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{SECT 0 {PARA 0 "" 0 "" {TEXT -1 0 "" }{TEXT 256 27 "Maple as a analyt
ical tool " }{TEXT 258 50 "maple_as_manipulator.mws (7/30/02, updated \+
7/3/04)" }}{PARA 0 "" 0 "" {TEXT -1 37 "Copyright 2002-2004, SUNY at B
uffalo." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT 257 
34 "Maple can do algebra and calculus." }}{PARA 0 "" 0 "" {TEXT -1 0 "
" }}{PARA 0 "" 0 "" {TEXT -1 18 "Solve an equation:" }}{EXCHG {PARA 0 
"> " 0 "" {MPLTEXT 1 0 51 "my_equation := x + y^2*x = 9;\nsolve(my_equ
ation,x);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%,my_equationG/,&%\"xG\"
\"\"*&)%\"yG\"\"#F(F'F(F(\"\"*" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,$*&
\"\"\"F%,&F%F%*$)%\"yG\"\"#F%F%!\"\"\"\"*" }}}{PARA 0 "" 0 "" {TEXT 
-1 76 "If there are multiple solutions, you'll need to pick out the on
e you want: \n" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 61 "solutions:
=solve(my_equation,y);\nsolutions[1];\nsolutions[2];\n" }{XPPMATH 20 "
6#>%*solutionsG6$*&*$-%%sqrtG6#,$*&%\"xG\"\"\",&F-F.\"\"*!\"\"F.F1F.F.
F-F1,$F&F1" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#*&*$-%%sqrtG6#,$*&%\"xG
\"\"\",&F*F+\"\"*!\"\"F+F.F+F+F*F." }}{PARA 11 "" 1 "" {XPPMATH 20 "6#
,$*&*$-%%sqrtG6#,$*&%\"xG\"\"\",&F+F,\"\"*!\"\"F,F/F,F,F+F/F/" }}}
{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 46 "Maple can
 also deal with systems of equations:" }}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 90 "restart:\neq1:=3*x+y*y=2;\neq2:=7*x-9*y=-1;\nsolve(\{
eq1,eq2\},\{x,y\});\nsolutions:=allvalues(%);" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#>%$eq1G/,&%\"xG\"\"$*$)%\"yG\"\"#\"\"\"F-F," }}{PARA 
11 "" 1 "" {XPPMATH 20 "6#>%$eq2G/,&%\"xG\"\"(*&\"\"*\"\"\"%\"yGF+!\"
\"F-" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#<$/%\"yG-%'RootOfG6$,(%#_ZG\"#
F\"#<!\"\"*&\"\"(\"\"\")F*\"\"#F0F0/%&labelG%$_L1G/%\"xG,&F&#\"\"*F/#F
0F/F-" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%*solutionsG6$<$/%\"yG,&#!#F
\"#9\"\"\"*&#F-F,F--%%sqrtG6#\"%07F-F-/%\"xG,&#!$d#\"#)*F-*&#\"\"*F9F-
F0F-F-<$/F(,&F*F-*&#F-F,F-*$F0F-F-!\"\"/F5,&F7F-*&#F<F9F-FBF-FC" }}}
{PARA 0 "" 0 "" {TEXT -1 52 "You can pick out the solution(s) you want
 like this:" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 13 "solutions[1];
" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#<$/%\"yG,&#!#F\"#9\"\"\"*&#F*F)F*-
%%sqrtG6#\"%07F*F*/%\"xG,&#!$d#\"#)*F**&#\"\"*F6F*F-F*F*" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 31 "eval([x,y],solutions[1]);\n%[1];" }
}{PARA 11 "" 1 "" {XPPMATH 20 "6#7$,&#!$d#\"#)*\"\"\"*&#\"\"*F'F(-%%sq
rtG6#\"%07F(F(,&#!#F\"#9F(*&#F(F3F(F,F(F(" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#,&#!$d#\"#)*\"\"\"*&#\"\"*F&F'-%%sqrtG6#\"%07F'F'" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 27 "assign(solutions[2]);\nx;\ny
;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,&#!$d#\"#)*\"\"\"*&#\"\"*F&F'*$-
%%sqrtG6#\"%07F'F'!\"\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,&#!#F\"#9
\"\"\"*&#F'F&F'*$-%%sqrtG6#\"%07F'F'!\"\"" }}}{PARA 0 "" 0 "" {TEXT 
-1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 38 "Maple can differentiate and int
egrate:" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 23 "restart:\ny:=sin(
x)+x^2;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"yG,&-%$sinG6#%\"xG\"\"
\"*$)F)\"\"#F*F*" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 10 "diff(y,
x);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,&-%$cosG6#%\"xG\"\"\"*&\"\"#F(
F'F(F(" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 9 "int(y,x);" }}
{PARA 11 "" 1 "" {XPPMATH 20 "6#,&-%$cosG6#%\"xG!\"\"*&#\"\"\"\"\"$F+)
F'F,F+F+" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 15 "int(y,x=0..Pi);
" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,&\"\"#\"\"\"*&#F%\"\"$F%)%#PiGF(F
%F%" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 4 "Th
e " }{TEXT 259 8 "assuming" }{TEXT -1 30 " operator is sometimes usefu
l:" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 10 "sqrt(x^2);" }}{PARA 
11 "" 1 "" {XPPMATH 20 "6#*$*$)%\"xG\"\"#\"\"\"#F(F'" }}}{EXCHG {PARA 
0 "> " 0 "" {MPLTEXT 1 0 23 "sqrt(x^2) assuming x>0;" }}{PARA 11 "" 1 
"" {XPPMATH 20 "6#%\"xG" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 76 "
int(exp(-a*x^2),x=0..infinity);\nint(exp(-a*x^2),x=0..infinity) assumi
ng a>0;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#-%&limitG6$,$*&#\"\"\"\"\"#
F)*(%#PiGF(%\"aG#!\"\"F*-%$erfG6#*&F-F(%\"xGF)F)F)F)/F4%)infinityG" }}
{PARA 11 "" 1 "" {XPPMATH 20 "6#,$*(\"\"#!\"\"%\"aG#F&F%%#PiG#\"\"\"F%
F+" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}{MARK "1 0" 0 }
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