elements.
I
Section range bracket
A line that,brackets” the elements of a section.
J
Prompt
By default,the Maple prompt is a greater-than symbol that indicates where to
enter Maple input.
K
Symbol palette
A collection of buttons for entering mathematical symbols in Maple.
L
Expression palette
A collection of templates for entering mathematical expressions in Maple.
M
Matrix palette
A collection of templates for entering matrices in Maple.
N
Vector palette
A collection of buttons for entering vectors in Maple.
1.5 Entering Expressions in Maple 5
1.5 Entering Expressions in Maple
To enter expressions at the prompt,use the keyboard,the palettes,or both,
Using the keyboard is the most direct method,but the palettes enable you to
enter a command without knowing its syntax.
There are two types of input display,Use Maple Notation to display input as
Maple syntax,Maple Notation is the default,Use Standard Math Notation
to display input in typeset notation as it appears in a textbook.
These examples step you through entering in various ways.
To enter the integral in Standard Math Notation by using the palettes:
1,Display the palettes,if necessary,From the View menu,choose Palettes,
then Show All Palettes,The Symbol,Expression,Matrix,and Vector
palettes are displayed,Move the palettes to the side of the worksheet,if
necessary.
2,If required,change the input to Standard Math Notation,(If there is a
question mark (?) after the prompt,the input is already set to Standard
Math Notation.) At the prompt,right-click,The context-sensitive menu is
displayed,Choose Standard Math.
3,On the Expression palette,click,The integral symbol appears,and
the question mark placeholder is selected.
4,On the Expression palette,click,The function sin appears,with
another placeholder,
5,Enter G91 (on the keyboard),and press TAB to go to the next placeholder.
6,Repeat step 5.
7,Enter G19 (zero),and press TAB.
8,On the Symbol palette,click,(It is in the bottom row.)
9,Press ENTER,
Your worksheet should resemble that of Figure 1-B on page 6,
x()sin xd
0
π
∫
6 Chapter 1,Introduction to Maple
Figure 1-B Integral input in Standard Math Notation
The next example shows you how you can use the palettes to enter the
expression and learn the Maple command syntax at the same time.
To enter the integral in Maple Notation by using the palettes:
1,On the Expression palette,click,The integral command appears,
and the %? placeholder is selected.
2,On the Expression palette,click,The function sin appears,with
another placeholder,
3,Enter G91 (on the keyboard),and press TAB to go to the next placeholder.
4,Repeat step 5.
5,Enter G19 (zero),and press TAB.
6,On the Symbol palette,click,(It is in the bottom row.)
7,Press ENTER,
Note,Maple appends a semicolon to the end of the command,This signifies the
end of the statement.
1.5 Entering Expressions in Maple 7
Your worksheet should look similar to the one in Figure 1-C.
Figure 1-C Integral input in Maple Notation
Now that you know the correct notation,you could enter the expression at the
prompt,For more information on entering expressions,see the examples in
the next chapter and refer to G34G90G82G85G78G86G75G72G72G87G15G72G91G83G85G72G86G86G76G82G81G86G15G72G81G87G72G85G76G81G74 (Enter
Expressions in Maple),For more information on using palettes,refer to
G34G90G82G85G78G86G75G72G72G87G15G72G91G83G85G72G86G86G76G82G81G86G15G83G68G79G72G87G87G72G86 (Overview of Palettes).
For the rest of this guide,it is assumed that you are entering expressions in
Maple Notation.
8 Chapter 1,Introduction to Maple
2 Solving a Problem
Chapter 2,Solving a ProblemThis chapter presents a mathematical problem with its solution,The
discussion of the problem and its solution introduces you to key features of the
Maple program,Do not worry too much about the mathematics,The purpose
of this problem is to show you Maple; the mathematics is secondary.
Note,When entering Maple commands,please keep in mind that they are case-
sensitive.
2.1 Scenario
A skier has made her way to the top of a mountain,She wants to take the
steepest path down,which she can find by performing the calculations
outlined in this chapter,Start by opening a new worksheet for this problem.
To open a new worksheet:
From the File menu,choose New.
2.2 Commands in Packages
Some of the commands used in the discussion are found in packages,A
package is a group of routines related to a particular area of mathematics,You
can always access commands in packages by using the long form,that is,
specifying both package and function name,G83G68G70G78G68G74G72G62G73G88G81G70G87G76G82G81G64G11G17G17G12,but to
be able to use the short form,that is,specify only the function name,use the
G90G76G87G75 command first.
9
10 Chapter 2,Solving a Problem
To access commands in the G83G79G82G87G86 package:
At the prompt,enter the following and press ENTER.
G90G76G87G75G11G83G79G82G87G86G12G30
After executing the command,Maple lists any warnings,followed by all of the
commands that are included in the package,For the G83G79G82G87G86 package,a
warning indicates that the name of one of the commands in the package,
G70G75G68G81G74G72G70G82G82G85G71G86G15G3is the same as a global name that is already defined,After
executing the G90G76G87G75 command,the original meaning of the command is not
available until you restart Maple,
For other methods of accessing commands in packages,refer to Section 3.7,
“The Organization of Maple,” in the Maple Learning Guide,For a list of all the
packages in Maple,refer to G34G76G81G71G72G91G15G83G68G70G78G68G74G72G86 (Index of descriptions for
packages of library functions).
2.3 Math and Visualization
Use some mathematical and visualization commands to determine basic
properties of the hill,If you want more information on any of the commands
used here,enter a question mark,followed by the name of the command,For
example,to find help on the exponential command,enter G34G72G91G83 (The
Expontential Function).
Suppose that the height at a point G11G91G15G92G12 of the hill is given by G73,in thousands
of feet.
To enter the expression in Maple:
At the prompt,enter the following and press ENTER:
G73G3G29G32G3G22G18G11G20G14G91G65G21G14G92G65G21G12G18G11G20G18G23G14G20G18G21G13G11G91G14G20G12G65G21G14G20G18G21G13G11G92G14G21G12G65G21G12G30
The expression for the shape of the hill is assigned to the name G73 by means of
the assignment operator,:=” so that it can be referred to in subsequent
calculations,For more information about assignments,refer to G34G29G32 (The
f
3
1 x
2
y
2
++()
1
4
---
x 1+()
2
2
-------------------
y 2+()
2
2
-------------------++
---------------------------------------------------------------------------------------------=
2.3 Math and Visualization 11
assignment statement),and for more information about names,refer to G34G81G68G80G72G86
(Names).
Plotting the hill
Before solving the problem,it would be helpful to get an idea of what the hill
looks like (and an idea of what the answer should be),
To plot the expression:
1,Right-click the output of the expression (for Macintosh,option-click),The
context-sensitive menu is displayed.
2,Choose Plots,3-D Plot,then x,y,Maple inserts the plot into the
worksheet.
Note,The content of context-sensitive menus varies depending on the cursor
location or selected expression,For more information,refer to
G34G90G82G85G78G86G75G72G72G87G15G72G91G83G85G72G86G86G76G82G81G86G15G80G68G81G76G83G88G79G68G87G72G70G86G80 (Use Context-Sensitive Menus
to Manipulate Expressions).
To add axes:
Right-click the plot (for Macintosh,option-click),choose Axes,then
Boxed.
To modify the axes ranges:
1,Right-click the plot (for Macintosh,option-click),choose Axes,then
Ranges.
2,In the Axis Range dialog box:
a.Under X Axis,click the button beside the top range box,Enter?G23 in
the top box,then enter G22 in the bottom box.
b.Similarly,change the Y Axis to range from?G23 to G22.
c.Click OK.
The visualization tools in Maple enable you to see the surface from more than
one angle.
To rotate the surface:
1,Click the plot to select it.
2,Place the pointer on the plot,but not directly on the surface of the hill.
3,Drag the plot in any direction,The surface rotates.
12 Chapter 2,Solving a Problem
Depending on how you rotated the plot,it may look similar to Figure 2-A.
Figure 2-A Plot of the hill
While you could look at the surface and guess what the highest point is,you
can obtain a more precise answer by using calculus.
Finding the maximum point of the surface
Determine the location of the top of the hill by taking partial derivatives,
setting them to G19,and solving for G91 and G92.
To find the partial derivative of G73 with respect to G91:
At the prompt,enter the following and press ENTER,
G73G91G3G29G32G3G71G76G73G73G11G73G15G91G12G30
2.3 Math and Visualization 13
To find the partial derivative of G73 with respect to G92:
At the prompt,enter the following and press ENTER.
G73G92G3G29G32G3G71G76G73G73G11G73G15G92G12G30
Since you are interested in the real solution,use the G73G86G82G79G89G72 command instead
of the more general G86G82G79G89G72 command.
To solve the system of equations G94G73G91G32G19G15G3G73G92G32G19G96:
At the prompt,enter the following and press ENTER.
G87G82G83G66G91G92G3G29G32G3G73G86G82G79G89G72G11G94G73G91G32G19G15G73G92G32G19G96G15G94G91G15G92G96G15G94G91G32G16G22G17G17G19G15G92G32G16G22G17G17G19G96G12G30
The top of the hill is therefore at approximately G94G91G3G32G3?G17G28G19G21G25G20G19G19G20G28G28G15
G92G3G32G3G16G20G17G27G19G24G21G21G19G19G23G19G96.
Note,Sets do not preserve order,so you may instead obtain the equivalent set,
{ G92G3G32G3?G20G17G27G19G24G21G21G19G19G23G19G15G3G91G3G32?G17G28G19G21G25G20G19G19G20G28G28G96.
Finding the skier’s starting point
Assume that the skier does not start at the peak but slightly to the side,To
approximate this location,add a small factor,say G19G17G19G24,to the G91G16 and G92G16
values,Assign these values to the variables G91 and G92 and then add the
approximating factor.
To assign the values to the variables:
At the prompt,enter the following and press ENTER.
G68G86G86G76G74G81G11G8G12G30
The ditto operator (%) refers to the result of the previous computation,For
more information,refer to G34G8 (The ditto operators).
To define the starting G91G16 and G92G16values,G91G20G3andG3G92G20,G3respectively:
At the prompt,enter the following and press ENTER.
G91G20G29G32G91G14G19G17G19G24G30
G92G20G29G32G92G14G19G17G19G24G30
The names G91 and G92 have values assigned to them,Since G91 and G92G3are used as
variables in future calculations,they must be unassigned before proceeding.
To unassign G91 and G92:
At the prompt,enter the following and press ENTER.
G91G29G32G183G91G183G30
G92G29G32G183G92G183G30
14 Chapter 2,Solving a Problem
To find the G93-coordinate of the starting point:
Evaluate the function representing the hill at the G91G16 and G92G16values
representing the starting point (G91G20G15G92G20),At the prompt,enter the following
and press ENTER.
G93G20G29G32G72G89G68G79G11G73G15G94G91G32G91G20G15G92G32G92G20G96G12G30
The numerical result {G91G20G3G32G16G17G27G24G21G25G20G19G19G20G28G28G3G15G3G92G20G3G32G3G16G20G17G26G24G24G21G21G19G19G23G19G15G3G93G20G3G32G3
G21G17G20G23G24G25G22G20G23G24G22G96 is an approximation of the skier’s starting point.
Finding the path down
Before you find the path,take a look at the level curves of the hill to get an
idea of the skier’s path.
To plot the level curves:
The G70G82G81G87G82G88G85G83G79G82G87 command with five contours suggests an interesting
shape,as shown in Figure 2-B,At the prompt,enter the following
command and press ENTER.
G70G82G81G87G82G88G85G83G79G82G87G11G73G15G3G91G32?G21G17G17G20G15G3G92G32?G22G17G17G20G15G3G70G82G81G87G82G88G85G86G32G24G15G3G73G76G79G79G72G71G32G87G85G88G72G12G30
Figure 2-B Level curves of the hill
2.4 Using a For Loop—Finding the Path 15
2.4 Using a For Loop—Finding the Path
Next,construct and plot the path on the surface of the hill that the skier
should take,The negative of the gradient (G73G11G91G15G92G12G3G82G85G3?G74G85G68G71G11G73G11G91G15G92G12) in the
Maple language),gives the G91 and G92G3components of the direction of steepest
descent,At each point G11G91G15G92G15G93G12 on the surface,the skier should travel in the
direction ofG73G11G91G15G92G12,while staying on the surface,SinceG73G11G91G15G92G12 changes
from point to point,you can break the process into steps,building an
approximation of the path of steepest descent,If the step size is too large,the
path may leave the surface of the hill,If the step size is too small,you derive
no benefit from the increased number of calculations.
Performing the initialization
Assume that the skier is currently at the starting point (G91G20G15G92G20G15G93G20),Use a
timestep of 0.1 and find 25 points along the path,Use the arrays G83G82G76G81G87G22G71 and
G85G82G88G87G72G22G71 to store the values of the computed points and the direction taken,
respectively,To simplify the calculation of the points and route,define vector
representations of the expressions for the hill and the derivatives with respect
to both G91 and G92.
To define vector representations of the expressions:
At the prompt,enter the following and press ENTER.
G74G29G32G72G89G68G79G11G73G15G94G91G32G51G62G20G64G15G92G32G51G62G21G64G96G12G30
G74G91G29G32G72G89G68G79G11G73G91G15G94G91G32G51G62G20G64G15G92G32G51G62G21G64G96G12G30
G74G92G29G32G72G89G68G79G11G73G92G15G94G91G32G51G62G20G64G15G92G32G51G62G21G64G96G12G30
To declare the arrays for storing the values at each timestep:
At the prompt,enter the following and press ENTER.
G83G82G76G81G87G22G71G29G32G36G85G85G68G92G11G20G17G17G21G24G12G30
G85G82G88G87G72G22G71G29G32G36G85G85G68G92G11G20G17G17G21G24G12G30
To define the initialization:
At the prompt,enter the following and press ENTER.
G87G76G80G72G86G87G72G83G29G32G19G17G20G30
G83G82G76G81G87G22G71G62G20G64G29G32G31G91G20G15G92G20G15G93G20G33G30
Note,The notation G31G91G20G15G92G20G15G93G20G33 defines a Vector while P[i] accesses the i
th
element of the list P,For more information about Vectors,refer to G34G57G72G70G87G82G85
(Vector - construct a Vector),For more information about lists,refer to G34G79G76G86G87G86
(Sets and Lists).
16 Chapter 2,Solving a Problem
Specifying the For Loop
To obtain the additional 24 points,use a G73G82G85 loop,A G73G82G85 loop repeatedly
executes a sequence of Maple commands entered between the G73G82G85 and G72G81G71G3
commands of the loop,that is,in the loop body,It executes the commands as
the value of a numeric variable,called an index,varies from its specified
initial value to its specified final value,The value of the index is incremented
after each execution of the commands in the body of the loop,The iteration
stops when the value of the index is greater than the specified final value,For
information on other programming structures in Maple,refer to the Maple
Introductory Programming Guide.
To start the G73G82G85 loop:
At the prompt,enter the following and press ENTER.
G73G82G85G3G76G3G73G85G82G80G3G20G3G87G82G3G21G23G3G71G82
Note,After you press ENTER,Maple returns the message:,Warning,premature
end of input.” It is simply reminding you that the G73G82G85 statement is not complete,To
continue entering your input without receiving this warning,use SHIFT+ENTER to
go to the next line.
The next commands comprise the body of the G73G82G85 loop,These commands find
the skier’s position at the end of each time step.
To construct the 3-D normalized negative of the gradient vectors:
At the prompt,enter the following and press ENTER.
G85G82G88G87G72G22G71G62G76G64G3G29G32G3G47G76G81G72G68G85G36G79G74G72G69G85G68G62G49G82G85G80G68G79G76G93G72G64G11G72G89G68G79G11G31G16G74G91G15G16G74G92G15G19G33G15G3
G51G32G83G82G76G81G87G22G71G62G76G64G12G12G30
To find the next point in the skier’s path:
At the prompt,enter the following and press ENTER.
G83G82G76G81G87G22G71G62G76G14G20G64G3G29G32G3
G72G89G68G79G11G31G51G62G20G64G15G51G62G21G64G15G74G33G15G51G32G83G82G76G81G87G22G71G62G76G64G14G87G76G80G72G86G87G72G83G13G85G82G88G87G72G22G71G62G76G64G12G30
To complete the G73G82G85 loop:
At the prompt,enter the following and press ENTER,Remember to end the
line with a colon to suppress the output.
G72G81G71G3G71G82G29
This command ends the G73G82G85 loop,After you press ENTER,the five commands in
the loop body are repeated 24 times,At the end of each iteration,the value of G76
is increased by 1,That is,for the first iteration,the value of G76 is its initial
value 1,for the second 2,and so on,For the last iteration the value of G76 is 24,
Maple exits at the end of the 24th iteration once G76 is set to 25 (since 25 is
outside of the bounds of the loop).
2.5 Visualization Revisited 17
To graph the path,you must convert the points representing the path of the
skier,which are stored in the G83G82G76G81G87G22G71 array,to a list.
To convert the G83G82G76G81G87G22G71 array to a list:
At the prompt,enter the following and press ENTER.
G79G76G86G87G83G82G76G81G87G86G22G71G3G29G32G3G62G86G72G84G11G3G70G82G81G89G72G85G87G11G3G83G82G76G81G87G22G71G62G76G64G15G3G79G76G86G87G3G12G15G3G76G32G20G17G17G21G24G3G12G64G29
You will use these lists in the next section.
2.5 Visualization Revisited
The visualization tools in Maple enable you to create different kinds of two-
and three-dimensional plots in a number of coordinate systems,In addition,
you can plot more than one element on a single set of axes,First assign the
individual plots to names,then plot them together by using the G71G76G86G83G79G68G92
command.
To plot the hill and assign it to the name G80G82G88G81G87G68G76G81:
At the prompt,enter the following and press ENTER,Remember to end the
line with a colon to suppress the output.
G80G82G88G81G87G68G76G81G3G29G32G3G83G79G82G87G22G71G11G73G15G3G91G32?G22G17G17G22G15G3G92G32?G23G17G17G23G15G3G68G91G72G86G32G69G82G91G72G71G12G29
To plot the set of points on the path as a straight line and assign it to
G83G68G87G75G22G71:
At the prompt,enter the following and press ENTER.
G83G68G87G75G22G71G3G29G32G3G83G82G76G81G87G83G79G82G87G22G71G11G79G76G86G87G83G82G76G81G87G86G22G71G15G3G86G87G92G79G72G32G79G76G81G72G15G3G70G82G79G82G85G32G85G72G71G12G29
To plot the starting point of the skier and assign it to G86G78G76G72G85:
At the prompt,enter the following and press ENTER.
G86G78G76G72G85G3G29G32G3G83G82G76G81G87G83G79G82G87G22G71G11G70G82G81G89G72G85G87G11G83G82G76G81G87G22G71G62G20G64G15G79G76G86G87G12G15G3G86G92G80G69G82G79G32G70G85G82G86G86G15G3
G86G92G80G69G82G79G86G76G93G72G32G24G19G15G70G82G79G82G85G32G92G72G79G79G82G90G12G29
To view all three elements at once,
At the prompt,enter the following and press ENTER.
G71G76G86G83G79G68G92G11G80G82G88G81G87G68G76G81G15G3G86G78G76G72G85G15G3G83G68G87G75G22G71G12G30
To rotate the surface of the plot to see the path:
1,Click the plot to select it.
2,Place the pointer on the plot,but not directly on the surface of the hill.
3,Drag the plot in any direction,The surface rotates.
18 Chapter 2,Solving a Problem
Your plot should look similar to that of Figure 2-C,For a list of all the
different types of plots,refer to G34G83G79G82G87G86G3(Introduction to the plots package),For
overview information on plots,refer to G34G90G82G85G78G86G75G72G72G87G15G83G79G82G87G76G81G87G72G85G73G68G70G72 (Overview
of Plotting),For information on different plot options,refer to G34G83G79G82G87G15G82G83G87G76G82G81G86G3
(plot[options]) and G34G83G79G82G87G22G71G15G82G83G87G76G82G81 (plot3d[option]).
Figure 2-C The skier’s starting position,the path,and the hill
Similarly,you could display a contour plot with the skier’s path.
2.6 Documenting Your Work 19
2.6 Documenting Your Work
You can document the steps you took to solve a problem by adding some text
to your worksheet,You can then format the text by using different predefined
styles,or you can define your own styles,In addition,you can insert formatted
mathematics in your text.
Adding text
Add a title to your worksheet,and add some text to describe the problem that
you are solving,You can also add text in other locations in the worksheet to
describe how you are solving the problem,
To add a title to your worksheet:
1,Insert a new execution group at the top of the worksheet,place the
insertion point on the top line,and from the Insert menu,choose
Execution Group,then Before Cursor,
2,Click to add text rather than a Maple command.
3,Enter the following text.
G55G75G72G3G54G78G76G72G85G183G86G3G51G68G87G75
4,From the style box (indicated in Figure 2-D),select Title.
5,Press ENTER,and enter your name,It is automatically formatted in the
Author style,
Figure 2-D Worksheet with a title; context bar for text
Style box
Choose styles for the text in your
worksheet.
Text insert button
Insert text in your worksheet.
20 Chapter 2,Solving a Problem
It is possible to redefine the styles (their alignment,font,underlining,and so
on),For more information,refer to G34G90G82G85G78G86G75G72G72G87G15G71G82G70G88G80G72G81G87G76G81G74G15G86G87G92G79G72G86
(Overview of Maple Text Styles).
To add a text description to the worksheet:
1,Place the insertion point on the first input command (the G90G76G87G75 command).
2,From the Insert menu,choose Execution Group,then Before Cursor,
A new prompt appears.
3,Click to add text.
4,Enter the following sentences:
G36G3G86G78G76G72G85G3G75G68G86G3G80G68G71G72G3G75G72G85G3G90G68G92G3G87G82G3G87G75G72G3G87G82G83G3G82G73G3G68G3G80G82G88G81G87G68G76G81G17G3G54G75G72G3G90G68G81G87G86G3G87G82G3
G87G68G78G72G3G87G75G72G3G86G87G72G72G83G72G86G87G3G83G68G87G75G3G71G82G90G81G15G3G90G75G76G70G75G3G86G75G72G3G70G68G81G3G73G76G81G71G3G69G92G3G83G72G85G73G82G85G80G76G81G74G3
G87G75G72G3G70G68G79G70G88G79G68G87G76G82G81G86G3G82G88G87G79G76G81G72G71G3G76G81G3G87G75G76G86G3G90G82G85G78G86G75G72G72G87G17
To add formatted math to the text:
1,To add another paragraph and an extra space to the worksheet,press
ENTER twice,
2,Enter the following text.
G54G88G83G83G82G86G72G3G87G75G68G87G3G87G75G72G3G75G72G76G74G75G87G3G68G87G3G68G3G83G82G76G81G87G3G11G91G15G92G12G3G82G73G3G87G75G72G3G75G76G79G79G3G76G86G3G74G76G89G72G81G3G69G92G3
G73G32G22G18G11G20G14G91G65G21G14G92G65G21G12G18G11G20G18G23G14G20G18G21G13G11G91G14G20G12G65G21G14G20G18G21G13G11G92G14G21G12G65G21G12G15G3G76G81G3G87G75G82G88G86G68G81G71G86G3G82G73G3
G73G72G72G87G17
3,Highlight the equation,
4,From the Format menu,choose Convert to,then Standard Math,The
equation appears in standard math notation.
Your worksheet should look like that in Figure 2-E on page 21.
2.6 Documenting Your Work 21
Figure 2-E Text description with formatted math
Structuring the worksheet with sections
You can add sections to your worksheet to group various elements,When you
enclose elements in a section (or indent them),Maple automatically inserts a
place for a section title,
To add and title a section:
1,Select the first two paragraphs in the worksheet,(They begin with,A
skier …” and end with,… in thousands of feet.”)
2,Click (Indent) on the toolbar,A large range bracket topped by a little
square appears to the left of the two paragraphs you selected.
3,Click next to the box,and enter the title of the section:
G51G85G82G69G79G72G80G3G39G72G86G70G85G76G83G87G76G82G81
Compare your worksheet to Figure 2-F on page 22,You can continue to
document each step in the problem,For more information about sections,refer
22 Chapter 2,Solving a Problem
to G34G90G82G85G78G86G75G72G72G87G15G71G82G70G88G80G72G81G87G76G81G74G15G86G87G85G88G70G87G88G85G76G81G74G21 (Structure Worksheets With
Sections).
Figure 2-F Worksheet with a titled section
Adding numbers
If you plan to print your worksheet,you may find it useful to add page
numbers to the bottom of the page.
To add page numbers (centered at the bottom of the page):
1,From the Format menu,choose Page Numbers.
2,In the Page Number dialog box,
a.Select the Show Page Numbers check box.
b.Under Vertical location,leave the default selection at Bottom.
c.Under Horizontal location,click Center.
d.Click OK.
For more information about the page number options,refer to
G34G90G82G85G78G86G75G72G72G87G15G71G82G70G88G80G72G81G87G76G81G74G15G83G68G74G72G81G88G80G69G72G85G86G3(Page Numbers).
2.7 Exporting to HTML 23
To save your worksheet:
From the File menu,choose Save,If you have not saved it previously,you
are prompted for a file location and name that ends with,mws (for Maple
worksheet).
2.7 Exporting to HTML
You can export your worksheet as an HTML file,(Maple worksheets can also
be exported to HTML with MathML,LaTeX,Maple text,plain text,Rich Text
Format (RTF),and Extensible Markup Language (XML),For more
information,refer to G34G90G82G85G78G86G75G72G72G87G15G80G68G81G68G74G76G81G74G15G72G91G83G82G85G87 (Export a Worksheet).)
To export a worksheet as HTML:
1,With the worksheet you want to export open,from the File menu,select
Export As,then HTML.
2,In the Save As dialog box,enter the name of the file,and click Save.
3,In the HTML Options dialog box,enter the name of the folder for the
images (plots and formatted math) in your worksheet.
4,The resulting HTML page will include the worksheet filename and all of
its sections as links,If you want these links to appear in a left frame,
select the Use Frames check box,If you prefer that the links be at the top
of the page,separated by a horizontal rule,clear the Use Frames check
box.
5,Click OK.
The HTML file is created,You can then open it in your Web browser.
For more information on how to export worksheets,refer to G34G90G82G85G78G86G75G72G72G87G15
G80G68G81G68G74G76G81G74G15G72G91G83G82G85G87G43G55G48G47 (Export as HTML),For information on how Maple
translates the worksheet to HTML,refer to
G34G90G82G85G78G86G75G72G72G87G15G80G68G81G68G74G76G81G74G15G72G91G83G82G85G87G87G82G43G55G48G47 (Translation of Maple Worksheets to
HTML).
24 Chapter 2,Solving a Problem
3 Getting More Information
Chapter 3,Getting More InformationThis guide is a brief introduction to the Maple program,Maple has many
other features,such as spreadsheets,an Excel link,and a MATLAB link,To
learn more,you can use the Maple help system,read the Maple 8 manuals,
and access other online resources.
3.1 The Help System
Maple provides a custom online help system consisting of over 3000 reference
pages,The help system is a convenient resource for determining the syntax of
Maple commands and for learning about the features of the Maple program.
Maple help pages
When you invoke a particular help page in Maple,it is displayed in a new
window,with the Help Browser at the top,Most help pages in Maple are
command reference pages,such as the one in Figure 3-A on page 26.
25
26 Chapter 3,Getting More Information
Figure 3-A Sample Help page
Help page toolbar
The help page toolbar provides commands that make it easier for you to use
the help system,Some of the commands are shown in Figure 3-B on page 27.
Help page name
Full name of the help page.
Help Browser
Tool for perusing
help file topics,Click
on a topic to display
either its subtopics or
its help page,A topic
has subtopics if the
topic name is
followed by an
ellipsis (…).
Name and
description
Statement of the name
and a brief description
of the Maple
command.
Examples
Sample Maple
commands,To copy
all the examples on a
help page,from the
Edit menu,choose
Copy Examples,You
can then paste these
examples into a Maple
worksheet and
execute them.
See Also
Section that contains
hyperlinks to related
topics.
3.1 The Help System 27
Figure 3-B Help toolbar
Getting help
Maple provides many ways of accessing the information in the help system.
The help command displays the help page of a specified command or topic.
The Help Browser lists the help pages in a hierarchy organized by topic,
Topic search finds a help page that matches a specific topic name.
Full text search finds help pages that contain a particular word or phrase.
Help command If you know,or can guess,the name of a help page,you can
access it by using the help command,It is the most direct method of obtaining
help,To use the help command,at the prompt,enter a question mark followed
by the command or topic on which you want help and press ENTER,Note that
you do not have to terminate a help command with either a semicolon or a
colon,For more information,refer to G34G75G72G79G83 (help).
Help Browser The Help Browser is a five-column table of contents that lists
the help pages by topic,Some topics are listed in more than one location,to
help you more easily find the information you need,For more information,
refer to G34G90G82G85G78G86G75G72G72G87G15G85G72G73G72G85G72G81G70G72G15G69G85G82G90G86G72 (Use the Help Browser).
Topic search Topic Search finds the help page that has the specified topic
name (for example,“ithprime”),It may find a help page that lists the specified
topic name as a synonym or an alternate spelling instead,Note that Topic
Search is not case-sensitive,To use Topic Search,from the Help menu,choose
Topic Search,Enter your Topic word and click Search,For more
information,refer to G34G90G82G85G78G86G75G72G72G87G15G75G72G79G83G15G87G82G83G76G70G86G72G68G85G70G75 (Perform a Topic
Search).
Back
Display the previously
viewed help page.
Forward
Display the subsequently
viewed help page.
Alpha forward
Display the help page that is next
alphabetically in the help system
hierarchy,
Alpha back
Display the help page that is
previous alphabetically in the
help system hierarchy,
Parent
Display the parent help
page.
Introduction
Display the Introduction to
Maple 8 page.
28 Chapter 3,Getting More Information
Full text search Full Text Search searches all the help pages and returns
results based on the frequency with which the text occurs,With this search,
you can search on more than one word,However,the results may include
pages that contain only one of the words listed in the Topic box,and not all of
them,Note that Full Text Search is not case-sensitive,To use Full Text
Search,from the Help menu,choose Full Text Search,Enter your word or
words,and click Search,For more information,refer to
G34G90G82G85G78G86G75G72G72G87G15G75G72G79G83G15G73G88G79G79G87G72G91G87G86G72G68G85G70G75 (Perform a Full Text Search).
3.2 Manual Set
The Maple software comes with the following manuals.
Title Content
Maple 8 Getting Started
Guide
This guide contains an introduction to the
graphical user interface and a tutorial that
outlines using Maple to solve mathematical
problems and create technical documents,In it,
there is additional information for new users about
the online help system,New User’s Tour,example
worksheets,and Waterloo Maple Inc,Web site.
Maple 8 Learning Guide This guide explains how Maple and the Maple
language work,It describes the most important
commands and uses them to solve technical
problems.User hints for Maplets are also described
in this guide.
Maple 8 Introductory
Programming Guide
1
1,The Student Edition does not include the Maple 8 Introductory Programming Guide
and the Maple 8 Advanced Programming Guide,These programming guides can be
purchased from school and specialty bookstores or directly from Waterloo Maple Inc.
This guide introduces the basic Maple
programming concepts,such as expressions,data
structures,looping and decision mechanisms,
procedures,input and output,debugging,and
Maplets.
Maple 8 Advanced
Programming Guide
1
This guide extends the basic Maple programming
concepts to more advanced topics,such as modules,
input and output,numerical programming,
graphics programming,and compiled code.
3.3 New User’s Tour 29
3.3 New User’s Tour
The New User’s Tour is a set of interactive worksheets that you can use to
learn about Maple,The worksheets present commands that every user should
know,The tour covers many areas of Maple,such as the worksheet
environment,numerical calculations,algebraic computations,graphics,
calculus,differential equations,linear algebra,finance and statistics,
programming,and online help,The New User’s Tour is easy to follow and a
single topic only takes 10 to 15 minutes to complete.
To access the New User’s Tour:
From the Help menu,choose New User’s Tour.
3.4 Example Worksheets
The example worksheets (there are about 80) contain examples from the
Maple programming language and from ten different areas of mathematics,
such as algebra,geometry,discrete mathematics,integration,integral
transforms,differential equations,general symbolics,general numerics,and
mathematical visualization.
To see the contents of the set of example worksheets:
At the prompt,enter G34G72G91G68G80G83G79G72G86G15G76G81G71G72G91 and press ENTER.
3.5 Web Sites
Waterloo Maple’s Web site has,among other things,information on products,
support,and services,
To visit Waterloo Maple’s Web site:
In your Web browser,enter this URL:
G90G90G90G17G80G68G83G79G72G86G82G73G87G17G70G82G80,or
From the Help menu in your Maple 8 session,select Maple on the Web,
and Maple Home Page.
The Maple Application Center,includes a forum for sharing solutions,
demonstrations of Maple PowerTools,and an online tutorial.
30 Chapter 3,Getting More Information
To visit The Maple Application Center Web site:
In your Web browser,enter this URL:
G90G90G90G17G80G68G83G79G72G68G83G83G86G17G70G82G80,or
From the Help menu in your Maple 8 session,select Maple on the Web,
and Application Center.
The Student Center,includes course help,Maple tutorials,and Maple
graphics.
To visit The Student Center Web site:
In your Web browser,enter this URL:
G90G90G90G17G80G68G83G79G72G23G86G87G88G71G72G81G87G86G17G70G82G80,or
From the Help menu in your Maple 8 session,select Maple on the Web,
and Student Center.
Symbols
c8 operator,13
:= operator,10; terminator,6
c34 command,4,27
A
address of Application Center Web
site,30
address of Web site,29
Advanced Programming Guide,28
Application Center,29
arrays
converting to a list,17
c68c86c86c76c74c81c3command,13
assigning names,10
Author text style,19
axes of plots,11
B
Back help button,27
bar,See toolbar
bracket,4
browser,See Help Browser
in packages,9
reference pages,25–26
computations,numeric and symbolic,1
contents of help,27
context bar,3,19
context-sensitive menus,11
c70c82c81c87c82c88c85c83c79c82c87 command,14
c70c82c81c89c72c85c87 command,17
copying help examples,26
D
derivatives,partial,12
c71c76c73c73 command,12
c71c76c86c83c79c68c92 command,17
ditto operator,13
document,See worksheets
E
equations,solving,13
c72c89c68c79c3command,16
examples in help,26
example worksheets,29
execution group,4,19–20
exporting worksheets,23
Expression palette,4–6
Index
31
buttons
in help toolbar,27
Indent,21
short cuts,3
Text insert,19
C
case-sensitive commands,9,27
centering page numbers,22
Command Line Maple,1–2
commands
case-sensitivity,9
help,4,27
how to enter,5
expressions
entering,5,7
referring to,10
F
finding help topics,27–28
floating toolbars,See palette
c73c82c85 loops,16
formatted math,20–21
formatting text,19
Forward help button,27
frames in HTML export,23
full text search,28
Index 32
G
Getting Started Guide,28
guides,28
H
headings
sections,21
worksheets,19
Help,26
Help Browser,25–27
help command,4,27
help pages,4,25–26
HTML export,23
I
images in HTML export,23
indenting worksheet elements,21
installing Maple,1
integrals,entering,5
Introduction page,2,27
Introductory Programming Guide,28
K
keyboard commands,5
L
LaTeX,23
launching Maple,1–2
Learning Guide,28
licensing Maple,1
list,17
M
manuals,28
Maple Advanced Programming
Guide,28
Maple Application Center,29
Maple Getting Started Guide,28
Maple help,25–28
Maple input,3
Maple Introductory Programming
Guide,28
Maple Learning Guide,10,28
Maple Notation,6
Maple output,4
Maplets,28
Maple window,2–3
Maple worksheets,See worksheets
mathematical expressions
entering,5,7
referring to,10
mathematics in text regions,20–21
MathML,23
Matrix palette,4
memory usage,2
menus,context-sensitive,11
N
names
assigning,11
help pages,26
new execution group,19–20
New User’s Tour,2,29
new worksheet,9
numbering pages,22
numerical solutions,1
O
online help,4,25–28
options
page numbers,22
plot,17–18
P
packages,9
page numbers,22
palette
Expression,4–6
general information,5–7
Matrix,4
Symbol,4–6
Vector,4
partial derivatives,12
plots
adding axes,11
contour,14
entering,11
name assignments,17
options,17–18
rotating,11,17
c83c79c82c87c86 package,10
positioning page numbers,22
Programming Guides
Advanced,28
Introductory,28
prompt,4,19–20
Q
question mark (c34) command,4,27
R
range brackets,4
range of plot axes,11
33 Index
reference pages,25–26
related help pages,26
right-click menus,11
rotating plots,11,17
RTF,23
S
saving worksheets,23
searching help system,27–28
section
heading,3
in a worksheet,4,21–22
range bracket,4
semicolon (c30) terminator,6
sets,13
shortcut buttons,See buttons
shortcut menus,11
Standard Math Notation,4–6
starting Maple,1–2
Student Center,30
styles for text,19
symbolic solutions,1
Symbol palette,4–6
syntax of commands,5
system of equations,solving,13
T
table of contents,help,27
text entry,19–21
titles
sections,21
worksheets,19
Title text style,19
toolbar
help page,26–27
main window,3,19
topic search,27
tutorial,See New User’s Tour
U
URL of Application Center Web site,30
URL of Web site,29
user interface elements,2–4
V
Vector palette,4
W
Web site address,29
window features,2–3
c90c76c87c75c3command,9–10,20
word processing,See text entry
worksheets
adding text,19
adding title,19
creating new,9
example,29
exporting to HTML,23
main window,1,4
numbering pages,22
saving,23
sections,4,21–22
X
x and y plot axes,11
XML,23
Index 34
command the brilliance of a thousand mathematicians
Advanced Programming Guide
Printed in Canada
Waterloo Maple Inc.
57 Erb Street West
Waterloo,Ontario | Canada N2L 6C2
tel,1.519.747.2373 | fax,1.519.747.5284
info@maplesoft.com | www.maplesoft.com
North American Sales,1.800.267.6583
2002 Waterloo Maple Inc,Maple is a registered trademark of Waterloo Maple Inc,
Advanced Programming Guide
