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{SECT 0 {EXCHG {PARA 266 "" 0 "" {TEXT 256 29 "A Quick Introduction to
 Maple" }{TEXT 257 2 "\n\n" }{TEXT 258 12 "Tim McLarnan" }{TEXT 259 2 
"\n\n" }{TEXT -1 0 "" }}{PARA 256 "" 0 "" {TEXT 260 1 "\n" }{TEXT 261 
13 "Introduction\n" }}{PARA 256 "" 0 "" {TEXT 262 606 "Maple is a tool
 for doing nearly anything you think of as computational in mathematic
s, as well as many things you may be surprised to find a machine doing
.  Examples include:\n\n* Anything you can do with a calculator.\n* Ex
act computations with fractions.\n* Adding, multiplying, and factoring
 polynomials.\n* Solving equations, either exactly or approximately.\n
* Simplifying algebraic expressions.\n* Plotting functions.\n\nThis le
aflet is a quick introduction to some of the salient things Maple can \+
do.  The idea has been to use the most common Maple functions in order
 to give you examples of their syntax.\n\n" }{TEXT 263 20 "Four Essent
ial Facts" }{TEXT 264 1 "\n" }}{PARA 256 "" 0 "" {TEXT 265 311 "(1) Th
e Maple prompt is the symbol >.\n(2) Maple commands always end with a \+
semicolon ;\n(3) Maple commands are always followed by ENTER. If you w
ant to type a command with more than one line, use SHIFT-ENTER to go d
own a line without executing a command.\n(4) Maple is case sensitive. \+
 Pi is not the same as pi.\n\n" }{TEXT 266 14 "Basic Commands" }{TEXT 
267 1 "\n" }}{PARA 256 "" 0 "" {TEXT 268 1 "+" }{TEXT 269 3 ", -" }
{TEXT 270 0 "" }{TEXT 271 2 ", " }{TEXT 272 1 "*" }{TEXT 273 6 ", and \+
" }{TEXT 274 1 "/" }{TEXT 275 20 " do what you expect:" }}{PARA 0 "> \+
" 0 "" {MPLTEXT 1 0 4 "2+5;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"\"(" 
}}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 22 "123456789 * 987654321;" }
}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"3p_j76jK>7" }}}{EXCHG {PARA 256 "" 
0 "" {TEXT 276 79 "Unlike most calculators, however, Maple does operat
ions with fractions exactly:" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 34 "1/2
 + 1/3 + 1/4 + 1/5 + 1/6 + 1/7;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6##\"
$B#\"$S\"" }}}{EXCHG {PARA 256 "" 0 "" {TEXT 277 32 "Other arithmetic \+
operations are\n" }{TEXT 278 3 "a^b" }{TEXT 279 32 ", which means a to
 the power b,\n" }{TEXT 280 2 "n!" }{TEXT 281 39 ", which means n fact
orial (1*2*3*4**n)." }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 4 "2^5;" }}
{PARA 11 "" 1 "" {XPPMATH 20 "6#\"#K" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 7 "2^1000;" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#\"i]lw$p!oc
?PoQCElJ)H/mn@a'oxk>rX\"H1xg%Ral\"fvw)Rn7%>e$)\\ZYI:#=az(=9rB10Y2@a)4B
C[xnX$R![d)puvd%)fVSJ#p&GXr=Do9`v\"Hn%fF\"eep:)y$)>$\\Ah$\\7^5Nq$)Q]PW
2O`0<\"[Sh0\"=+g!\\]U[4Kni=2'3:2\"" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 13 "(355/113)^10;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6##\";
Dc^.6(3$G!y[*yJ\"6\\[JAA**QnXR$" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 
1 0 3 "4!;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"#C" }}}{EXCHG {PARA 0 
"> " 0 "" {MPLTEXT 1 0 5 "125!;" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#\"]
x+++++++++++++++!)3xJr+lbPEV_bqaevX$))=yf!QT$>>;I1ud+$fW0kkLJ#f\\*)G$H
)o'))f8;LcJN3:B)f()eU#\\r[OS&fd3g\"\\-xwV(*4E*))o<xE)=" }}}{EXCHG 
{PARA 256 "" 0 "" {TEXT 282 134 "Is it  surprise to you that 125! ends
 in so many zeros?\nCan you find a way to compute how many zeros are a
t the end of n! for any n?\n\n" }{TEXT 283 8 "Warning:" }{TEXT 284 
182 "  Trying anything too huge (like 10000!) will probably make your \+
computer freeze up, forcing you to turn off the machine and start over
, and needlessly antagonizing your professor.\n\n" }{TEXT 285 10 "ifac
tor(n)" }{TEXT 286 21 " factors the integer " }{TEXT 454 1 "n" }{TEXT 
455 13 " into primes:" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "ifactor (3
15);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#*()-%!G6#\"\"$\"\"#\"\"\"-F&6#
\"\"&F*-F&6#\"\"(F*" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "20!-1
2!;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"4+%Qwp2?!HV#" }}}{EXCHG 
{PARA 256 "" 0 "" {TEXT 287 291 "The most recent result (2432902007697
638400) can be easily included in any subsequent  calculation without \+
having to type it.  The percent character (%) is used to refer to the \+
last expression computed by Maple.  Similarly, %% is the expression be
fore %, and %%% is the expression before %%." }}{PARA 0 "" 0 "" {TEXT 
-1 0 "" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 11 "ifactor(%);" }}{PARA 11 "
" 1 "" {XPPMATH 20 "6#*.)-%!G6#\"\"#\"#5\"\"\")-F&6#\"\"$\"\"&F*)-F&6#
F/F(F*-F&6#\"\"(F*)-F&6#\"#6F.F*-F&6#\")>h(>%F*" }}}{EXCHG {PARA 256 "
" 0 "" {TEXT 288 92 "(How long would that have taken by hand?)  This r
esult can be checked by multiplying it out:" }}{PARA 0 "> " 0 "" 
{MPLTEXT 1 0 10 "expand(%);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"4+%Qw
p2?!HV#" }}}{EXCHG {PARA 256 "" 0 "" {TEXT 289 22 "Decimal Approximati
ons" }{TEXT 290 1 "\n" }}{PARA 256 "" 0 "" {TEXT 291 94 "Maple's norma
l mode of computation is exact arithmetic, with no roundoff or truncat
ion errors." }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "(2^30/3^20)*sqrt(2);
" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,$*$-%%sqrtG6#\"\"#\"\"\"#\"+C=ut5
\"+,Wy'[$" }}}{EXCHG {PARA 256 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "
" {TEXT -1 0 "" }}{PARA 256 "" 0 "" {TEXT 292 13 "The function " }
{TEXT 293 7 "evalf()" }{TEXT 294 58 " gives a numerical approximation \+
to this exact expression:" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 9 "evalf(%
);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"+%=;]N%!#5" }}}{EXCHG {PARA 
256 "" 0 "" {TEXT 295 33 "If 10 digits aren't enough, give " }{TEXT 
296 5 "evalf" }{TEXT 297 65 " an optional second argument to tell it h
ow many digits you need:" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "evalf(%
%, 60);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"gn(R,F-S^n7W!>9)\\t!)**p
M+yEa(p(\\=;]N%!#g" }}}{EXCHG {PARA 256 "" 0 "" {TEXT 298 11 "Maple us
es " }{TEXT 299 2 "Pi" }{TEXT 300 23 ", not pi, to represent " }
{XPPEDIT 19 1 "Pi;" "6#%#PiG" }{TEXT 461 118 ".  Notice what this mean
s: variable names in Maple are case-sensitive.\nWould you like to know
 the first few digits of " }{XPPEDIT 18 0 "Pi;" "6#%#PiG" }{TEXT 463 
1 "?" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "evalf(Pi, 80);" }}{PARA 12 
"" 1 "" {XPPMATH 20 "6#$\"[p!4iG1k\"yI#fW\\(4#e5v$*Rpr>%)G]zKQVEYQKz*e
`EfTJ!#z" }}}{EXCHG {PARA 256 "" 0 "" {TEXT 301 1 "\n" }{TEXT 429 1 "V
" }{TEXT 302 19 "ariable Expressions" }{TEXT 303 1 "\n" }}{PARA 256 "
" 0 "" {TEXT 304 32 "Maple also works with variables." }}{PARA 0 "> " 
0 "" {MPLTEXT 1 0 26 "(x+7) * (x^2+1) * (x-2)^5;" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#*(,&%\"xG\"\"\"\"\"(F&F&,&*$)F%\"\"#F&F&F&F&F&),&F%F&F+
!\"\"\"\"&F&" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 10 "expand(%);
" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,4*$)%\"xG\"\")\"\"\"F(*&\"\"$F()F
&\"\"(F(!\"\"*&\"#HF()F&\"\"'F(F-*&\"$(>F()F&\"\"&F(F(*&\"$5&F()F&\"\"
%F(F-*&\"$G(F()F&F*F(F(*&\"$/(F()F&\"\"#F(F-*&\"$G&F(F&F(F(\"$C#F-" }}
}{EXCHG {PARA 256 "" 0 "" {TEXT 305 135 "At  this point, Maple has for
gotten where it got this polynomial.  It's just a random polynomial of
 degree 8.  But Maple can factor it:" }}{PARA 0 "> " 0 "" {MPLTEXT 1 
0 10 "factor(%);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#*(,&%\"xG\"\"\"\"
\"(F&F&,&*$)F%\"\"#F&F&F&F&F&),&F%F&F+!\"\"\"\"&F&" }}}{EXCHG {PARA 
256 "" 0 "" {TEXT 306 187 "Could you have factored this polynomial as \+
fast as Maple did?  Could you have factored it at all?\n(If you think \+
about it a bit, your answers to these questions should be \"no\" and \+
\"yes.\")\n" }}{PARA 256 "" 0 "" {TEXT 307 29 "Assignment and Simplifi
cation" }{TEXT 308 1 "\n" }}{PARA 256 "" 0 "" {TEXT 309 97 "Often we n
eed to assign a name to the result of a computation.  Maple does this \+
using the syntax\n" }{TEXT 310 8 "variable" }{TEXT 311 1 " " }{TEXT 
312 2 ":=" }{TEXT 313 1 " " }{TEXT 314 5 "value" }{TEXT 315 73 ";\nIn \+
making an assignment, Maple does some obvious simplifications first." 
}}{PARA 0 "> " 0 "" {MPLTEXT 1 0 22 "e1 := (x+y)^3*(x+y)^2;" }}{PARA 
11 "" 1 "" {XPPMATH 20 "6#>%#e1G*$),&%\"xG\"\"\"%\"yGF)\"\"&F)" }}}
{EXCHG {PARA 256 "" 0 "" {TEXT 316 37 "Maple has a built in function c
alled " }{TEXT 317 8 "simplify" }{TEXT 318 139 ", which tries to simpl
ify expressions.  It does not always find the simplest form of an expr
ession, but it is a start.  Here is an example:" }}{PARA 0 "> " 0 "" 
{MPLTEXT 1 0 30 "e2 := (x^3-y^3)/(x^2+x-y-y^2);" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#>%#e2G*&,&*$)%\"xG\"\"$\"\"\"F+*$)%\"yGF*F+!\"\"F+,**$)
F)\"\"#F+F+F)F+F.F/*$)F.F3F+F/F/" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 
0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 13 "simplify(e2);" }{TEXT -1 0 "" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#*&,(*$)%\"xG\"\"#\"\"\"F)*&%\"yGF)F'F)F)*$)F+F(F)F)F),(
F'F)F)F)F+F)!\"\"" }}}{EXCHG {PARA 256 "" 0 "" {TEXT 319 57 "To unders
tand what went on here, we can use the commands " }{TEXT 320 5 "numer
" }{TEXT 321 5 " and " }{TEXT 322 5 "denom" }{TEXT 323 69 " (to take t
he numerator and denominator of a fraction) together with " }{TEXT 
324 6 "factor" }{TEXT 325 1 ":" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 18 "f
actor(numer(e2));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#*&,&%\"xG\"\"\"%
\"yG!\"\"F&,(*$)F%\"\"#F&F&*&F'F&F%F&F&*$)F'F,F&F&F&" }}}{EXCHG {PARA 
0 "> " 0 "" {MPLTEXT 1 0 18 "factor(denom(e2));" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#*&,(%\"xG\"\"\"F&F&%\"yGF&F&,&F%F&F'!\"\"F&" }}}{EXCHG 
{PARA 256 "" 0 "" {TEXT 326 8 "So what " }{TEXT 327 8 "simplify" }
{TEXT 328 94 " did was to find and remove the common factor of (xy).  \+
In this particular case, the commands " }{TEXT 329 6 "factor" }{TEXT 
330 5 " and " }{TEXT 331 8 "simplify" }{TEXT 332 19 " do the same thin
g:" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 11 "factor(e2);" }}{PARA 11 "" 1 
"" {XPPMATH 20 "6#*&,(*$)%\"xG\"\"#\"\"\"F)*&%\"yGF)F'F)F)*$)F+F(F)F)F
),(F'F)F)F)F+F)!\"\"" }}}{EXCHG {PARA 256 "" 0 "" {TEXT 333 17 "Solvin
g Equations" }{TEXT 334 1 "\n" }}{PARA 256 "" 0 "" {TEXT 335 176 "Mapl
e can also solve equations, even symbolic ones.  Notice the syntax of \+
the commands below.  You have to specify first the equation, then the \+
variables you want to solve for." }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 24 
"solve(x^2+5*x+2 = 0, x);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6$,&#!\"&\"
\"#\"\"\"*&#F'F&F'-%%sqrtG6#\"#<F'F',&F$F'*&#F'F&F'*$F*F'F'!\"\"" }}}
{EXCHG {PARA 256 "" 0 "" {TEXT 336 178 "This quadratic equation had tw
o solutions (separated by a comma), just as you would expect.\n\nIf yo
u want a decimal approximation instead of an exact solution to an equa
tion, use " }{TEXT 337 6 "fsolve" }{TEXT 338 12 " instead of " }{TEXT 
339 5 "solve" }{TEXT 340 1 "." }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 25 "fs
olve(x^2+5*x+2 = 0, x);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6$$!+8GbhX!\"
*$!+s=Z%Q%!#5" }}}{EXCHG {PARA 256 "" 0 "" {TEXT 341 5 "solve" }{TEXT 
342 5 " and " }{TEXT 343 6 "fsolve" }{TEXT 344 114 " can also deal wit
h systems of more than one equation.  You need to give them a set of e
quations (in set brackets " }{TEXT 345 3 "\{ \}" }{TEXT 346 66 ") foll
owed by a set of variables to solve for.  Here's an example:" }}{PARA 
0 "> " 0 "" {MPLTEXT 1 0 29 "solve(\{x+y=5, x-y=2\}, \{x,y\});" }}
{PARA 11 "" 1 "" {XPPMATH 20 "6#<$/%\"yG#\"\"$\"\"#/%\"xG#\"\"(F(" }}}
{EXCHG {PARA 256 "" 0 "" {TEXT 347 92 "Now let's get more adventuresom
e and try to solve an equation containing symbolic constants:" }}
{PARA 0 "> " 0 "" {MPLTEXT 1 0 24 "solve(a*x^2+b*x+c=0, x);" }}{PARA 
11 "" 1 "" {XPPMATH 20 "6$,$*&%\"aG!\"\",&%\"bGF&*$-%%sqrtG6#,&*$)F(\"
\"#\"\"\"F1*(\"\"%F1F%F1%\"cGF1F&F1F1F1#F1F0,$*&F%F&,&F(F&F)F&F1F5" }}
}{EXCHG {PARA 256 "" 0 "" {TEXT 348 58 "Do you recognize this answer? \+
 It's the quadratic formula!" }}{PARA 256 "" 0 "" {TEXT 430 139 "\nDid
 you know that there was a similar formula for solving cubic equations
?  It's a bit more complicated:  its output will fill the screen." }}
{PARA 0 "> " 0 "" {MPLTEXT 1 0 38 "solve(a*x^3 + b*x^2 + c*x + d = 0, \+
x);" }}{PARA 12 "" 1 "" {XPPMATH 20 "6%,(*&%\"aG!\"\",**(%\"cG\"\"\"%
\"bGF*F%F*\"#O*(\"$3\"F*%\"dGF*)F%\"\"#F*F&*&\"\")F*)F+\"\"$F*F&**\"#7
F*-%%sqrtG6#F5F*-F96#,,*&)F)F5F*F%F*\"\"%*&)F)F1F*)F+F1F*F&*,\"#=F*F)F
*F+F*F%F*F/F*F&*(\"#FF*)F/F1F*F0F*F**(F@F*F/F*F4F*F*F*F%F*F*#F*F5#F*\"
\"'*&#F1F5F**(,&*&F)F*F%F*F5*$FCF*F&F*F%F&F'#F&F5F*F&*&#F*F5F**&F+F*F%
F&F*F&,*F$#F&F7**FJF*FPF*F%F&F'FSF**&#F*F5F*FVF*F&*(^##F*F1F*F8F*,&F$F
K**#F1F5F*FPF*F%F&F'FSF*F*F*,*F$FX**FJF*FPF*F%F&F'FSF**&#F*F5F*FVF*F&*
(^##F&F1F*F8F*FinF*F*" }}}{EXCHG {PARA 256 "" 0 "" {TEXT 349 184 "\nLo
ok at this answer a bit until you undertand the notation.  There are t
hree roots, which are written separated by commas.  The second and thi
rd roots also involve the square root of " }{XPPEDIT 18 0 "-1;" "6#,$
\"\"\"!\"\"" }{TEXT 462 24 ", which Maple writes as " }{TEXT 431 1 "I
" }{TEXT 432 3 ".\n\n" }{TEXT 350 14 "Warning again:" }{TEXT 351 1 " \+
" }{TEXT 450 1 "I" }{TEXT 451 8 " isn't  " }{TEXT 452 1 "i" }{TEXT 
453 93 ".  Case matters to Maple.\nMaple can also solve the general fo
urth degree equation (add in an " }{XPPEDIT 445 0 "x^4" "6#*$%\"xG\"\"
%" }{TEXT 444 69 " term), though the output now fills several screens.
  Can it do more?" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 54 "solve(a*x^5 + \+
b*x^4 + c*x^3 + d*x^2 + e*x + f = 0, x);" }}{PARA 11 "" 1 "" {XPPMATH 
20 "6#-%'RootOfG6#,.*&%\"aG\"\"\")%#_ZG\"\"&F)F)*&%\"bGF))F+\"\"%F)F)*
&%\"cGF))F+\"\"$F)F)*&%\"dGF))F+\"\"#F)F)*&%\"eGF)F+F)F)%\"fGF)" }}}
{EXCHG {PARA 256 "" 0 "" {TEXT 352 371 "\nWhy can't Maple solve this e
quation?  Because Evariste Galois proved shortly before his death at t
he age of 20 that there is not general formula like the quadratic form
ula which solves polynomial equations of degree 5 and higher.  (That i
s, there is no formula solving all  such equations.  For particular va
lues of the coefficients, there are often simple solutions.)\n\n" }
{TEXT 353 6 "fsolve" }{TEXT 354 79 " still works to find approximate s
olutions to equations of high degree, though:" }}{PARA 0 "> " 0 "" 
{MPLTEXT 1 0 21 "fsolve(x^5+x+1=0, x);" }}{PARA 11 "" 1 "" {XPPMATH 
20 "6#$!+imx[v!#5" }}}{EXCHG {PAGEBK }{PARA 256 "" 0 "" {TEXT -1 0 "" 
}{TEXT 355 15 "Plotting Graphs" }{TEXT 356 1 "\n" }}{PARA 256 "" 0 "" 
{TEXT 433 169 "Maple only found one solution to the last equation.  Ho
w can we convince ourselves there is only one?  One way to begin to bu
ild evidence might be to graph the function." }{TEXT -1 0 "" }}{PARA 
0 "> " 0 "" {MPLTEXT 1 0 23 "plot(x^5+x+1, x=-2..2);" }}{PARA 13 "" 1 
"" {GLPLOT2D 210 152 152 {PLOTDATA 2 "6%-%'CURVESG6$7S7$$!\"#\"\"!$!#L
F*7$$!3MLLL$Q6G\">!#<$!3$>><v9$*>l#!#;7$$!3bmm;M!\\p$=F0$!30>:qW\"G`<#
F37$$!3MLLL))Qj^<F0$!3Q,!QgM[Ts\"F37$$!3ALLL=Kvl;F0$!3)p\">&oIj!\\8F37
$$!3wmm;C2G!e\"F0$!3H/+Jp6cV5F37$$!3OLL$3yO5]\"F0$!3&\\9D\"*fm57)F07$$
!3&*****\\nU)*=9F0$!3X&GgU`)*=<'F07$$!3SLL$3WDTL\"F0$!3Z'GcgM\\1c%F07$
$!35++]d(Q&\\7F0$!3!yaC?KqcH$F07$$!3hmmmc4`i6F0$!3z6IUog)eG#F07$$!3KLL
LQW*e3\"F0$!3q&[Q7=fdf\"F07$$!3w++++()>'***!#=$!3d1**QWm?x**Fco7$$!3E+
+++0\"*H\"*Fco$!3#GEsB\"RYtaFco7$$!35++++83&H)Fco$!3q63A1TYAAFco7$$!3
\\LLL3k(p`(Fco$\"3<.*Rh<A**3$!#?7$$!3Anmmmj^NmFco$\"3Z()[]l24y?Fco7$$!
3(zmmmYh=(eFco$\"32%Ht>j+,V$Fco7$$!3+,++v#\\N)\\Fco$\"37(Q&Qfy04ZFco7$
$!3commmCC(>%Fco$\"3zJ3hoZ\\scFco7$$!39*****\\FRXL$Fco$\"3I:'**o'RBCmF
co7$$!3t*****\\#=/8DFco$\"3Z>8Jb^$pZ(Fco7$$!3=mmm;a*el\"Fco$\"3.QE=(ff
GM)Fco7$$!3jomm;Wn(o)!#>$\"3xVrIoI=J\"*Fco7$$!3IqLLL$eV(>Fep$\"3amjm;k
D!)**Fco7$$\"3)Qjmm\"f`@')F\\s$\"3w#>ME7?i3\"F07$$\"3%z****\\nZ)H;Fco$
\"3+'3jtx*4j6F07$$\"3ckmm;$y*eCFco$\"3t>;CgozY7F07$$\"3f)******R^bJ$Fc
o$\"3:bn=m<cN8F07$$\"3&e*****\\5a`TFco$\"37hk/8irF9F07$$\"3'o****\\7RV
'\\Fco$\"3%)*Q5MH&eE:F07$$\"3X'*****\\@fkeFco$\"3,()Q-\"*>$el\"F07$$\"
3_ILLL&4Nn'Fco$\"3e:=kBar*z\"F07$$\"3A*******\\,s`(Fco$\"3_:a$o!*op*>F
07$$\"3%[mm;zM)>$)Fco$\"3buD-AnhIAF07$$\"3L*******pfa<*Fco$\"3\"f*=%Q,
%)yc#F07$$\"38HLLeg`!)**Fco$\"3%p2OeWf$))HF07$$\"3w****\\#G2A3\"F0$\"3
aAmgw<hmNF07$$\"3;LLL$)G[k6F0$\"3&3c<?'Qs0VF07$$\"3#)****\\7yh]7F0$\"3
\"342,uC*4`F07$$\"3xmmm')fdL8F0$\"3Tmz'Rn.9b'F07$$\"3bmmm,FT=9F0$\"3dR
=:]*\\(f\")F07$$\"3FLL$e#pa-:F0$\"3Eb\"f)G&)4;5F37$$\"3*)******Rv&)z:F
0$\"3Eo)Qa(**>U7F37$$\"3HLLLGUYo;F0$\"3#*R=6mY!)f:F37$$\"3_mmm1^rZ<F0$
\"3!*ekhZJR0>F37$$\"34++]sI@K=F0$\"3w$oh'>..[BF37$$\"34++]2%)38>F0$\"3
IK@6rc(Q&GF37$$\"\"#F*$\"#NF*-%'COLOURG6&%$RGBG$\"#5!\"\"$F*F*Fc[l-%+A
XESLABELSG6$Q\"x6\"Q!Fh[l-%%VIEWG6$;F(Fhz%(DEFAULTG" 1 2 0 1 10 0 2 9 
1 4 2 1.000000 45.000000 45.000000 0 0 "Curve 1" }}}}{EXCHG {PARA 256 
"" 0 "" {TEXT 357 66 "This at least suggests there is only one root be
tween x=2 and x=2." }}{PARA 256 "" 0 "" {TEXT 358 50 "Maple sometimes \+
makes an unhelpful choice of axes:" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 
27 "plot(x^3 - 1/x^2, x=-2..2);" }}{PARA 13 "" 1 "" {GLPLOT2D 206 137 
137 {PLOTDATA 2 "6%-%'CURVESG6$7co7$$!\"#\"\"!$!3+++++++]#)!#<7$$!3MLL
L$Q6G\">F-$!35Nn#*[]*>F(F-7$$!3bmm;M!\\p$=F-$!3=P:7()y\"\\\\'F-7$$!3ML
LL))Qj^<F-$!3-m2&H5A.q&F-7$$!3ALLL=Kvl;F-$!3\"*H&*olmT#)\\F-7$$!3wmm;C
2G!e\"F-$!3.D9w(H\\oM%F-7$$!3OLL$3yO5]\"F-$!3+$*p0,Q$e#QF-7$$!3&*****
\\nU)*=9F-$!3a*zF.i\"z`LF-7$$!3SLL$3WDTL\"F-$!3OFdL3(Hk$HF-7$$!35++]d(
Q&\\7F-$!3;K[M(HO9f#F-7$$!3hmmmc4`i6F-$!3S'yjW!e16BF-7$$!3KLLLQW*e3\"F
-$!3y$3pf32&G@F-7$$!3w++++()>'***!#=$!3+\"zdrt?'**>F-7$$!3E++++0\"*H\"
*Fbo$!3B!ekBP52'>F-7$$!35++++83&H)Fbo$!3!)*[r9a#3C?F-7$$!3\\LLL3k(p`(F
bo$!3!))=&)HfA&)=#F-7$$!3Anmmmj^NmFbo$!3@&z[h/PLc#F-7$$!3(zmmmYh=(eFbo
$!32_TX`5z-JF-7$$!3+,++v#\\N)\\Fbo$!3BMmU$)=A]TF-7$$!3commmCC(>%Fbo$!3
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" {TEXT 360 31 "There are many options for the " }{TEXT 361 4 "plot" }
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" "Curve 4" "Curve 5" }}}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 493 "One pro
blem with this plot is that you may not be sure which curve is which. \+
To make matters worse, Maple doesn't always assign the same colors to \+
curves: the next time you run it, the colors might change. Here's a wa
y to deal with that: make the functions an ordered list (in square bra
ckets) instead of an unordered set (in curly braces), and give an addi
tional argument listing the colors you want for each curve. To plot si
n(x) in black, cos(x) in red, and arctan(x) in blue, you could say" }}
{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 
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000000-%+AXESLABELSG6%%\"xG%\"yGQ!F/" 1 2 0 1 10 0 2 1 1 2 2 1.000000 
81.000000 70.000000 0 0 "Curve 1" }}}}{EXCHG {PARA 256 "" 0 "" {TEXT 
367 281 "(To obtain this picture, I ran the Maple command, clicked on \+
the picture, and then played with the choices on the Tool Bar until I \+
got the view I wanted.  One can also view this 3-dimensional surface a
s a contour plot.  You can make contour plots from 3D plots using the \+
Tool Bar.\n" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 256 "" 0 "" 
{TEXT 368 5 "Help!" }{TEXT 369 1 "\n" }}{PARA 256 "" 0 "" {TEXT 370 
163 "In order to use Maple effectively, you'll need to know where to g
et help.  An excellent and convenient source is Maple's online help, w
hich is available under the " }{TEXT 459 4 "Help" }{TEXT 460 80 " menu
 item.  You can also access help directly from the Maple prompt, like \+
this:" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "?coeffs;" }}}{EXCHG {PARA 
256 "" 0 "" {TEXT 371 292 "The output appears in another window, but h
ere it is. It includes a calling sequence, usually some obtuse discuss
ion.  Most usefully, it ends with examples and with suggestions of oth
er related functions to look at.  All functions and libraries which Ma
ple knows about have online help items." }}}{SECT 0 {PARA 0 "" 0 "" 
{TEXT 26 10 "Function: " }{TEXT -1 62 "coeffs - extract all coefficien
ts of a multivariate polynomial" }}{PARA 0 "" 0 "usage" {TEXT 26 17 "C
alling Sequence:" }{TEXT -1 22 "\n   coeffs(p, x, 't');" }}{PARA 0 "" 
0 "" {TEXT 26 11 "Parameters:" }{TEXT -1 4 "\n   " }{TEXT 23 4 "p - " 
}{TEXT -1 27 "multivariate polynomial\n   " }{TEXT 23 4 "x - " }{TEXT 
-1 58 "(optional) indeterminate or list/set of indeterminates\n   " }
{TEXT 23 4 "t - " }{TEXT -1 15 "(optional) name" }}}{SECT 0 {PARA 0 "
" 0 "synopsis" {TEXT 26 12 "Description:" }}{PARA 15 "" 0 "" {TEXT -1 
135 "The coeffs function returns an expression sequence of all the coe
fficients of the polynomial p with respect to the indeterminate(s) x. \+
" }}{PARA 15 "" 0 "" {TEXT -1 109 "If x is not specified, coeffs compu
tes the coefficients with respect to all the indeterminates of p (see \+
the " }{HYPERLNK 17 "indets" 2 "indets" "" }{TEXT -1 202 " function). \+
If a third argument t is specified (call by name), it is assigned an e
xpression sequence of the terms of p. There is a one-to-one correspond
ence between the coefficients and the terms of p. " }}{PARA 15 "" 0 "
" {TEXT -1 78 "Note that p must be collected with respect to the appro
priate indeterminates. " }}}{SECT 0 {PARA 0 "" 0 "examples" {TEXT 26 
9 "Examples:" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 23 "s := 3*v^2*y
^2+2*v*y^3;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"sG,&*&)%\"vG\"\"#\"
\"\")%\"yGF)F*\"\"$*(F)F*F(F*)F,F-F*F*" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 12 "coeffs( s );" }}{PARA 11 "" 1 "" {XPPMATH 20 "6$\"\"#
\"\"$" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "coeffs( s, v, 't' \+
);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6$,$*$)%\"yG\"\"#\"\"\"\"\"$,$*$)F
&F)F(F'" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 2 "t;" }}{PARA 11 "
" 1 "" {XPPMATH 20 "6$*$)%\"vG\"\"#\"\"\"F%" }}}}{SECT 0 {PARA 0 "" 0 
"seealso" {TEXT 26 10 "See Also: " }{HYPERLNK 17 "collect" 2 "collect
" "" }{TEXT -1 2 ", " }{HYPERLNK 17 "coeff" 2 "coeff" "" }{TEXT -1 2 "
, " }{HYPERLNK 17 "tcoeff" 2 "tcoeff" "" }{TEXT -1 2 ", " }{HYPERLNK 
17 "lcoeff" 2 "lcoeff" "" }{TEXT -1 2 ", " }{HYPERLNK 17 "indets" 2 "i
ndets" "" }{TEXT -1 2 "  " }}}{EXCHG {PARA 256 "" 0 "" {TEXT -1 0 "" }
}{PARA 256 "" 0 "" {TEXT 372 282 "The bookshelf in the Math/CS Lounge \+
on the second floor of Dennis contains a fair number of manuals for va
rious versions of Maple. The basics of the program haven't changed muc
h, so any of these manuals should get you started. Other students, fac
ulty, etc. are also good resources.\n" }}{PARA 256 "" 0 "" {TEXT 374 
19 "Substitutions, etc." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 256 "
" 0 "" {TEXT 375 182 "Here are a few more commands which are useful in
 calculus.  We begin by defining an expression, making some substituti
ons, and computing its derivative directly from the definition:\n" }}
{PARA 0 "> " 0 "" {MPLTEXT 1 0 11 "f := x^2+x;" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#>%\"fG,&*$)%\"xG\"\"#\"\"\"F*F(F*" }}}{EXCHG {PARA 0 ">
 " 0 "" {MPLTEXT 1 0 13 "subs(x=3, f);" }}{PARA 0 "" 0 "" {TEXT -1 0 "
" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"#7" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 15 "subs(x=x+h, f);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,(
*$),&%\"xG\"\"\"%\"hGF(\"\"#F(F(F'F(F)F(" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 10 "expand(%);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,,*$)%
\"xG\"\"#\"\"\"F(*(F'F(F&F(%\"hGF(F(*$)F*F'F(F(F&F(F*F(" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 4 "%-f;" }}{PARA 11 "" 1 "" {XPPMATH 
20 "6#,(*&%\"xG\"\"\"%\"hGF&\"\"#*$)F'F(F&F&F'F&" }}}{EXCHG {PARA 0 ">
 " 0 "" {MPLTEXT 1 0 4 "%/h;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#*&,(*&
%\"xG\"\"\"%\"hGF'\"\"#*$)F(F)F'F'F(F'F'F(!\"\"" }}}{EXCHG {PARA 0 "> \+
" 0 "" {MPLTEXT 1 0 12 "simplify(%);" }}{PARA 11 "" 1 "" {XPPMATH 20 "
6#,(%\"xG\"\"#%\"hG\"\"\"F'F'" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 
0 14 "limit(%, h=0);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,&%\"xG\"\"#\"
\"\"F&" }}}{EXCHG {PARA 256 "" 0 "" {TEXT -1 0 "" }}{PARA 256 "" 0 "" 
{TEXT 376 18 "Defining Functions" }{TEXT 377 1 "\n" }}{PARA 256 "" 0 "
" {TEXT 378 52 "An irritating feature of this calculation was using " 
}{TEXT 379 12 "subs(x=3, f)" }{TEXT 380 58 " to compute f when x=3.  W
e'd like to be able just to say " }{TEXT 381 4 "f(3)" }{TEXT 382 177 "
, but we can't, because f is just an expression, not a function.  So h
ow would we define a function in Maple?  There are 2 ways.  For simple
 one-line functions, we can do  this:" }}{PARA 0 "" 0 "" {TEXT -1 0 "
" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "g := x -> x^2;" }}{PARA 11 "" 
1 "" {XPPMATH 20 "6#>%\"gGf*6#%\"xG6\"6$%)operatorG%&arrowGF(*$)9$\"\"
#\"\"\"F(F(F(" }}}{EXCHG {PARA 256 "" 0 "" {TEXT 457 43 "This defines \+
g as the function taking x to " }{XPPEDIT 458 0 "x^2;" "6#*$%\"xG\"\"#
" }{TEXT 456 49 ".  We can now use g just like any other function:" }}
{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 5 "g(x)
;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#*$)%\"xG\"\"#\"\"\"" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 5 "g(3);" }}{PARA 11 "" 1 "" {XPPMATH 
20 "6#\"\"*" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 7 "g(x+h);" }}
{PARA 11 "" 1 "" {XPPMATH 20 "6#*$),&%\"xG\"\"\"%\"hGF'\"\"#F'" }}}
{EXCHG {PARA 256 "" 0 "" {TEXT 383 91 "More complicated functions are \+
defined in a more complicated way.  Begin the function with " }}{PARA 
256 "" 0 "" {TEXT 384 5 "proc(" }{TEXT 435 9 "variables" }{TEXT 385 1 
")" }{TEXT 386 18 ", and end it with " }{TEXT 387 9 "end proc;" }
{TEXT 388 122 ". Here, for instance, is a function which takes 2 argum
ents, and returns the larger of the two, assuming both are numbers:" }
}{PARA 0 "> " 0 "" {MPLTEXT 1 0 59 "h := proc(x,y)\n\011\011if x>y the
n x\n\011\011else y\n\011\011end if\n\011end proc;" }}{PARA 11 "" 1 "
" {XPPMATH 20 "6#>%\"hGf*6$%\"xG%\"yG6\"F)F)@%29%9$F-F,F)F)F)" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "h(3, 5);" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#\"\"&" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 7 "h(5,
3);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"\"&" }}}{EXCHG {PARA 256 "" 
0 "" {TEXT -1 0 "" }{TEXT 389 23 "More Calculus Functions" }{TEXT 390 
1 "\n" }}{PARA 256 "" 0 "" {TEXT 391 92 "Maple can directly compute de
rivatives, sums, integrals and limits.  Here are some examples:" }}
{PARA 0 "> " 0 "" {MPLTEXT 1 0 18 "diff(sin(x^2), x);" }}{PARA 11 "" 
1 "" {XPPMATH 20 "6#,$*&-%$cosG6#*$)%\"xG\"\"#\"\"\"F,F*F,F+" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "int(x^2, x);" }}{PARA 11 "" 
1 "" {XPPMATH 20 "6#,$*$)%\"xG\"\"$\"\"\"#F(F'" }}}{EXCHG {PARA 0 "> \+
" 0 "" {MPLTEXT 1 0 17 "int(x^2, x=1..4);" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#\"#@" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 18 "sum(
k^2, k=1..10);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"$&Q" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 26 "sum(1/k^2, k=1..infinity);" }}
{PARA 11 "" 1 "" {XPPMATH 20 "6#,$*$)%#PiG\"\"#\"\"\"#F(\"\"'" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 35 "y := limit((x^2-3*x+2)/(x-1)
, x=1);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"yG!\"\"" }}}{EXCHG 
{PARA 256 "" 0 "" {TEXT -1 0 "" }}{PARA 256 "" 0 "" {TEXT -1 0 "" }}
{PARA 256 "" 0 "" {TEXT 392 5 "Oops!" }{TEXT 393 1 "\n" }}{PARA 256 "
" 0 "" {TEXT 394 124 "Like any powerful tool, Maple offers any number \+
of ways for you to make mistakes.  Here are some particularly popular \+
ones:\n" }}{PARA 256 "" 0 "" {TEXT 395 10 "Mistake 1:" }{TEXT 396 178 
"  Forgetting you have assigned a value to a variable.  Right now, for
 instance, y has a value: it is -1. I'll therefore get into loads of t
rouble if I try to use y as a variable:" }}{PARA 0 "" 0 "" {TEXT -1 0 
"" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 28 "plot(x^2, x=-1..1, y=-1..2);" 
}}{PARA 8 "" 1 "" {TEXT -1 35 "Error, (in plot) invalid arguments\n" }
}}{EXCHG {PARA 256 "" 0 "" {TEXT -1 0 "" }{TEXT 397 97 "To fix this, I
 need to tell Maple that y is now just the variable y again.  I do tha
t by saying  " }{TEXT 398 7 "y:='y';" }}{PARA 0 "> " 0 "" {MPLTEXT 1 
0 2 "y;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#!\"\"" }}}{EXCHG {PARA 0 ">
 " 0 "" {MPLTEXT 1 0 9 "y := 'y';" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>
%\"yGF$" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 2 "y;" }}{PARA 11 "
" 1 "" {XPPMATH 20 "6#%\"yG" }}}{EXCHG {PARA 256 "" 0 "" {TEXT 436 1 "
\n" }{TEXT 437 10 "Mistake 2:" }{TEXT 438 162 " Forgetting a semicolon
.  If you do this, Maple thinks the expression you want it to evaluate
 is not over.  It will therefore give you an unhelpful error message:
" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 3 "2+6" }}{PARA 0 "> " 0 "" 
{MPLTEXT 1 0 0 "" }}{PARA 7 "" 1 "" {TEXT -1 32 "Warning, premature en
d of input\n" }}}{EXCHG {PARA 256 "" 0 "" {TEXT 439 70 "One possible r
esponse is to type the semicolon and to hit enter again:" }}{PARA 0 ">
 " 0 "" {MPLTEXT 1 0 3 "2+6" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 1 ";" }}
{PARA 11 "" 1 "" {XPPMATH 20 "6#\"\")" }}}{EXCHG {PARA 256 "" 0 "" 
{TEXT -1 0 "" }}{PARA 256 "" 0 "" {TEXT 399 10 "Mistake 3:" }{TEXT 
400 35 "  Order of operations.  Maple does " }{TEXT 401 1 "^" }{TEXT 
402 13 " first, then " }{TEXT 403 1 "*" }{TEXT 404 5 " and " }{TEXT 
405 1 "/" }{TEXT 406 7 ", then " }{TEXT 407 1 "+" }{TEXT 408 5 " and \+
" }{TEXT 409 0 "" }{TEXT 410 26 ".  Notice the difference:\n" }}{PARA 
0 "> " 0 "" {MPLTEXT 1 0 6 "x^1/2;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#
,$%\"xG#\"\"\"\"\"#" }}}{EXCHG {PARA 256 "" 0 "" {TEXT 411 66 "Since M
aple does exponentiation before division, it reads this as " }
{XPPEDIT 447 0 "x^`1`/2" "6#*&)%\"xG%\"1G\"\"\"\"\"#!\"\"" }{TEXT 446 
2 " ." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "x^(1/2);" }}{PARA 
11 "" 1 "" {XPPMATH 20 "6#*$-%%sqrtG6#%\"xG\"\"\"" }}}{EXCHG {PARA 
256 "" 0 "" {TEXT 412 33 "This is the correct way to write " }
{XPPEDIT 449 0 "x^`1/2`" "6#)%\"xG%$1/2G" }{TEXT 448 3 " .\n" }}{PARA 
256 "" 0 "" {TEXT 413 10 "Mistake 4:" }{TEXT 414 14 "  Leaving out " }
{TEXT 415 1 "*" }{TEXT 416 45 " in multiplication.  I do this all the \+
time.\n" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 7 "x^2+2x;" }}{PARA 8 "" 1 "
" {TEXT -1 31 "Error, missing operator or `;`\n" }}}{EXCHG {PARA 0 "> \+
" 0 "" {MPLTEXT 1 0 21 "solve(x^2+bx+c=0, x);" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6$*$-%%sqrtG6#,&%#bxG!\"\"%\"cGF)\"\"\",$F#F)" }}}{EXCHG 
{PARA 256 "" 0 "" {TEXT 417 47 "\nHere we got the wrong answer because
 we wrote " }{TEXT 418 2 "bx" }{TEXT 419 51 ", which Maple reads as a \+
new variable, rather than " }{TEXT 420 3 "b*x" }{TEXT 421 26 ", which \+
is what we meant.\n" }}}{EXCHG {PARA 256 "" 0 "" {TEXT 422 10 "Mistake
 5:" }{TEXT 423 82 "  Case sensitivity, or forgetting the name of a Ma
ple command.  Here are examples:" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 10 
"evalf(pi);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#%#piG" }}}{EXCHG {PARA 
0 "> " 0 "" {MPLTEXT 1 0 10 "evalf(Pi);" }}{PARA 11 "" 1 "" {XPPMATH 
20 "6#$\"+aEfTJ!\"*" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 19 "lim(sin(x)/x, x=0);" }}
{PARA 11 "" 1 "" {XPPMATH 20 "6#-%$limG6$*&-%$sinG6#%\"xG\"\"\"F*!\"\"
/F*\"\"!" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 21 "limit(sin(x)/x,
 x=0);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"\"\"" }}}{EXCHG {PARA 256 
"" 0 "" {TEXT -1 0 "" }}{PARA 256 "" 0 "" {TEXT 424 10 "Mistake 6:" }
{TEXT 425 107 "  Notation for trig functions.  This is really just a f
law in normal mathematical notation.  When we write " }{XPPEDIT 443 0 
"`sin`^2*x" "6#*&%$sinG\"\"#%\"xG\"\"\"" }{TEXT 440 18 ", what we mean
 is " }{XPPEDIT 442 0 "[sin(x)]^2" "6#*$7#-%$sinG6#%\"xG\"\"#" }{TEXT 
441 125 ".  This shorthand is horribly misleading, but it is universal
.  Maple is only capable of understanding the second expression." }}
{PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "sin^2*x;" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#*&)%$sinG\"\"#\"\"\"%\"xGF'" }}}{EXCHG {PARA 0 "> " 0 "
" {MPLTEXT 1 0 15 "evalf(sin^2*1);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#
*$)%$sinG\"\"#\"\"\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 9 "sin(
x)^2;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#*$)-%$sinG6#%\"xG\"\"#\"\"\"
" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 16 "evalf(sin(1)^2);" }}
{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"+$=M23(!#5" }}}{EXCHG {PARA 0 "" 0 
"" {TEXT -1 0 "" }}{PARA 4 "" 0 "" {TEXT -1 15 "Formatting Text" }}
{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 126 "Maple ca
n be used as a sort of mathematical word-processor, though it's a bit \+
rough.  The basic commands you need to know are:" }}{PARA 0 "" 0 "" 
{TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 40 "To type text into Maple, \+
hit the little " }{TEXT 467 1 "T" }{TEXT -1 49 " button near the top o
f the Maple window, or use " }{TEXT 468 14 "Insert -> Text" }{TEXT -1 
98 " or its keyboard shortcut.  This will turn the current group into \+
text instead of a Maple command." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}
{PARA 0 "" 0 "" {TEXT -1 60 "To insert a new Maple command or a new bl
ock of text, go to " }{TEXT 469 25 "Insert -> Execution Group" }{TEXT 
-1 123 ", and either insert a new block before or after the one contai
ning the cursor.  There are also keyboard shortcuts for this." }}
{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 80 "To insert
 superscripts or other mathematical expressions into Maple text, go to
 " }{TEXT 470 23 "Insert -> Standard Math" }{TEXT -1 274 ", then use t
he input area near the top of the window to type the mathematical expr
ession you want in Maple syntax.  Maple should now stick that expressi
on into your worksheet.  This may take you a bit of playing around.  I
t's pretty clunky, but I can usually get it to work." }}{PARA 0 "" 0 "
" {TEXT -1 0 "" }}}{EXCHG {PARA 256 "" 0 "" {TEXT 426 6 "\nIndex" }
{TEXT 427 1 "\n" }}{PARA 256 "" 0 "" {TEXT 428 443 "Is there more to l
earn about Maple?  Yes!  Maple is a very broad and powerful system for
 mathematical computation.  It has more than 2000 built-in functions. \+
 The large majority of these have never been used by anyone at Earlham
.  Here is a very quick glossary of the most important functions for a
 calculus student.  More information on all these is available through
 Maple's online help, or in the written and human sources mentioned ab
ove:\n" }}}{EXCHG {PARA 267 "" 0 "" {TEXT -1 3005 "+, -, *, /         \+
Add, subtract, multiply, divide.\n^                  Raise a number to
 a power.\n!                  Factorial.\n->                 Used in p
rocedure definitions.\n=                  Used in inputting equations.
\n:=                 Used to assign a value to a variable.\n<, >, <=, \+
>=, <>   Mean <, >, , , and , resp.\n%, %%, %%%         Previous expre
ssions.\n..                 An interval.\n[ ]                List. Lis
ts are ordered.\n\{ \}                Set. Sets are unordered.\nabs   \+
             Computes the absolute value of a number.\ncoeff          \+
    Get one coefficient of a polynomial.\ncollect            Collect c
oefficients of like powers.\ncombine            Combine terms into a s
ingle term.\nconvert            Convert from one data type to another.
\ncos                Cosine. Arguments are in radians.\nD             \+
     Differential operator.\ndenom              Denominator.\ndiff    \+
           Differentiate.\nE, exp(1)          The base for natural log
s.\nevalf              Evaluate an expression as a decimal approximati
on.\nexp                Exponential function.  exp(x) = E^x.\nexpand  \+
           Expand out an expression.\nfactor             Factor a poly
nomial.\nfor...do...end do  Repeat commands.\nfsolve             Find \+
approximate solutions to one or more equations.\nhelp               Ge
t help on a function.\nif...then...else...end if    Conditionals.\nifa
ctor            Factor an integer.\nint                Integrate a fun
ction.\nInt                Write down the integral, but don't evaluate
. Use with changevar.\nlimit              Compute limits.\nLimit      \+
        Write doen but don't evaluate a limit.\nln, log            Com
pute natural logs.  ln(x)=log(x)log10(x).\nmax                Compute \+
the maximum of 2 or more numbers.\nmin                Compute the mini
mum of 2 or more numbers.\nnormal             Put a fraction in normal
 form.  A useful special case of simplify.\nnumer              Numerat
or.\nop                 Pick out one part of an expression.\nplot     \+
          Plot a graph.\nplot3d             Plot a 3D graph.\nprint   \+
           Pretty-print an expression.\nproc               Define a pr
ocedure.\nproduct            Product of finitely or infinitely many te
rms.\nquo                Quotient of 2 polynomials.\nrem              \+
  Remainder of 2 polynomials.\nsimplify           Try to simplify an e
xpression.\nsin                Sine.  The arguments to trig functions \+
should be in radians.\nsolve              Solve 1 or more equations ex
actly.\nsort               Sort a list or the terms in a polynomial.\n
sqrt               Square root.\nstudent            The student calcul
us package.  Very useful.\nstudent[changevar] Do a change of variables
 (integration by substitution).\nsum                Sum of finitely or
 infinitely many terms.\nSum                Sum written down, but not \+
worked out.\nTaylor             Taylor series expansion.\nvalue       \+
       evaluate a Sum, Limit, or Int.\nwith               Load a libra
ry package.  Example: with(student);" }}}}{MARK "91 9 2" 274 }
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