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{SECT 0 {PARA 256 "" 0 "" {TEXT 287 28 "More on Basic Maple Commands" 
}}{PARA 257 "" 0 "" {TEXT -1 10 "A. J. Meir" }}{PARA 258 "" 0 "" 
{TEXT -1 0 "" }}{PARA 258 "" 0 "" {TEXT -1 46 "Copyright (C) A. J. Mei
r. All rights reserved." }}{PARA 258 "" 0 "" {TEXT -1 492 "This worksh
eet is for educational use only. No part of this publication may be re
produced or transmitted for profit in any form or by any means, electr
onic or mechanical, including photocopy, recording, or any information
 storage and retrieval system without prior written permission from th
e author. Not for profit distribution of the software is allowed witho
ut prior written permission, providing that the worksheet is not modif
ied in any way and full credit to the author is acknowledged." }}
{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT 288 91 "(This do
cument is largely based on a similar document originally written by P.
 G. Schmidt.)" }{TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 
0 "" 0 "" {TEXT -1 406 "To familiarize yourself with the basics of Map
le's syntax, carefully type and execute each of the following commands
 (one at a time, and in the given order). Most are self-explanatory. I
n each case, try to guess what the command will cause Maple to do, bef
ore executing it to see what happens. If you can't figure out what a g
iven command \"does\", consult the online help manual (see Item 5 on t
he handout \"" }{HYPERLNK 17 "Introduction to Maple" 1 "intro.mws" "" 
}{TEXT -1 3 "\")." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 ">
 " 0 "" {MPLTEXT 1 0 8 "restart;" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}
{PARA 0 "" 0 "" {TEXT -1 280 "(Note: You should enter this command whe
never you open a new worksheet, so that Maple starts \"with a clean sl
ate\". From time to time, you may want to re-execute the command, in o
rder to clear Maple's computing engine; this will have no effect on th
e appearance of your worksheet.)" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 
1 0 28 "2+3;  2-3;  2*3;  2/3;  2^3;" }}{PARA 11 "" 1 "" {XPPMATH 20 "
6#\"\"&" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#!\"\"" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#\"\"'" }}{PARA 11 "" 1 "" {XPPMATH 20 "6##\"\"#\"\"$" }
}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"\")" }}}{PARA 0 "" 0 "" {TEXT -1 0 
"" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 27 "1/3;  evalf(1/3);  1.0/
3.0;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6##\"\"\"\"\"$" }}{PARA 11 "" 1 
"" {XPPMATH 20 "6#$\"+LLLLL!#5" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"+
LLLLL!#5" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 77 "Pi;  evalf(Pi);  evalf(Pi,20);  sqrt(2);  evalf(sqrt(
2));  evalf(sqrt(2),30);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#%#PiG" }}
{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"+aEfTJ!\"*" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#$\"5&QKz*e`EfTJ!#>" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#*
$-%%sqrtG6#\"\"#\"\"\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"+iN@99!\"
*" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"?@C()o,)[]4tBc8UT\"!#H" }}}
{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 8 "(Note:  " 
}{TEXT 286 5 "evalf" }{TEXT -1 2 "  " }{TEXT 256 50 "stands for \"eval
uate as a floating-point number\".)" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }
}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 62 "factor(x^2-1);  expand((x-1
)*(x+1));  simplify((x^2-1)/(x-1));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6
#*&,&%\"xG\"\"\"F&!\"\"F&,&F%F&F&F&F&" }}{PARA 11 "" 1 "" {XPPMATH 20 
"6#,&*$)%\"xG\"\"#\"\"\"F(F(!\"\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,
&%\"xG\"\"\"F%F%" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 ">
 " 0 "" {MPLTEXT 1 0 59 "solve(x^2-1=0,x);  solve(a^2-b^2=1,a);  solve
(a^2-b^2=1,b);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6$\"\"\"!\"\"" }}
{PARA 11 "" 1 "" {XPPMATH 20 "6$*$-%%sqrtG6#,&\"\"\"F(*$)%\"bG\"\"#F(F
(F(,$F#!\"\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6$*$-%%sqrtG6#,&*$)%\"aG
\"\"#\"\"\"F,F,!\"\"F,,$F#F-" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 74 "solve(\{a+b=1,a-b=2\},\{a,b
\});  solve(\{a+b+c=0,a+2*b+3*c=1,a-b-c=2\},\{a,b,c\});" }}{PARA 11 "
" 1 "" {XPPMATH 20 "6#<$/%\"bG#!\"\"\"\"#/%\"aG#\"\"$F(" }}{PARA 11 "
" 1 "" {XPPMATH 20 "6#<%/%\"aG\"\"\"/%\"bG!\"$/%\"cG\"\"#" }}}{PARA 0 
"" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 39 "solv
e(cos(x)=x,x);  fsolve(cos(x)=x,x);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6
#-%'RootOfG6#,&%#_ZG\"\"\"-%$cosG6#F'!\"\"" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#$\"+K8&3R(!#5" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}
{PARA 0 "" 0 "" {TEXT -1 21 "(Note: The equation  " }{XPPEDIT 18 0 "co
s(x)=x" "6#/-%$cosG6#%\"xGF'" }{TEXT -1 19 "  cannot be solved " }
{TEXT 257 12 "symbolically" }{TEXT -1 21 "; this explains why  " }
{TEXT 258 5 "solve" }{TEXT -1 106 "  fails to produce a useful answer.
 However, the equation does have a unique solution, which can be found
 " }{TEXT 259 11 "numerically" }{TEXT -1 9 ", using  " }{TEXT 260 6 "f
solve" }{TEXT -1 2 ".)" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 16 "y:=c*exp(x);  y;" }}{PARA 11 "" 1 "
" {XPPMATH 20 "6#>%\"yG*&%\"cG\"\"\"-%$expG6#%\"xGF'" }}{PARA 11 "" 1 
"" {XPPMATH 20 "6#*&%\"cG\"\"\"-%$expG6#%\"xGF%" }}}{PARA 0 "" 0 "" 
{TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 69 "c:=1;  y;  c
:=2;  y;  c:=Pi;  y;  c:=a;  y;  c:='c';  y;  y:='y';  y;" }}{PARA 11 
"" 1 "" {XPPMATH 20 "6#>%\"cG\"\"\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6
#-%$expG6#%\"xG" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"cG\"\"#" }}
{PARA 11 "" 1 "" {XPPMATH 20 "6#,$-%$expG6#%\"xG\"\"#" }}{PARA 11 "" 
1 "" {XPPMATH 20 "6#>%\"cG%#PiG" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#*&%
#PiG\"\"\"-%$expG6#%\"xGF%" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"cG%
\"aG" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#*&%\"aG\"\"\"-%$expG6#%\"xGF%
" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"cGF$" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#*&%\"cG\"\"\"-%$expG6#%\"xGF%" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#>%\"yGF$" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#%\"yG" }}}
{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 21 "(Note: Th
e commands  " }{TEXT 261 6 "c:='c'" }{TEXT 263 3 "  a" }{TEXT -1 4 "nd
  " }{TEXT 262 6 "y:='y'" }{TEXT -1 39 "  \"undefine\" the respective \+
variables.)" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "
" {MPLTEXT 1 0 55 "y:=x^2-1;  plot(y,x=-3..3);  subs(x=0,y);  subs(x=3
,y);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"yG,&*$)%\"xG\"\"#\"\"\"F*F
*!\"\"" }}{PARA 13 "" 1 "" {GLPLOT2D 295 295 295 {PLOTDATA 2 "6%-%'CUR
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***\\KCnu\"F0$\"3#\\qYv'e/^?F07$$\"3s***\\(=n#f(=F0$\"3SS,7a55>DF07$$
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'>$[FF0$\"3[`(R=ngKb'F07$$\"37++D6EjpGF0$\"3G%\\\\NK\"zMsF07$$\"\"$F*F
+-%'COLOURG6&%$RGBG$\"#5!\"\"$F*F*F_[l-%+AXESLABELSG6$Q\"x6\"Q!6\"-%%V
IEWG6$;F(Ffz%(DEFAULTG" 1 2 0 1 10 0 2 9 1 4 2 1.000000 45.000000 
45.000000 0 0 "Curve 1" }}}{PARA 11 "" 1 "" {XPPMATH 20 "6#!\"\"" }}
{PARA 11 "" 1 "" {XPPMATH 20 "6#\"\")" }}}{PARA 0 "" 0 "" {TEXT -1 0 "
" }}{PARA 0 "" 0 "" {TEXT -1 8 "(Note:  " }{TEXT 284 4 "subs" }{TEXT 
-1 26 "  stands for\"substitute\".)" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }
}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 73 "solve(y=0,x);  limit(y,x=0)
;  limit(y,x=infinity);  diff(y,x);  int(y,x);" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6$\"\"\"!\"\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#!\"\"" }
}{PARA 11 "" 1 "" {XPPMATH 20 "6#%)infinityG" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#,$%\"xG\"\"#" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,&*$)%
\"xG\"\"$\"\"\"#F(F'F&!\"\"" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 49 "limit(sin(x)/x,x=0);  limit(
sin(x)/x,x=infinity);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"\"\"" }}
{PARA 11 "" 1 "" {XPPMATH 20 "6#\"\"!" }}}{PARA 0 "" 0 "" {TEXT -1 0 "
" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 45 "diff(exp(x)*sin(x),x);  \+
int(exp(x)*sin(x),x);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,&*&-%$expG6#
%\"xG\"\"\"-%$sinGF'F)F)*&F%F)-%$cosGF'F)F)" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#,&*&-%$expG6#%\"xG\"\"\"-%$cosGF'F)#!\"\"\"\"#*(#F)F.F)
F%F)-%$sinGF'F)F)" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "
> " 0 "" {MPLTEXT 1 0 58 "int(exp(x)*sin(x),x=0..Pi);  int(exp(-x^2),x
=0..infinity);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,&-%$expG6#%#PiG#\"
\"\"\"\"#F(F)" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,$*$-%%sqrtG6#%#PiG\"
\"\"#F)\"\"#" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" 
{TEXT -1 197 "The rest of this handout is concerned with graphing. Sev
eral Maple routines related to graphing are not automatically availabl
e when you start Maple; they must be loaded separately. To do so, ente
r" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 12 "with(plots);" }}{PARA 7 "" 1 "" {TEXT -1 50 "Warning,
 the name changecoords has been redefined\n" }}{PARA 12 "" 1 "" 
{XPPMATH 20 "6#7U%(animateG%*animate3dG%-animatecurveG%-changecoordsG%
,complexplotG%.complexplot3dG%*conformalG%,contourplotG%.contourplot3d
G%*coordplotG%,coordplot3dG%-cylinderplotG%,densityplotG%(displayG%*di
splay3dG%*fieldplotG%,fieldplot3dG%)gradplotG%+gradplot3dG%-implicitpl
otG%/implicitplot3dG%(inequalG%-listcontplotG%/listcontplot3dG%0listde
nsityplotG%)listplotG%+listplot3dG%+loglogplotG%(logplotG%+matrixplotG
%(odeplotG%'paretoG%*pointplotG%,pointplot3dG%*polarplotG%,polygonplot
G%.polygonplot3dG%4polyhedra_supportedG%.polyhedraplotG%'replotG%*root
locusG%,semilogplotG%+setoptionsG%-setoptions3dG%+spacecurveG%1sparsem
atrixplotG%+sphereplotG%)surfdataG%)textplotG%+textplot3dG%)tubeplotG
" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 388 "upo
n which Maple should print a list of commands -- the contents of the p
ackage of routines that is being loaded. If you just want to load the \+
package, without having its contents displayed, end the command with a
 colon (:) instead of a semicolon (;).  (Generally, using a colon inst
ead of a semicolon at the end of a command prevents Maple's response f
rom being displayed on the screen.)" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }
}{PARA 0 "" 0 "" {TEXT -1 119 "Now execute the following commands to l
earn about some useful \"options\" that are available with the basic p
lot command." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 
"" {MPLTEXT 1 0 32 "y:=cos(x)/x;  plot(y,x=-10..10);" }}{PARA 11 "" 1 
"" {XPPMATH 20 "6#>%\"yG*&-%$cosG6#%\"xG\"\"\"F)!\"\"" }}{PARA 13 "" 
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{XPPEDIT 18 0 "y" "6#%\"yG" }{TEXT -1 49 ". Check out what happens if \+
you omit the quotes.)" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 
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{PARA 0 "" 0 "" {TEXT -1 32 "Next, let's graph the function  " }
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Fdy$\"3'zJ5N%>c$)GFbt7$Fiy$\"3m1s;)='Q@JFbt7$F^z$\"3y&Hlqx+mR$Fbt7$Fcz
$\"31O,^&*er#o$Fbt7$Fhz$\"3fLvj%Q2r,%Fbt-F][l6&F_[lF`[lF`[lFb[l-%+AXES
LABELSG6$Q\"x6\"Q\"yFg^m-%%VIEWG6$;F(Fhz;Fb[l$\"#gF*" 1 2 0 1 10 0 2 
9 1 4 2 1.000000 45.000000 45.000000 0 0 "Curve 1" "Curve 2" "Curve 3
" }}}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 146 "bu
t this method is very cumbersome if you need more than two or three gr
aphs or if the functions to be plotted are complicated. Here's a short
cut:" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 54 "s:=seq(c*exp(x),c=1..3);  plot(\{s\},x=-1..3,'y'=0..6
0);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"sG6%-%$expG6#%\"xG,$F&\"\"#
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Fcu$\"3I1[$>-LGx*F-7$Fhu$\"37'z`y%Gif5Fbt7$F]v$\"3!>$o?1,@b6Fbt7$Fbv$
\"3))y$>Fu_#\\7Fbt7$Fgv$\"3'yG=4.[3O\"Fbt7$F\\w$\"3gX.99w$\\Z\"Fbt7$Fa
w$\"3#Rg:/JJWg\"Fbt7$Ffw$\"3BK!)=B$>?u\"Fbt7$F[x$\"3GJ^%y&)>()*=Fbt7$F
`x$\"3I6#p<A_H1#Fbt7$Fex$\"3sq09)e/cC#Fbt7$Fjx$\"3!H%)[JG7FW#Fbt7$F_y$
\"3W]L&ek^!REFbt7$Fdy$\"3'zJ5N%>c$)GFbt7$Fiy$\"3m1s;)='Q@JFbt7$F^z$\"3
y&Hlqx+mR$Fbt7$Fcz$\"31O,^&*er#o$Fbt7$Fhz$\"3fLvj%Q2r,%Fbt-F][l6&F_[lF
`[lF`[lFb[l-%+AXESLABELSG6$Q\"x6\"Q\"yFg^m-%%VIEWG6$;F(Fhz;Fb[l$\"#gF*
" 1 2 0 1 10 0 2 9 1 4 2 1.000000 45.000000 45.000000 0 0 "Curve 1" "C
urve 2" "Curve 3" }}}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" 
{TEXT -1 8 "(Note:  " }{TEXT 285 3 "seq" }{TEXT -1 58 ",  which stands
 for \"sequence\", is a Maple command, while " }{XPPEDIT 18 0 "s" "6#%
\"sG" }{TEXT -1 124 " is just a variable that we use as a name for the
 sequence of functions to be plotted; we could just as well have calle
d it " }{XPPEDIT 18 0 "bunch_of_functions" "6#%3bunch_of_functionsG" }
{TEXT -1 25 " or something like that.)" }}{PARA 0 "" 0 "" {TEXT -1 0 "
" }}{PARA 0 "" 0 "" {TEXT -1 27 "What if you want to change " }
{XPPEDIT 18 0 "c" "6#%\"cG" }{TEXT -1 4 " in " }{TEXT 266 11 "non-inte
ger" }{TEXT -1 46 " increments? As an example, try the following:" }}
{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 
51 "s:=seq((c/5)*exp(x),c=-10..10);  plot(\{s\},x=-1..3);" }}{PARA 12 
"" 1 "" {XPPMATH 20 "6#>%\"sG67,$-%$expG6#%\"xG!\"#,$F'#!\"*\"\"&,$F'#
!\")F/,$F'#!\"(F/,$F'#!\"'F/,$F'!\"\",$F'#!\"%F/,$F'#!\"$F/,$F'#F+F/,$
F'#F:F/\"\"!,$F'#\"\"\"F/,$F'#\"\"#F/,$F'#\"\"$F/,$F'#\"\"%F/F',$F'#\"
\"'F/,$F'#\"\"(F/,$F'#\"\")F/,$F'#\"\"*F/,$F'FK" }}{PARA 13 "" 1 "" 
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