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{SECT 0 {EXCHG {PARA 0 "" 0 "" {TEXT 256 16 "introduction.mws" }{TEXT
-1 3 " " }}{PARA 0 "" 0 "" {TEXT 262 21 "Introduction to Maple" }}
{PARA 0 "" 0 "" {TEXT -1 6 " " }{TEXT 263 105 "Revised by Holly G
aff and Lou Gross from versions posted to Web by Matthew Miller at Uni
v. South Carolina" }}{PARA 260 "" 0 "" {TEXT -1 0 "" }}{PARA 261 "" 0
"" {TEXT -1 10 "OBJECTIVE:" }}{PARA 262 "" 0 "" {TEXT -1 119 "- learn \+
basic command structure for Maple including: entering mathematical exp
ressions, plotting and solving equations " }}{PARA 263 "" 0 "" {TEXT
-1 0 "" }}{PARA 264 "" 0 "" {TEXT -1 1506 "WHAT IS MAPLE AND HOW CAN I
T BE USED? \nThe 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 produce the exact symbolic solutions you obtained by hand, the \+
numerical approximations you found using a calculator, and the graphs \+
you have drawn. Maple is one of several CASs; other major examples are
(all commercially produced) Mathematica, MATLAB, Macsyma, Derive, and
MathCad. There are some free versions of general math software packa
ges available (one is simply called R), but none of these have the ver
satility of commercial packages. Maple is generally preferable over MA
TLAB for symbolic maniputaions and simple plotting of functions, but M
ATLAB has advantages for numerical analysis, particularly using matrix
es. Maple can find roots of equations, optimize functions, estimate de
rivatives and integrals numerically, compute derivative and integral f
ormulas, plot and analyze data, and visualize geometric objects and tr
ansformations. \n\n\nDOCUMENTATION and ON-LINE HELP\nThe help pages de
scribe the syntax of each command, a brief description of the algorith
m that has been implemented, and a few examples illustrating the use o
f the command. To obtain help on the command func, type: ?func. The \+
Help Browser, an interactive interface to the entire Maple help system
, can be brought up by clicking on Help Menu, found at the top of the \+
Maple window.\n" }}{PARA 265 "" 0 "" {TEXT -1 435 "RUNNING MAPLE\nFor \+
our sessions in the computer labs, Maple can be strated by simply goin
g to the Program Menu (button on the lower left of the screen) and goi
ng to Maple in the Program applications, or by finding where it is ins
talled on the hard drive and clicking on the wmaple icon. It will also
start automatically from any \"Maple leaf\" icon, which typically sta
nd for files with a .mws extension standing for Maple Worksheet file.
" }}{PARA 266 "" 0 "" {TEXT -1 0 "" }}{PARA 267 "" 0 "" {TEXT -1 16 "G
ETTING STARTED " }}{PARA 268 "" 0 "" {TEXT -1 1039 "After opening Mapl
e, position the cursor arrow on the menu item File and click the left \+
button once. You can select New to obtain a fresh, empty worksheet. Or
you can select Open to choose an existing worksheet (the name will al
ways end with .mws), either by double clicking on the name or by selec
ting the name and then Load. Once in a worksheet the current location \+
is marked by a vertical bar. You can move around by moving the mouse a
nd then clicking the left button once, by using the arrow keys, or by \+
using the scroll bar up and down arrows on the right side of this wind
ow followed by finer adjustment with the mouse. A command is entered a
nd executed by positioning the cursor anywhere on the desired line and
pressing Return. Several worksheets can be open simultaneously, and \+
if you use the Window option to arrange them side by side, this can be
quite useful because you can cut and paste between them. They do, how
ever, share the computational engine, so beware: if x = 3 in one works
heet it will also be 3 in all the others!" }}{PARA 269 "" 0 "" {TEXT
-1 0 "" }}{PARA 270 "" 0 "" {TEXT -1 7 "TOOLBAR" }}{PARA 271 "" 0 ""
{TEXT -1 0 "" }}{PARA 272 "" 0 "" {TEXT -1 251 "There is a toolbar at \+
the top of the window with many options to open a new worksheet, open \+
an exosting one, save or print the current worksheet, cut and paste, u
ndo the last operation insert text, insert a new operation point, stop
calculation, etc. " }}{PARA 273 "" 0 "" {TEXT -1 102 "\nIt is probabl
y a good idea to begin EVERY worksheet that you create with the follow
ing two commands. " }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "restart:" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "with(plots): " }}}{PARA 0 "
" 0 "" {TEXT -1 0 "" }}{SECT 0 {PARA 0 "" 0 "" {TEXT 259 132 "BASIC FA
CTS\n\nThe basic symbols:\n\n - assignments are made with := (plain \+
= has a different meaning) -- think of this as giving the " }{TEXT
257 5 "value" }{TEXT 260 31 " of the right hand side to the " }{TEXT
258 4 "name" }{TEXT 261 881 " that appears on the left hand side\n - e
very command is terminated by a semi-colon ( ; ) or colon ( : ) -- wit
h the latter the computation is done, but the result is not displayed
\n - the percent symbol ( % ) refers to the result of the immediate
ly preceding computation (which might not have been the previous line)
\n - Maple is case sensitive -- that is, the names x and X are differe
nt, pi and Pi are not the same thing\n - \{ \} -- set notation (most
ly used in the context of plotting a bunch of functions simultaneously
)\n - .. as in a .. b -- this is how Maple indicates the interval [a
, b], that is, the real numbers from a to b\n - ? or help -- a request
to Maple for information\n\nMathematical functions have their standar
d names, or ones that are easily guessed:\n + (plus) , - (minus) , * \+
(times) , / (divided by) , ^ (raised to the power) , sin, cos, tan, ab
s, sqrt, ..." }{TEXT -1 1 "\n" }}{PARA 274 "" 0 "" {TEXT -1 376 "In th
e following lines,commands are exectuted as you press the \"Enter\" ke
y. You can do this consectively, or you can group commands. The bracke
ts to the left of commands are section ranges which can be modified to
make sections readable and to structure the entire worksheet. To jum
p to any command, use the mouse and click in front of the command line
(after the > prompt). " }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG
{PARA 0 "> " 0 "" {MPLTEXT 1 0 26 "N:= 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 78 "
v:= sin( Pi / 4 ) : # Note that lines that end with : differ from thos
e with ;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 2 "v;" }}}{EXCHG
{PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "sin( -Pi / 2 ) ;" }}}{EXCHG {PARA
0 "> " 0 "" {MPLTEXT 1 0 23 "3 / ( 5 - sqrt( N ) ) ;" }}}{EXCHG {PARA
0 "> " 0 "" {MPLTEXT 1 0 6 "4! ; " }}}{EXCHG {PARA 0 "> " 0 ""
{MPLTEXT 1 0 5 "50! ;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 24 "Di
gits:= 70: evalf(Pi);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 35 "D
igits:= 10: e:= exp(1); evalf(e);" }}}{EXCHG {PARA 0 "> " 0 ""
{MPLTEXT 1 0 25 "f:= 2 * x^2 - 7 * x + 5 ;" }}}{EXCHG {PARA 0 "> " 0 "
" {MPLTEXT 1 0 20 "solve( f = 0 , x ) ;" }}}{EXCHG {PARA 0 "> " 0 ""
{MPLTEXT 1 0 13 "factor( f ) ;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT
1 0 27 "solve( z = 3 * t + 4 , t );" }}}{EXCHG {PARA 0 "> " 0 ""
{MPLTEXT 1 0 38 "solve( a * x^2 + b * x + c = 0 , x ) ;" }}}{EXCHG
{PARA 0 "> " 0 "" {MPLTEXT 1 0 38 "solve( 25 * exp( k * 400 ) = 50 , k
);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 66 "evalf( % ); # Hint: \+
this is short for \"floating point evaluation.\"" }}}{EXCHG {PARA 0 "
" 0 "" {TEXT 264 250 "To produce the input prompt > you can use the \+
Insert key on the menu bar, followed by Execution Group and either Aft
er Cursor or Before Cursor. Alternatively, use the [> button in the
menu bar if you want the cursor after the present location. " }}
{PARA 275 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT
-1 0 "" }}{PARA 0 "" 0 "" {TEXT 265 252 "PLOTTING\nGraphs of functions
are produced by the plot command. In its simplest form, plot needs to
know the function to be plotted and the range of values for the indep
endent variable. Note that a .. b is Maple's way of describing the int
erval [a, b]. " }{TEXT -1 1 " " }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 67 "p
lot( 3 * t - 2 , t = -3 .. 6 ) ; # WAIT FOR THE GRAPH TO APPEAR!!" }}
}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 35 "plot( sin(3*x), x = -2*Pi .
. 2*Pi);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 26 "y:= 3.5 * exp (
0.2 * t );" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 22 "plot( y, t =
0 .. 10);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 ""
{TEXT 266 66 "We illustrate how to plot data points, and the logarithm
function." }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 159 "pop:= [ 508, 711, 91
2, 1131, 1590, 1811, 2015, 2249, 2509, 3008, 3610, 3967 ];\nyr:= [ 165
0, 1750, 1800, 1850, 1900, 1920, 1930, 1940, 1950, 1960, 1970, 1975 ];
" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 276 "" 0 "" {TEXT
-1 259 "The map command is very flexible. It gives you a way to system
atically do the same thing to a whole list of numbers. The zip comman
d joins together two lists in alternation! An alternative is to use \+
the seq (sequence) command, doing the zipping \"manually\"." }}{PARA
0 "> " 0 "" {MPLTEXT 1 0 36 "log10pop:= evalf( map( log10, pop));" }}
{PARA 0 "> " 0 "" {MPLTEXT 1 0 35 "lnpop:= evalf( map( ln, pop)); \+
" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 38 "adjustedyr:= map( n -> n - 1650
, yr );" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 55 "data:= zip( (a,b
) -> [op( [a,b] )] , adjustedyr, pop );" }}{PARA 0 "> " 0 "" {MPLTEXT
1 0 66 "log10data:= zip( (a,b) -> [op( [a,b] )] , adjustedyr, log10po
p );" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 59 "lndata:= zip( (a,b) -> [op(
[a,b] )] , adjustedyr, lnpop );" }}}{EXCHG {PARA 0 "> " 0 ""
{MPLTEXT 1 0 55 "data2:= [ seq( [adjustedyr[k], pop[k]], k = 1 .. 12 )
];" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 277 "" 0 "" {TEXT
-1 277 "Finally we do the actual plotting. There is a large variety of
styles that you can select, either in the command itself, or after th
e fact from the menu which you can bring up by clicking on the graph r
egion itself. You can change for example the style = POINT to style = \+
LINE " }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 61 "plot( data , style = POINT
, title = `Population vs. time` );" }}}{EXCHG {PARA 0 "> " 0 ""
{MPLTEXT 1 0 89 "plot( data2, style = LINE, title = `Population vs. ti
me`, thickness = 2, color = green );" }}}{EXCHG {PARA 0 "> " 0 ""
{MPLTEXT 1 0 66 "plot( log10data, style = POINT, title = `Log10 of pop
vs. time`); " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 60 "plot( lnda
ta, style = POINT, title = `Ln of pop vs. time`);" }}}{EXCHG {PARA 0
"" 0 "" {TEXT -1 0 "" }}{PARA 278 "" 0 "" {TEXT -1 341 "We have two wa
ys to make logarithmic plots. We can either take log of the data valu
es, as we did above, or we can use the built-in Maple command. The out
put is labeled differently, as you will see. To make the comparison ea
sier we will give the plots names (NOTE: named plot commands must end
with a colon!) and display them side by side. " }}}{EXCHG {PARA 0 "> \+
" 0 "" {MPLTEXT 1 0 67 "PlotA:=plot(log10data, title=`Log10 of pop vs.
time`, thickness=2):" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 68 "PlotB:=log
plot(data, title=`Logplot of pop vs. time`, thickness=2):" }}}{EXCHG
{PARA 0 "> " 0 "" {MPLTEXT 1 0 55 "Digits:= 4: # Needed to avoid bug i
n display( array ) " }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 35 "display( ar
ray( [PlotA, PlotB] ) );" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 12
"Digits:= 10:" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0
"" {TEXT 267 47 "Here are a few more functions and their graphs." }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 39 "f:= sin(x); g:= 2 * x^2 ; \+
p:= f * g ;" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 49 "h := cos ( (1/4) * x
) ; s:= 0.2 * sin(2*x) + h ;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1
0 125 "p:= p; plot( p, x = -3 .. 3); # p:= p; is not necessary but i
t is a handy way for us to remember what we are plotting here." }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 117 "# For display purposes it i
s a good idea to put a blank (or comment, as here) command line after \+
a plot command line." }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 1 "\n" }
{TEXT 268 486 "Position the cursor on a point on the graph and click t
he left button. The numbers that appear on the upper-left third line o
f the menu bar are the coordinates of the current location of the curs
or. Use this technique to identify the maximum and minimum values of p
(x) on the interval [-3, 3], and the x-values at which these are found
. By highlighting the graph in this way, you can also modify a variet
y of graph attributes, including the scale and for 3-d plots the viewi
ng angle. " }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 1 "\n" }{TEXT 269 101
"To plot more than one function in a single window, just specify the f
unctions to be plotted as a set." }}}{EXCHG {PARA 0 "> " 0 ""
{MPLTEXT 1 0 59 "h:= h; s:= s; plot( \{ h , s \}, x = - 6* Pi .. 6 \+
* Pi ) ;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 57 "g:= g; p:= p; \+
plot( \{ g , - g , p \} , x= -16 .. 16 );" }}}{EXCHG {PARA 0 "" 0 "
" {TEXT -1 0 "" }}{PARA 279 "" 0 "" {TEXT -1 195 "The following plotti
ng commands are just for fun. Since we have already assigned a value \+
to v, if we want to use this letter over again, we have to reset v to \+
be just plain \"v\" and not a number." }}}{EXCHG {PARA 0 "> " 0 ""
{MPLTEXT 1 0 2 "v;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "v:= 'v
';" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 99 "fieldplot( [v, -sin(w
) - 0.1*v], w = -2 .. 8, v = -2 .. 2, grid=[20, 20], arrows=SLIM, colo
r=BLUE);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG
{PARA 280 "" 0 "" {TEXT -1 482 "HOUSECLEANING\nIf you click on a plot \+
a box enclosing the plot will appear and the menu bar will change--the
keys Style, Axes, and Projection are very useful for making after the
fact modifications to the appearance of the plot--try them! Also you
can expand or contract the bounding box by dragging the little blips \+
on the edges. To get rid of the plot entirely simultaneously hold dow
n the Control (Cntrl) key and tap Delete (Del); or use the menu bar Ed
it and Delete Paragraph. " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0
"" }}}{EXCHG {PARA 281 "" 0 "" {TEXT -1 228 "DERIVATIVES AND INTEGRALS
\nMaple can do derivatives and integrals. For this, we first load th
e student package. Try to predict the effect of each command before m
ashing Return. After the given problems, try some of your own. " }}
{PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "with(student);" }}}{EXCHG {PARA 0 "
> " 0 "" {MPLTEXT 1 0 32 "f:= 3 * x^ 4 - 2 * x + 5 / x^3 ;" }}}{EXCHG
{PARA 0 "> " 0 "" {MPLTEXT 1 0 15 "diff( f , x ) ;" }}}{EXCHG {PARA 0
"> " 0 "" {MPLTEXT 1 0 25 "diff( Pi * R^2 * H , R );" }}}{EXCHG {PARA
0 "> " 0 "" {MPLTEXT 1 0 17 "F:= t * sin(t) ;" }}}{EXCHG {PARA 0 "> \+
" 0 "" {MPLTEXT 1 0 28 "deriv_of_F:= diff( F , t );" }}}{EXCHG {PARA
0 "> " 0 "" {MPLTEXT 1 0 30 "easy_integral:= Int( f , x ) ;" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 24 "value( easy_integral ) ;" }}
}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 23 "g:= z^2 * exp(- z^3 ) ;" }}
}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 24 "plot( g , z = 0 .. 2 ) ;" }
}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 41 "medium_integral:= Int( g ,
z = 0 .. 2 ) ;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 25 "value( m
edium_integral );" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "evalf(
% ) ;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 48 "hard_integral:= I
nt( 1 / ( y * (10 - y )) , y );" }}}{EXCHG {PARA 282 "" 0 "" {TEXT -1
196 "OOPS! Maple remembered, although I did not, that y already has a
definite value, and can't be a variable of integration. Let's recall
that value, and then reset y before attempting the integral." }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 2 "y;" }}}{EXCHG {PARA 0 "> " 0
"" {MPLTEXT 1 0 57 "y:= 'y'; hard_integral:= Int( 1 / ( y * (10 - y ))
, y );" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 23 "value( hard_inte
gral );" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG
{PARA 0 "" 0 "" {TEXT 270 18 "SAVING A WORKSHEET" }}{PARA 283 "" 0 ""
{TEXT -1 408 "To save it select File in the menu bar, and then either \+
Save (which will destroy the original version of intro.ms) or Save As.
.. (which will leave intro.mws untouched, and will request a new name \+
for this modified version). Worksheet names should always end with .mw
s; also unless you really need the output it is usually a good idea to
remove it before saving -- to do this, select Edit, then Remove Outpu
t." }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 62 "# Have you saved your work? \+
Check out the options under File." }}}{EXCHG {PARA 0 "> " 0 ""
{MPLTEXT 1 0 63 "# quit The only Maple command that doesn't need a \+
semicolon!" }}}}{MARK "0 0 0" 1 }{VIEWOPTS 1 1 0 1 1 1803 1 1 1 1 }
{PAGENUMBERS 0 1 2 33 1 1 }