{VERSION 5 0 "IBM INTEL NT" "5.0" }
{USTYLETAB {CSTYLE "Maple Input" -1 0 "Courier" 0 1 255 0 0 1 0 1 0 0 
1 0 0 0 0 1 }{CSTYLE "2D Math" -1 2 "Times" 0 1 0 0 0 0 0 0 2 0 0 0 0 
0 0 1 }{CSTYLE "2D Output" 2 20 "" 0 1 0 0 255 1 0 0 0 0 0 0 0 0 0 1 }
{PSTYLE "Normal" -1 0 1 {CSTYLE "" -1 -1 "Times" 1 12 0 0 0 1 2 2 2 2 
2 2 1 1 1 1 }1 1 0 0 0 0 1 0 1 0 2 2 0 1 }{PSTYLE "Maple Output" -1 
11 1 {CSTYLE "" -1 -1 "Times" 1 12 0 0 0 1 2 2 2 2 2 2 1 1 1 1 }3 3 0 
0 0 0 1 0 1 0 2 2 0 1 }}
{SECT 0 {EXCHG {PARA 0 "" 0 "" {TEXT -1 8 "Sec. 9.1" }{MPLTEXT 1 0 0 "
" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 50 "grad:=proc(f);[diff(f,x
),diff(f,y),diff(f,z)] end:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 
56 "div:=proc(g);diff(g[1],x)+diff(g[2],y)+diff(g[3],z) end:" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 97 "curl:=proc(g);[diff(g[3],y)-
diff(g[2],z),diff(g[1],z)-diff(g[3],x),diff(g[2],x)-diff(g[1],y)]end:
" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 51 "dot:=proc(r,q);simplify
(add(r[i]*q[i],i=1..3)) end:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 
0 83 "cross:=proc(r,q);[r[2]*q[3]-r[3]*q[2],r[3]*q[1]-r[1]*q[3],r[1]*q
[2]-r[2]*q[1]] end:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 41 "mag:
=proc(q);sqrt(add(q[i]^2,i=1..3))end:" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 52 "plugin:=proc(g,r);eval(g,\{x=r[1],y=r[2],z=r[3]\})end
:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 92 "findf:=proc(g) local h
;h:=int(g[1],x);h:=h+int(g[2]-diff(h,y),y);h+int(g[3]-diff(h,z),z)end:
" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 3 "Q8:" }{MPLTEXT 1 0 0 "" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 44 "g:=[x-y,y-z,z-x]:  r:=[2*cos
(t),t,2*sin(t)]:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 52 "int(dot
(plugin(g,r),diff(r,t)),t=0..2*Pi); evalf(%);" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#,&*&\"\")\"\"\"%#PiGF&!\"\"*&\"\"#F&)F'F*F&F&" }}{PARA 
11 "" 1 "" {XPPMATH 20 "6#$!*UKNR&!\")" }}}{EXCHG {PARA 0 "" 0 "" 
{TEXT -1 4 "Q10:" }{MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 46 "g:=[cosh(x),sinh(y),exp(z)]:   r:=[t,t^2,t^3]:" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 50 "int(dot(plugin(g,r),diff(r,t
)),t=0..2);  evalf(%);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,*-%%sinhG6#
\"\"#\"\"\"-%%coshG6#\"\"%F(-%$expG6#\"\")F(F'!\"\"" }}{PARA 11 "" 1 "
" {XPPMATH 20 "6#$\"+!3$*)4I!\"'" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 
4 "Q14:" }{MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 
25 "r:=[2*cos(t),2*sin(t),0]:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 
0 46 "int(plugin(x^3*y,r)*mag(diff(r,t)),t=0..Pi/2);" }}{PARA 11 "" 1 
"" {XPPMATH 20 "6#\"\")" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 4 "Q16:" }
{MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 13 "r:=[t,t
,t^2]:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 55 "int(plugin(sqrt(2
+x^2+3*y^2),r)*mag(diff(r,t)),t=0..3);" }}{PARA 11 "" 1 "" {XPPMATH 
20 "6#\"#U" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG 
{PARA 0 "" 0 "" {TEXT -1 7 "Set 9.2" }{MPLTEXT 1 0 0 "" }}}{EXCHG 
{PARA 0 "" 0 "" {TEXT -1 3 "Q4:" }{MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 
"> " 0 "" {MPLTEXT 1 0 42 "g:=[cos(x)*cos(2*y),-2*sin(x)*sin(2*y),0];
" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"gG7%*&-%$cosG6#%\"xG\"\"\"-F(6
#,$*&\"\"#F+%\"yGF+F+F+,$*(F0F+-%$sinGF)F+-F5F-F+!\"\"\"\"!" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "curl(g);   #check" }}{PARA 
11 "" 1 "" {XPPMATH 20 "6#7%\"\"!F$F$" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 12 "f:=findf(g);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"f
G*&-%$cosG6#,$*&\"\"#\"\"\"%\"yGF,F,F,-%$sinG6#%\"xGF," }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 55 "plugin(f,[Pi/4,0,0])-plugin(f,[Pi/2
,-Pi,0]);  evalf(%);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,&*&\"\"#!\"\"
F%#\"\"\"F%F(F(F&" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$!+!>K*GH!#5" }}}
{EXCHG {PARA 0 "" 0 "" {TEXT -1 3 "Q8:" }{MPLTEXT 1 0 0 "" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 36 "g:=[-z*sin(x*z),cos(y),-x*sin(x*z)]
;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"gG7%,$*&%\"zG\"\"\"-%$sinG6#*
&%\"xGF)F(F)F)!\"\"-%$cosG6#%\"yG,$*&F.F)F*F)F/" }}}{EXCHG {PARA 0 "> \+
" 0 "" {MPLTEXT 1 0 17 "curl(g);   #check" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#7%\"\"!F$F$" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 
12 "f:=findf(g);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"fG,&-%$cosG6#*
&%\"xG\"\"\"%\"zGF+F+-%$sinG6#%\"yGF+" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 41 "plugin(f,[0,Pi,1])-plugin(f,[Pi,Pi/2,2]);" }}{PARA 
11 "" 1 "" {XPPMATH 20 "6#!\"\"" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 4 
"Q18:" }{MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 38 
"g:=[y*exp(x*y),2*x*exp(x*y),exp(2*z)];" }}{PARA 11 "" 1 "" {XPPMATH 
20 "6#>%\"gG7%*&%\"yG\"\"\"-%$expG6#*&%\"xGF(F'F(F(,$*(\"\"#F(F-F(F)F(
F(-F*6#,$*&F0F(%\"zGF(F(" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "
curl(g);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#7%\"\"!F$,&-%$expG6#*&%\"x
G\"\"\"%\"yGF+F+*(F*F+F,F+F&F+F+" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 
20 "not path independent" }{MPLTEXT 1 0 0 "" }}}}{MARK "37" 0 }
{VIEWOPTS 1 1 0 1 1 1803 1 1 1 1 }{PAGENUMBERS 0 1 2 33 1 1 }