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6 "Maple " }{TEXT 289 12 "\275\307\275\300 2000.03" }}{SECT 1 {PARA 3 
"" 0 "" {TEXT 291 13 "Example 1.2.4" }{TEXT -1 0 "" }}{EXCHG {PARA 0 "
> " 0 "" {MPLTEXT 1 0 8 "restart;" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 13 "with(linalg):" }}{PARA 7 "" 1 "" {TEXT -1 32 "Warning
, new definition for norm" }}{PARA 7 "" 1 "" {TEXT -1 33 "Warning, new
 definition for trace" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 23 "A:
=vector(3, [-1,2,7]);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"AG-%'vect
orG6#7%!\"\"\"\"#\"\"(" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 23 "B
:=vector(3, [-3,1,5]);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"BG-%'vec
torG6#7%!\"$\"\"\"\"\"&" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 19 "
innerprod(A-B,A-B);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"\"*" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "sqrt(%);" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#\"\"$" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 13 "nor
m(A-B, 2);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"\"$" }}}}{SECT 1 
{PARA 3 "" 0 "" {TEXT -1 0 "" }{TEXT 273 13 "Example 1.2.7" }{TEXT -1 
0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "restart;" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 13 "with(linalg):" }}{PARA 7 "" 1 "" 
{TEXT -1 32 "Warning, new definition for norm" }}{PARA 7 "" 1 "" 
{TEXT -1 33 "Warning, new definition for trace" }}}{EXCHG {PARA 0 "> \+
" 0 "" {MPLTEXT 1 0 30 "A:='A': A:=vector(3, [1,3,7]);" }}{PARA 11 "" 
1 "" {XPPMATH 20 "6#>%\"AG-%'vectorG6#7%\"\"\"\"\"$\"\"(" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 31 "B:='B': B:=vector(3, [-1,0,6]);" }}
{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"BG-%'vectorG6#7%!\"\"\"\"!\"\"'" }
}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 24 "C:=vector(3, [0,-1,-2]);" 
}}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"CG-%'vectorG6#7%\"\"!!\"\"!\"#" 
}}}{PARA 257 "" 0 "" {TEXT 274 8 "Because " }{TEXT 276 1 "D" }{TEXT 
275 72 " is reserved for the differential operator, let us use the oth
er symbol " }{TEXT 278 1 "E" }{TEXT 277 16 " for the vector " }{TEXT 
279 1 "D" }{TEXT 280 1 "." }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 25 
"E:=vector(3, [-2,-4,-3]);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"EG-%
'vectorG6#7%!\"#!\"%!\"$" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 11 
"evalm(B-A);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#-%'vectorG6#7%!\"#!\"$
!\"\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 11 "evalm(E-C);" }}
{PARA 11 "" 1 "" {XPPMATH 20 "6#-%'vectorG6#7%!\"#!\"$!\"\"" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 19 "evalm((B-A)-(E-C));" }}
{PARA 11 "" 1 "" {XPPMATH 20 "6#-%'vectorG6#7%\"\"!F'F'" }}}}{SECT 1 
{PARA 3 "" 0 "" {TEXT -1 0 "" }{TEXT 281 14 "Example 1.2.11" }{TEXT 
-1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "restart;" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 13 "with(linalg):" }}{PARA 7 "" 
1 "" {TEXT -1 32 "Warning, new definition for norm" }}{PARA 7 "" 1 "" 
{TEXT -1 33 "Warning, new definition for trace" }}}{EXCHG {PARA 0 "> \+
" 0 "" {MPLTEXT 1 0 39 "A:='A': A:=vector(3, [a[1],a[2],a[3]]);" }}
{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"AG-%'vectorG6#7%&%\"aG6#\"\"\"&F*6
#\"\"#&F*6#\"\"$" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 39 "B:='B':
 B:=vector(3, [b[1],b[2],b[3]]);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%
\"BG-%'vectorG6#7%&%\"bG6#\"\"\"&F*6#\"\"#&F*6#\"\"$" }}}{EXCHG {PARA 
0 "> " 0 "" {MPLTEXT 1 0 10 "1/2*(A+B);" }}{PARA 11 "" 1 "" {XPPMATH 
20 "6#,&%\"AG#\"\"\"\"\"#%\"BGF%" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 12 "B+1/2*(A-B);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,&%\"
AG#\"\"\"\"\"#%\"BGF%" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "ev
alm(1/2*(A+B));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#-%'vectorG6#7%,&&%
\"aG6#\"\"\"#F+\"\"#&%\"bGF*F,,&&F)6#F-F,&F/F2F,,&&F)6#\"\"$F,&F/F6F,
" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 19 "evalm(B+1/2*(A-B));" }
{TEXT -1 0 "" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#-%'vectorG6#7%,&&%\"aG
6#\"\"\"#F+\"\"#&%\"bGF*F,,&&F)6#F-F,&F/F2F,,&&F)6#\"\"$F,&F/F6F," }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "evalm(%%-%);" }}{PARA 11 "" 
1 "" {XPPMATH 20 "6#-%'vectorG6#7%\"\"!F'F'" }}}}{SECT 1 {PARA 3 "" 0 
"" {TEXT -1 0 "" }{TEXT 282 14 "Example 1.2.12" }{TEXT -1 0 "" }}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "restart;" }}}{EXCHG {PARA 0 "
> " 0 "" {MPLTEXT 1 0 13 "with(linalg):" }}{PARA 7 "" 1 "" {TEXT -1 
32 "Warning, new definition for norm" }}{PARA 7 "" 1 "" {TEXT -1 33 "W
arning, new definition for trace" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 49 "X:=vector(2, [10^5*cos(Pi/12), 10^5*sin(Pi/12)]);" }}
{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"XG-%'vectorG6#7$,$*&-%%sqrtG6#\"\"
'\"\"\",&\"\"\"F1*$-F,6#\"\"$F/#F1F5F1\"&+]#,$*&F+F/,&F1F1F2#!\"\"F5F1
F7" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 53 "Y:=vector(2, [2*10^5*
cos(theta), 2*10^5*sin(theta)]);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%
\"YG-%'vectorG6#7$,$-%$cosG6#%&thetaG\"'++?,$-%$sinGF,F." }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 24 "Z:=simplify(evalm(X+Y));" }}{PARA 
11 "" 1 "" {XPPMATH 20 "6#>%\"ZG-%'vectorG6#7$,(*&-%%sqrtG6#\"\"$\"\"
\"-F,6#\"\"#F/\"&+]#*$F0F/F3-%$cosG6#%&thetaG\"'++?,(F*F3F4!&+]#-%$sin
GF7F9" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 5 "Z[2];" }}{PARA 11 "
" 1 "" {XPPMATH 20 "6#,(*&-%%sqrtG6#\"\"$\"\"\"-F&6#\"\"#F)\"&+]#*$F*F
)!&+]#-%$sinG6#%&thetaG\"'++?" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 
0 21 "solve(Z[2]=0, theta);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#-%'arcs
inG6#,&*&-%%sqrtG6#\"\"$\"\"\"-F)6#\"\"#F,#!\"\"\"\")*$F-F,#\"\"\"F2" 
}}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "evalf(%,20);" }}{PARA 11 
"" 1 "" {XPPMATH 20 "6#$!5z*>$f'yrMxH\"!#?" }}}{EXCHG {PARA 0 "> " 0 "
" {MPLTEXT 1 0 35 "evalf(arcsin(-1/2*sin(Pi/12)), 20);" }}{PARA 11 "" 
1 "" {XPPMATH 20 "6#$!5z*>$f'yrMxH\"!#?" }}}{PARA 0 "" 0 "" {TEXT 283 
37 "By changing the radian to the degree!" }}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 22 "evalf(%*(180/Pi), 20);" }}{PARA 11 "" 1 "" {XPPMATH 
20 "6#$!5.B`=8EAZNu!#>" }}}}{SECT 1 {PARA 3 "" 0 "" {TEXT -1 0 "" }
{TEXT 284 13 "Exercise 1.2 " }{TEXT 286 11 "Problem 11." }{TEXT -1 0 "
" }{TEXT 285 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "restart;
" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 13 "with(linalg):" }}{PARA 
7 "" 1 "" {TEXT -1 32 "Warning, new definition for norm" }}{PARA 7 "" 
1 "" {TEXT -1 33 "Warning, new definition for trace" }}}{EXCHG {PARA 
0 "> " 0 "" {MPLTEXT 1 0 30 "A:='A': A:=vector(2, [0,-20]);" }}{PARA 
11 "" 1 "" {XPPMATH 20 "6#>%\"AG-%'vectorG6#7$\"\"!!#?" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 52 "B:='B': B:=vector(2, [100*cos(Pi/3)
,100*sin(Pi/3)]);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"BG-%'vectorG6
#7$\"#],$*$-%%sqrtG6#\"\"$\"\"\"F)" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 50 "C:='C': C:=vector(2, [F*cos(theta),F*sin(theta)]);" }
}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"CG-%'vectorG6#7$*&%\"FG\"\"\"-%$c
osG6#%&thetaGF+*&F*\"\"\"-%$sinGF.F+" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 16 "X:=evalm(A+B+C);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>
%\"XG-%'vectorG6#7$,&\"#]\"\"\"*&%\"FGF+-%$cosG6#%&thetaGF+F+,(!#?F+*$
-%%sqrtG6#\"\"$\"\"\"F**&F-F9-%$sinGF0F+F+" }}}{EXCHG {PARA 0 "> " 0 "
" {MPLTEXT 1 0 31 "theta[1]:= solve(X[1]=0,theta);" }}{PARA 11 "" 1 "
" {XPPMATH 20 "6#>&%&thetaG6#\"\"\",&%#PiGF'-%'arccosG6#,$*&\"\"\"F/%
\"FG!\"\"\"#]!\"\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 31 "theta
[2]:= solve(X[2]=0,theta);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>&%&thet
aG6#\"\"#,$-%'arcsinG6#,$*&,&!\"#\"\"\"*$-%%sqrtG6#\"\"$\"\"\"\"\"&F6%
\"FG!\"\"\"#5!\"\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 32 "T:= s
olve(theta[1]=theta[2], F);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"TG,
$*$-%%sqrtG6#,&\"#E\"\"\"*$-F(6#\"\"$\"\"\"!\"&F1!#?" }}}{EXCHG {PARA 
0 "> " 0 "" {MPLTEXT 1 0 12 "simplify(T);" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#,$*$-%%sqrtG6#,&\"#E\"\"\"*$-F&6#\"\"$\"\"\"!\"&F/!#?" 
}}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 28 "theta:= subs(F=T, theta[1
]);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%&thetaG,&%#PiG\"\"\"-%'arccos
G6#,$*&\"\"\"F-*$-%%sqrtG6#,&\"#EF'*$-F06#\"\"$F-!\"&F-!\"\"#F8\"\"#!
\"\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 11 "tan(theta);" }}
{PARA 11 "" 1 "" {XPPMATH 20 "6#,$*&-%%sqrtG6#,&\"\"%\"\"\"*&\"\"\"F,,
&\"#EF**$-F&6#\"\"$F,!\"&!\"\"!#DF,-F&6#F-F,#F*\"\"&" }}}{EXCHG {PARA 
0 "> " 0 "" {MPLTEXT 1 0 12 "simplify(%);" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#,&#!\"#\"\"&\"\"\"*$-%%sqrtG6#\"\"$\"\"\"F'" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 13 "evalf(%, 20);" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#$\"5NHx)ov!30K8!#>" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 50 "C:='C': C:=vector(2, [T*cos(theta),T*sin(theta)]);" }
}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"CG-%'vectorG6#7$!#],$*&-%%sqrtG6#
,&\"\"%\"\"\"*&\"\"\"F3,&\"#EF1*$-F-6#\"\"$F3!\"&!\"\"!#DF3-F-6#F4F3!#
5" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "simplify(%);" }}{PARA 
11 "" 1 "" {XPPMATH 20 "6#-%'vectorG6#7$!#],&\"#?\"\"\"*$-%%sqrtG6#\"
\"$\"\"\"F'" }}}}{SECT 1 {PARA 3 "" 0 "" {TEXT -1 0 "" }{TEXT 293 13 "
Example 1.3.6" }{TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 
8 "restart;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 13 "with(linalg)
:" }}{PARA 7 "" 1 "" {TEXT -1 32 "Warning, new definition for norm" }}
{PARA 7 "" 1 "" {TEXT -1 33 "Warning, new definition for trace" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 23 "A:=vector(3, [2,-1,2]);" }}
{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"AG-%'vectorG6#7%\"\"#!\"\"F)" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 23 "B:=vector(3, [1,-1,0]);" }}
{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"BG-%'vectorG6#7%\"\"\"!\"\"\"\"!" 
}}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 18 "a:=innerprod(A,B);" }}
{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"aG\"\"$" }}}{EXCHG {PARA 0 "> " 0 
"" {MPLTEXT 1 0 14 "b:=norm(A, 2);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#
>%\"bG\"\"$" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "c:=norm(B, 2
);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"cG*$-%%sqrtG6#\"\"#\"\"\"" }
}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 24 "theta:= arccos(a/(b*c));" 
}}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%&thetaG,$%#PiG#\"\"\"\"\"%" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}{SECT 1 {PARA 3 "" 0 "
" {TEXT -1 0 "" }{TEXT 294 14 "Example 1.3.11" }{TEXT -1 0 "" }}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "restart;" }}}{EXCHG {PARA 0 "
> " 0 "" {MPLTEXT 1 0 13 "with(linalg):" }}{PARA 7 "" 1 "" {TEXT -1 
32 "Warning, new definition for norm" }}{PARA 7 "" 1 "" {TEXT -1 33 "W
arning, new definition for trace" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 22 "A:=vector(3, [1,2,3]);" }}{PARA 11 "" 1 "" {XPPMATH 
20 "6#>%\"AG-%'vectorG6#7%\"\"\"\"\"#\"\"$" }}}{EXCHG {PARA 0 "> " 0 "
" {MPLTEXT 1 0 22 "B:=vector(3, [4,5,6]);" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#>%\"BG-%'vectorG6#7%\"\"%\"\"&\"\"'" }}}{EXCHG {PARA 0 
"> " 0 "" {MPLTEXT 1 0 11 "evalm(B-A);" }}{PARA 11 "" 1 "" {XPPMATH 
20 "6#-%'vectorG6#7%\"\"$F'F'" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 
0 21 "V:= evalm(A+t*(B-A));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"VG-
%'vectorG6#7%,&\"\"\"F*%\"tG\"\"$,&\"\"#F*F+F,,&F,F*F+F," }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 5 "V[1];" }}{PARA 11 "" 1 "" {XPPMATH 
20 "6#,&\"\"\"F$%\"tG\"\"$" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 
12 "with(plots):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 52 "a:= spa
cecurve(V, t=-7..7, thickness=3, axes=FRAME):" }}}{EXCHG {PARA 0 "> " 
0 "" {MPLTEXT 1 0 54 "b:= textplot3d(\{[1,2,3,`(1,2,3)`],[4,5,6,`(4,5,
6)`]\}):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 15 "display3d(a,b);
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