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{SECT 0 {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 18
"" 0 "" {TEXT -1 49 "Systemwide Workshop for Calculus and Maple at USC
" }}{PARA 18 "" 0 "" {TEXT 256 23 "Introduction to Maple 8" }}{PARA
256 "" 0 "" {TEXT -1 16 "Douglas B. Meade" }}{PARA 256 "" 0 "" {TEXT
-1 10 "E-mail: " }{TEXT 257 17 "meade@math.sc.edu" }{TEXT -1 7 " \+
" }}{PARA 256 "" 0 "" {TEXT -1 11 "WWW URL: " }{URLLINK 17 "http:
//www.math.sc.edu/~meade/" 4 "http://www.math.sc.edu/~meade/" "" }
{TEXT -1 1 " " }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{SECT 1 {PARA 3 ""
0 "" {TEXT -1 10 "Objectives" }}{EXCHG {PARA 15 "" 0 "" {TEXT -1 26 "W
orking with the Maple GUI" }}{PARA 15 "" 0 "" {TEXT -1 33 "Entering ma
thematical expressions" }}{PARA 15 "" 0 "" {TEXT -1 29 "Plotting funct
ions and points" }}{PARA 15 "" 0 "" {TEXT -1 41 "The fundamentals for \+
algebra and calculus" }}{PARA 15 "" 0 "" {TEXT -1 7 "Maplets" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}{SECT 1 {PARA 3 "" 0 "
" {TEXT -1 14 "What is Maple?" }}{EXCHG {PARA 0 "" 0 "" {TEXT -1 597 "
Much of your mathematical background has probably been focused on deve
loping the ability to solve equations and explore functions. The sophi
sticated manipulation of symbols and expressions that you use to solve
equations and investigate functions can also be performed by software
packages called computer algebra systems (CAS). A CAS can be use to g
enerate the exact symbolic solutions you obtained by hand, the numeric
al approximations you found using a calculator, and the graphs you hav
e drawn. Maple is one of several CAS's; other major examples are Mathe
matica, Macsyma, Derive, and MathCad." }}{PARA 0 "" 0 "" {TEXT -1 0 "
" }}{PARA 0 "" 0 "" {URLLINK 17 "Maple" 4 "http://www.maplesoft.com/pr
oducts/Maple8/" "" }{TEXT -1 17 " is a product of " }{URLLINK 17 "Mapl
esoft" 4 "http://www.maplesoft.com/" "" }{TEXT -1 67 " (formerly Water
loo Maple). Other products in the Maple suite are " }{URLLINK 17 "Map
leNet" 4 "http://www.maplesoft.com/maplenet" "" }{TEXT -1 5 " and " }
{URLLINK 17 "MapleTA" 4 "http://www.maplesoft.com/mapleta/" "" }{TEXT
-1 1 "." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG
{PARA 0 "" 0 "" {TEXT -1 219 "Maple can be used in many different ways
. In a course where students are developing manual manipulative skill
s, the primary uses of Maple are likely to be the graphical display of
functions and the use of custom-built " }{HYPERLNK 17 "maplets" 2 "ma
plets" "" }{TEXT -1 333 " illustrating a specific concept from the cou
rse. In later courses Maple's symbolic manipulation features can be u
tilized by students to emphasize higher-level concepts by letting the \+
software assist with the manipulations. As students become familiar w
ith Maple they should see that it will be of use in a wide variety of \+
courses." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}{SECT 1
{PARA 3 "" 0 "" {TEXT -1 34 "Getting Started with the Maple GUI" }}
{SECT 1 {PARA 4 "" 0 "" {TEXT -1 29 "Documentation and Online Help" }}
{EXCHG {PARA 0 "" 0 "" {TEXT -1 256 "The on-line help for Maple is ver
y good. The help pages describe the syntax of each command, a brief de
scription of the algorithm that has been implemented, and a few exampl
es illustrating the use of the command. To obtain help on the command \+
func , type: " }{TEXT 19 5 "?func" }{TEXT -1 27 " in any input region.
The " }{TEXT 258 4 "Help" }{TEXT -1 99 " dropdown menu on the menu b
ar provides a number of different ways to access Maple's help system. \+
" }{TEXT 259 12 "Topic Search" }{TEXT -1 5 " and " }{TEXT 260 16 "Ful
l Text Search" }{TEXT -1 64 " are two interactive interfaces to the en
tire Maple help system." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 ""
0 "" {TEXT -1 27 "To get started, select the " }{TEXT 263 8 "Glossary
" }{TEXT -1 128 " entry and take a few minutes to become familiar with
some of the terminology related to Maple and its graphical user inter
face." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 56 "
If you have more time and are a new Maple user take the " }{TEXT 261
15 "New User's Tour" }{TEXT -1 57 "; if you have used earlier versions
of Maple, select the " }{TEXT 262 10 "What's New" }{TEXT -1 7 " entry
." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 168 "A f
inal suggestion is that anytime you want to see the Maple help for a c
ommand or other word in a Maple worksheet, position the cursor anywher
e in that word and press " }{TEXT 264 7 "Ctrl-F1" }{TEXT -1 42 ". Thi
s is Maple's context-sensitive help." }}}{EXCHG {PARA 0 "> " 0 ""
{MPLTEXT 1 0 0 "" }}}}{SECT 1 {PARA 4 "" 0 "" {TEXT -1 10 "Worksheets
" }}{EXCHG {PARA 0 "" 0 "" {TEXT -1 119 "The worksheet is the basic Ma
ple document. (Use Maple's context-sensitve help to view the online h
elp for worksheets.)" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "
" {TEXT -1 120 "You have already learned how to open up a worksheet. \+
After Maple is opened, position the cursor arrow on the menu item " }
{TEXT 266 4 "File" }{TEXT -1 49 " and click the left button once. You
can select " }{TEXT 267 3 "New" }{TEXT -1 56 " to obtain a fresh, emp
ty worksheet. Or you can select " }{TEXT 268 4 "Open" }{TEXT -1 64 " \+
to choose an existing worksheet (the name will always end with " }
{TEXT 265 4 ".mws" }{TEXT -1 100 "), either by double clicking on the \+
name or by selecting the name and then pressing the Open button." }}
{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 463 "Once in \+
a worksheet the current location is marked by the cursor, a vertical b
ar. You can move around by moving the mouse and then clicking the lef
t button once, by using the arrow keys, or by using the scroll bar up \+
and down arrows on the right side of this window followed by finer adj
ustment with the mouse. An input region (marked by the > prompt with \+
words in bright red) is executed by positioning the cursor anywhere on
the desired line and pressing the " }{TEXT 269 5 "Enter" }{TEXT -1
88 " key. In summary: use the mouse to position yourself within a Map
le worksheet, and the " }{TEXT 270 5 "Enter" }{TEXT -1 48 " key to ins
truct Maple to actually do something." }}{PARA 0 "" 0 "" {TEXT -1 0 "
" }}{PARA 0 "" 0 "" {TEXT -1 97 "It is probably a good idea to begin E
VERY worksheet that you create with the following commands. " }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "restart;" }}}{EXCHG {PARA 0 "
> " 0 "" {MPLTEXT 1 0 14 "with( plots );" }}}{EXCHG {PARA 0 "> " 0 ""
{MPLTEXT 1 0 27 "with( Student[Calculus1] );" }}}{EXCHG {PARA 0 "> "
0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 456 "Maple's
output is shown in blue immediately following the execution group con
taining the command(s). The context menus provide one way to perform \+
additional operations. To use a context menu, select the output, or p
ortion of output, and click the right mouse button. After a few secon
ds a menu will appear; the entries in this menu are operations that ar
e most common for an object of this type. (Try this on some of the out
put later in this worksheet.)" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1
0 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 171 "Remember to save your w
ork periodically. If you forget to save your work and the computer cr
ashes you will lose any work done since the last time you saved the wo
rksheet." }}}}{SECT 1 {PARA 4 "" 0 "" {TEXT -1 21 "Essential Maple Fac
ts" }}{EXCHG {PARA 0 "" 0 "" {TEXT -1 181 "Maple is a computer languag
e; it cannot read your mind. You need to learn how to communicate wit
h Maple. The Maple 8 Quick Reference Guide is available as a PDF file
on the WWW at" }}{PARA 256 "" 0 "" {TEXT -1 2 " " }{URLLINK 17 "http
://www.math.sc.edu/~meade/maple/maple-ref.pdf" 4 "http://www.math.sc.e
du/~meade/maple/maple-ref.pdf" "" }{TEXT -1 3 ". " }}}{EXCHG {PARA 0
"> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 28 "A f
ew of the essentials are:" }}{PARA 15 "" 0 "" {TEXT -1 26 "assignments
are made with " }{TEXT 19 2 ":=" }{TEXT -1 8 " (plain " }{TEXT 19 1 "
=" }{TEXT -1 129 " has a different meaning)\nthink of this as giving t
he value of the right hand side to the name that appears on the left h
and side" }}{PARA 15 "" 0 "" {TEXT -1 46 "every command is terminated \+
by a semi-colon ( " }{TEXT 19 1 ";" }{TEXT -1 14 " ) or colon ( " }
{TEXT 19 1 ":" }{TEXT -1 75 " )\nwith the latter the computation is do
ne, but the result is not displayed" }}{PARA 15 "" 0 "" {TEXT -1 19 "t
he percent sign ( " }{TEXT 19 1 "%" }{TEXT -1 64 " ) refers to the res
ult of the immediately preceding computation" }}{PARA 15 "" 0 ""
{TEXT -1 46 "Maple is case sensitive -- that is, the names " }{TEXT
19 1 "x" }{TEXT -1 5 " and " }{TEXT 19 1 "X" }{TEXT -1 16 " are differ
ent, " }{TEXT 19 2 "pi" }{TEXT -1 2 ", " }{TEXT 19 2 "Pi" }{TEXT -1 6
", and " }{TEXT 19 2 "PI" }{TEXT -1 18 " are all different" }}{PARA
15 "" 0 "" {TEXT 19 3 "\{ \}" }{TEXT -1 97 " -- set notation (mostly u
sed in specifying a system of equations or a set of unknown variables)
)" }}{PARA 15 "" 0 "" {TEXT 19 6 "a .. b" }{TEXT -1 47 " -- this is ho
w Maple indicates the interval [ " }{XPPEDIT 18 0 "a" "6#%\"aG" }
{TEXT -1 2 ", " }{XPPEDIT 18 0 "b" "6#%\"bG" }{TEXT -1 36 " ] , that i
s, the real numbers from " }{XPPEDIT 18 0 "a" "6#%\"aG" }{TEXT -1 4 " \+
to " }{XPPEDIT 18 0 "b" "6#%\"bG" }{TEXT -1 1 " " }}{PARA 15 "" 0 ""
{TEXT 19 1 "?" }{TEXT -1 4 " or " }{TEXT 19 4 "help" }{TEXT -1 67 " --
a request to Maple for information from the online help archive" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "" 0 ""
{TEXT -1 84 "The standard mathematical functions are denoted by their \+
standard symbols and names:" }}{PARA 256 "" 0 "" {TEXT 19 1 "+" }
{TEXT -1 10 " (plus) , " }{TEXT 19 1 "-" }{TEXT -1 11 " (minus) , " }
{TEXT 19 1 "*" }{TEXT -1 11 " (times) , " }{TEXT 19 1 "/" }{TEXT -1
16 " (divided by) , " }{TEXT 19 1 "^" }{TEXT -1 25 " (raised to the po
wer) , " }{TEXT 19 3 "sin" }{TEXT -1 2 ", " }{TEXT 19 3 "cos" }{TEXT
-1 2 ", " }{TEXT 19 3 "tan" }{TEXT -1 2 ", " }{TEXT 19 3 "abs" }{TEXT
-1 2 ", " }{TEXT 19 4 "sqrt" }{TEXT -1 6 ", ... " }}}{EXCHG {PARA 0 ">
" 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PAGEBK }{PARA 0 "" 0 "" {TEXT -1
0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 147 "In the following lines, u
se paper and pencil to first predict what you think Maple will do. The
n execute the command and see what actually happens!" }}}{EXCHG {PARA
0 "> " 0 "" {MPLTEXT 1 0 29 "number:= 4 * 6 + 12 / 6 - 1 ;" }}}{EXCHG
{PARA 0 "> " 0 "" {MPLTEXT 1 0 16 "power:= (-3)^3 ;" }}}{EXCHG {PARA
0 "> " 0 "" {MPLTEXT 1 0 9 "abs( % );" }}}{EXCHG {PARA 0 "> " 0 ""
{MPLTEXT 1 0 4 "Pi ;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 18 "v :
= sin( Pi/4 ) :" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 10 "w := v^2
;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 2 "v;" }}}{EXCHG {PARA 0
"> " 0 "" {MPLTEXT 1 0 12 "tan( Pi/2 );" }}}{EXCHG {PARA 0 "> " 0 ""
{MPLTEXT 1 0 28 "3 / ( 5 - sqrt( number ) ) ;" }}}{EXCHG {PARA 0 "> "
0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 81 "Now ente
r some commands of your own! To produce the input prompt ( > ) use th
e " }{TEXT 271 2 "[>" }{TEXT -1 253 " button in the Menu Bar. Be gen
erous with the space bar to make your commands easy to read, and to ed
it (modify after the fact). Go back to the tangent calculation above \+
(remember how to reposition the cursor!) and change it to compute the \+
tangent of " }{XPPEDIT 18 0 "Pi/3" "6#*&%#PiG\"\"\"\"\"$!\"\"" }{TEXT
-1 29 ". Find how Maple represents " }{XPPEDIT 18 0 "i=sqrt(-1)" "6#/
%\"iG-%%sqrtG6#,$\"\"\"!\"\"" }{TEXT -1 53 ". Use Maple to find the r
eal and imaginary parts of " }{XPPEDIT 18 0 "i^i" "6#)%\"iGF$" }{TEXT
-1 1 "." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG
{PARA 0 "" 0 "" {TEXT -1 152 "Next we define some functions for later \+
use. Notice how Maple uses the current value for any name that appear
s on the right-hand side of an assignment." }}}{EXCHG {PARA 0 "> " 0 "
" {MPLTEXT 1 0 16 "f := sin( 2*x );" }}}{EXCHG {PARA 0 "> " 0 ""
{MPLTEXT 1 0 14 "g := 4 * x^2 ;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT
1 0 24 "h := 0.25 * cos( 8*x ) ;" }}}{EXCHG {PARA 0 "> " 0 ""
{MPLTEXT 1 0 12 "p := f * g ;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1
0 12 "q := f * h ;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "s := \+
f + h ;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}{EXCHG
{PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PAGEBK }{PARA 0 "" 0 "
" {TEXT -1 0 "" }}}}{SECT 1 {PARA 3 "" 0 "" {TEXT -1 8 "Plotting" }}
{EXCHG {PARA 0 "" 0 "" {TEXT -1 188 "Graphs of functions are produced \+
by the plot command. In its simplest form, plot needs to know the fun
ction to be plotted and the range of values for the independent variab
le. Note that " }{TEXT 19 4 "a..b" }{TEXT -1 45 " is Maple's way of d
escribing the interval [ " }{XPPEDIT 18 0 "a" "6#%\"aG" }{TEXT -1 2 ",
" }{XPPEDIT 18 0 "b" "6#%\"bG" }{TEXT -1 242 " ]. Observe that some \+
of the graphs have personalized titles. When you actually print plots
to turn in to be graded, they MUST have a title and signature [by you
r initials or last name]. Again, try to predict the output before tap
ping the " }{TEXT 272 5 "Enter" }{TEXT -1 6 " key! " }}}{EXCHG {PARA
0 "> " 0 "" {MPLTEXT 1 0 67 "plot( 3 * t - 2 , t = -3 .. 10 ) ; # WAIT
FOR THE GRAPH TO APPEAR!!" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0
31 "plot( f , x = -Pi .. 2 * Pi ) ;" }}}{EXCHG {PARA 0 "> " 0 ""
{MPLTEXT 1 0 52 "plot( p , x = -6 .. 8 , title = ` f * g [by DM] ` );
" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 ""
0 "" {TEXT -1 93 "These plots are nice, but what information do they c
onvey? Let's concentrate on the plot of " }{TEXT 19 1 "p" }{TEXT -1
10 ", that is " }{TEXT 19 3 "f*g" }{TEXT -1 262 ". Position the curso
r on a point on the graph and click the left mouse button. The number
s that appear on the upper-left corner are the coordinates of the curr
ent location of the cursor. Use this technique to estimate the global
maximum and minimum values of " }{TEXT 19 3 "f*g" }{TEXT -1 34 " on t
he interval [-6, 8], and the " }{XPPEDIT 18 0 "x" "6#%\"xG" }{TEXT -1
116 "-values at which these are found. Where do other (local) minima \+
and maxima occur? Can you guess the exact values? " }}}{EXCHG {PARA
0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1
0 80 "plot(2 * u^3 + 4 * u - 5 , u = -10 .. 7 , title = ` cubic functi
on [by DM] ` ) ;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}
{EXCHG {PARA 0 "" 0 "" {TEXT -1 40 "Where does the cubic function cros
s the " }{XPPEDIT 18 0 "u" "6#%\"uG" }{TEXT -1 155 "-axis? Maybe it wo
uld be helpful to cut down the plotting interval from [-10, 7] to [-1,
3], or even narrower, say to [0, 1.5]. Try it. Can you find the " }
{XPPEDIT 18 0 "u" "6#%\"uG" }{TEXT -1 212 "-intercept to 2-decimal poi
nt accuracy by this process? It is a powerful method, which we call Z
OOMING IN. (You will be expected to remember this and use this regula
rly at various times throughout this course.)" }}}{EXCHG {PARA 0 "> "
0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 28 "pl
ot( s , x = 0 .. 3 * Pi );" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0
29 "plot( q , x = -1.2 .. 1.2 ) ;" }}}{EXCHG {PARA 0 "> " 0 ""
{MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 34 "Can you expla
in why the graphs of " }{TEXT 19 1 "s" }{TEXT -1 5 " and " }{TEXT 19
1 "q" }{TEXT -1 117 " look the way they do? One way to answer this qu
estion is to include the graphs of f and h along with the plot of s."
}}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 31 "plot( [ s, f, h ], x=0..3
*Pi );" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 107 "Maple's choice of colo
rs is not optimal. Alternate colors can be specified as an optional a
rgument to the " }{HYPERLNK 17 "plot" 2 "plot" "" }{TEXT -1 9 " comman
d:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 54 "plot( [ s, f, h ], x=
0..3*Pi, color=[red,cyan,pink] );" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1
459 "Some features of the plot can be controlled interactively. Click
the left mouse button anywhere in a graph. A frame should appear aro
und the plot; the plot can be resized by dragging the control points. \+
The context menu for a plot contains entries for tweaking the plot. \+
Use the context menu to add a legend to the plot, then customize the l
egend labels to make a more informative picture. (Legends can be adde
d directly at the command line as well, see " }{HYPERLNK 17 "?plot,opt
ions" 2 "plot,options" "" }{TEXT -1 2 ".)" }}}{EXCHG {PARA 0 "> " 0 "
" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 93 "plot(
[ s, f, h ], x=0..3*Pi,\n color=[red,cyan,pink],\n legend=[
\"s=f+h\",\"f\",\"h\"] );" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0
0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 249 "This only touches the sur
face (pun intended!) of Maple's graphical capabilities. Maple is able
to produce high-quality renderings of 3D surfaces with real-time rota
tion, 2D and 3D animations, vector fields, solutions of differential e
quations, ...." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}
{EXCHG {PAGEBK }{PARA 0 "" 0 "" {TEXT -1 0 "" }}}}{SECT 1 {PARA 3 ""
0 "" {TEXT -1 7 "Algebra" }}{EXCHG {PARA 0 "" 0 "" {TEXT -1 30 "Consid
er the rational function" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 27
"F := (t^2+3*t+2)^3/(t+1)^4;" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 80 "T
here are a number of commands that could be used to ``simplify'' this \+
function:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "simplify( F );
" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "factor( F );" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "" 0 ""
{TEXT -1 47 "If you want to extract parts of the expression:" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 39 "Fnum := numer( F );\nFden :=
denom( F );" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 31 "expand( Fnu
m );\nexpand( Fden );" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 51 "and reco
mbine them to form an equivalent expression" }}}{EXCHG {PARA 0 "> " 0
"" {MPLTEXT 1 0 38 "F2 := expand( Fnum ) / expand( Fden );" }}}{EXCHG
{PARA 0 "> " 0 "" {MPLTEXT 1 0 38 "F3 := factor( Fnum ) / factor( Fden
);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 80 "Note that Maple automatica
lly simplifies results prior to displaying the result." }}}{EXCHG
{PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT
-1 37 "Compare the results of the following " }{HYPERLNK 17 "solve" 2
"solve" "" }{TEXT -1 10 " commands:" }}}{EXCHG {PARA 0 "> " 0 ""
{MPLTEXT 1 0 16 "solve( F=0, t );" }}}{EXCHG {PARA 0 "> " 0 ""
{MPLTEXT 1 0 23 "solve( numer(F)=0, t );" }}}{EXCHG {PARA 0 "> " 0 ""
{MPLTEXT 1 0 25 "solve( numer(F)=0, \{t\} );" }}}{EXCHG {PARA 0 "> "
0 "" {MPLTEXT 1 0 27 "\{ solve( numer(F)=0, t ) \};" }}}{EXCHG {PARA
0 "> " 0 "" {MPLTEXT 1 0 27 "[ solve( numer(F)=0, t ) ];" }}}{EXCHG
{PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT
-1 61 "The syntax to solve a system of equations is illustrated with"
}}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 49 "sys := \{ x^2 + y^2 = 6,
\n 2*x + y = 4 \}:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1
0 16 "var := \{ x, y \}:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 26
"sol1 := solve( sys, var );" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0
26 "sol2 := allvalues( sol1 );" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT
1 0 22 "sol3 := evalf( sol2 );" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT
1 0 27 "sol4 := fsolve( sys, var );" }}}{EXCHG {PARA 0 "> " 0 ""
{MPLTEXT 1 0 0 "" }}}{EXCHG {PAGEBK }{PARA 0 "" 0 "" {TEXT -1 0 "" }}}
}{SECT 1 {PARA 3 "" 0 "" {TEXT -1 8 "Calculus" }}{SECT 1 {PARA 4 "" 0
"" {TEXT -1 6 "Limits" }}{EXCHG {PARA 0 "" 0 "" {TEXT -1 94 "Maple sup
ports both two-sided and one-sided limits. In the first examples, the
inert command " }{HYPERLNK 17 "Limit" 2 "Limit" "" }{TEXT -1 5 " and \+
" }{HYPERLNK 17 "value" 2 "value" "" }{TEXT -1 47 " are used to create
a nicer visual presentation" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1
0 2 "F;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 40 "L1 := Limit( F, \+
t=1 ):\nL1 = value( L1 );" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0
44 "Lm1 := Limit( F, t=-1 ):\nLm1 = value( Lm1 );" }}}{EXCHG {PARA 0 "
> " 0 "" {MPLTEXT 1 0 50 "limit( F, t=-1, left ) <> limit( F, t=-1, ri
ght );" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}{SECT 1
{PARA 4 "" 0 "" {TEXT -1 11 "Derivatives" }}{EXCHG {PARA 0 "" 0 ""
{TEXT -1 38 "Derivatives are computed with Maple's " }{HYPERLNK 17 "di
ff" 2 "diff" "" }{TEXT -1 54 " command. There is an inert differentia
tion command, " }{HYPERLNK 17 "Diff" 2 "Diff" "" }{TEXT -1 39 ", that \+
can be used as shown above with " }{HYPERLNK 17 "Limit" 2 "Limit" "" }
{TEXT -1 2 ".)" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 2 "q;" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 19 "Dq := diff( q, x );" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 23 "SP := solve( Dq=0, x );" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "" 0 ""
{TEXT -1 131 "Compare the above results with the same operations appli
ed to the same function - except that the coefficient is a rational nu
mber." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 29 "q2 := convert( q, \+
rational );" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 21 "Dq2 := diff(
q2, x );" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 23 "SP2 := solve( \+
Dq2, x );" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 13 "evalf( SP2 );
" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 151 "In general, Maple returns fl
oating point results only when explicitly requested by the user or whe
n the input arguments include floating point numbers." }}}{EXCHG
{PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}{SECT 1 {PARA 4 "" 0 "" {TEXT
-1 9 "Integrals" }}{EXCHG {PARA 0 "" 0 "" {TEXT -1 55 "Definite and in
definite integrals are handled with the " }{HYPERLNK 17 "int" 2 "int"
"" }{TEXT -1 6 " (and " }{HYPERLNK 17 "Int" 2 "Int" "" }{TEXT -1 11 ")
commands." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 2 "s;" }}}{EXCHG
{PARA 0 "> " 0 "" {MPLTEXT 1 0 66 "S := Int( s, x ); # Notice there
is no constant of integration!" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT
1 0 19 "S = value( S ) + C;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0
0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 78 "And, now for definite inte
grals with floating-point and rational coefficients:" }}}{EXCHG {PARA
0 "> " 0 "" {MPLTEXT 1 0 28 "S2 := int( s, x=0..2*Pi/3 );" }}}{EXCHG
{PARA 0 "> " 0 "" {MPLTEXT 1 0 30 "s2a := convert( s, rational );" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 31 "S2a := int( s2a, x=0..2*Pi/3
);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 13 "evalf( S2a );" }}}
{EXCHG {PARA 0 "" 0 "" {TEXT -1 76 "Note that these values are obtaine
d via the Fundamental Theorem of Calculus." }}{PARA 0 "" 0 "" {TEXT
-1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 13 "Maple can do " }{HYPERLNK 17 "n
umerical integration" 2 "int,numerical" "" }{TEXT -1 176 " (but does n
ot use the methods generally taught in Calculus). For this problem a \+
numerically computed approximation to the definite integral could be o
btained with the use of " }{HYPERLNK 17 "evalf" 2 "evalf" "" }{TEXT
-1 5 " and " }{HYPERLNK 17 "Int" 2 "Int" "" }{TEXT -1 1 ":" }}}{EXCHG
{PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 ""
{MPLTEXT 1 0 16 "G := t*sin(t^2);" }}}{EXCHG {PARA 0 "> " 0 ""
{MPLTEXT 1 0 19 "plot( G, t=0..10 );" }}}{EXCHG {PARA 0 "> " 0 ""
{MPLTEXT 1 0 24 "q1 := Int( G, t=0..10 );" }}}{EXCHG {PARA 0 "> " 0 "
" {MPLTEXT 1 0 12 "value( q1 );" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT
1 0 12 "evalf( q1 );" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}
}{EXCHG {PARA 0 "" 0 "" {TEXT -1 30 "For educational purposes, the " }
{HYPERLNK 17 "ApproximateInt" 2 "Student,Calculus1,ApproximateInt" ""
}{TEXT -1 16 " command in the " }{HYPERLNK 17 "Student[Calculus1]" 2 "
Student,Calculus1" "" }{TEXT -1 65 " package knows about all of the me
thods taught in Calculus. The " }{TEXT 273 22 "ApproximateIntegration
" }{TEXT -1 9 " maplet [" }{URLLINK 17 "Maplet Viewer" 4 "http://www.m
ath.sc.edu/~meade/Bb-CalcI-WMI/Calculus1Maplets/ApproximateIntegration
.maplet" "" }{TEXT -1 2 "][" }{URLLINK 17 "MapleNet" 4 "http://maple.m
ath.sc.edu/maplenet/meade/CalculusI/ApproximateIntegration.html" "" }
{TEXT -1 33 "] is a built around this command." }}}{EXCHG {PARA 0 "> \+
" 0 "" {MPLTEXT 1 0 0 "" }}}}}{SECT 1 {PARA 3 "" 0 "" {TEXT -1 7 "Mapl
ets" }}{EXCHG {PARA 0 "" 0 "" {TEXT -1 146 "This topic requires more t
ime and space than is available in this session. I offered a 2-hour w
orkshop in Maplets at ICTCM XV last November. The " }{URLLINK 17 "work
sheet" 4 "http://www.math.sc.edu/~meade/ictcm2002/MapletWorkshop2002.m
ws" "" }{TEXT -1 6 ", and " }{URLLINK 17 "all other files" 4 "http://w
ww.math.sc.edu/~meade/ictcm2002/wkshop.zip" "" }{TEXT -1 51 ", for tha
t workshop can be downloaded from the WWW." }}{PARA 0 "" 0 "" {TEXT
-1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 148 "If you are not interested in m
aplet programming, you should still take a look at some of the maplets
that are available for use with Calculus. The " }{HYPERLNK 17 "inter
active" 2 "plots,interactive" "" }{TEXT -1 16 " command in the " }
{HYPERLNK 17 "plots" 2 "plots" "" }{TEXT -1 45 " package is one of the
most involved maplets." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 28 "
interactive( x*y*sin(x+y) );" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1
0 0 "" }}}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA
0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}{MARK "0 0 0" 0 }{VIEWOPTS 1 1 0 1
1 1803 1 1 1 1 }{PAGENUMBERS 0 1 2 33 1 1 }