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{SECT 0 {EXCHG {PARA 261 "" 0 "" {TEXT 256 25 "Konservative vektorfelt
er" }{MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 256 "" 0 "" {TEXT -1 26 "Al bru
g er p\345 eget ansvar." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 
0 "" {TEXT -1 41 "Vejledning:\n1) Udfyld v\346rdier for opgaven" }}
{PARA 0 "" 0 "" {TEXT -1 53 "2) G\345 til bunden af maple-arket og try
k \"!!!\"-knappen" }{MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 257 "" 0 "" 
{TEXT -1 21 "-- Skriv vektorfeltet" }{MPLTEXT 1 0 0 "" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 48 "H:=[y/(sqrt(1-x^2*y^2)), x/(sqrt(1-
x^2*y^2))-4];" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"HG7$*&%\"yG\"\"\"
,&F(F(*&)%\"xG\"\"#F()F'F-F(!\"\"#F/F-,&*&F,F(F)F0F(\"\"%F/" }}}
{EXCHG {PARA 0 "" 0 "" {TEXT -1 39 "Vi benytter krydsdifferentationsre
glen:" }}{PARA 0 "" 0 "" {TEXT 257 29 "Er vektorfeltet konservativt?" 
}{MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 19 "DH1y:=
diff(H[1],y);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%%DH1yG,&*&\"\"\"F'*
$,&F'F'*&)%\"xG\"\"#F')%\"yGF-F'!\"\"#F'F-F0F'*(F/F-F)#!\"$F-F,F-F'" }
}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 19 "DH2x:=diff(H[2],x);" }}
{PARA 11 "" 1 "" {XPPMATH 20 "6#>%%DH2xG,&*&\"\"\"F'*$,&F'F'*&)%\"xG\"
\"#F')%\"yGF-F'!\"\"#F'F-F0F'*(F/F-F)#!\"$F-F,F-F'" }}}{EXCHG {PARA 0 
"> " 0 "" {MPLTEXT 1 0 14 "is(DH1y=DH2x);" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#%%trueG" }}}{EXCHG {PARA 258 "" 0 "" {TEXT -1 28 "Hvad \+
er potentialfunktionen?" }{MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "" 0 "" 
{TEXT -1 33 "Vi integrerer H1 med hensyn til x" }{MPLTEXT 1 0 0 "" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 24 "phi := int(H[1],x) + cy;" }}
{PARA 11 "" 1 "" {XPPMATH 20 "6#>%$phiG,&*(%\"yG\"\"\"*$)F'\"\"#F(#!\"
\"F+-%'arctanG6#*(F)#F(F+%\"xGF(,&F(F(*&)F3F+F(F*F(F-F,F(F(*&\"\"%F(F'
F(F-" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 34 "Og differentierer med hen
syn til y" }{MPLTEXT 1 0 1 "." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 
0 28 "simplify(diff(phi,y)) + dcy;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#
,&*&%\"xG\"\"\",&F&F&*&)F%\"\"#F&)%\"yGF*F&!\"\"#F-F*F&%$dcyGF&" }}}
{EXCHG {PARA 0 "" 0 "" {TEXT -1 83 "Vi sammenligner med H2, og differe
nsen er en funktion af y, afledt med hensyn til y" }{MPLTEXT 1 0 0 "" 
}}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 51 "dcy:=solve(simplify(diff(
phi,y)) + dcy = H[2],dcy);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%$dcyG!
\"%" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "cy := int(dcy,y);" }
}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#cyG,$*&\"\"%\"\"\"%\"yGF(!\"\"" }}
}{EXCHG {PARA 0 "" 0 "" {TEXT -1 32 "Vi kender nu potentialfunktionen
" }{MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 4 "phi;
" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,&*(%\"yG\"\"\"*$)F%\"\"#F&#!\"\"F
)-%'arctanG6#*(F'#F&F)%\"xGF&,&F&F&*&)F1F)F&F(F&F+F*F&F&*&\"\"%F&F%F&F
+" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 258 64 "Vi vil udregne et kurveinte
gral over det konservative vektorfelt" }}{PARA 0 "" 0 "" {TEXT 259 30 
"-- Definer evt. parameterkurve" }{MPLTEXT 1 0 0 "" }}{PARA 0 "> " 0 "
" {MPLTEXT 1 0 24 "r:=t->[t/2,sqrt(2+t^2)];" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#>%\"rGf*6#%\"tG6\"6$%)operatorG%&arrowGF(7$,$*&#\"\"\"
\"\"#F09$F0F0-%%sqrtG6#,&F1F0*$)F2F1F0F0F(F(F(" }}}{EXCHG {PARA 260 "
" 0 "" {TEXT -1 21 "-- Definer startpunkt" }{MPLTEXT 1 0 0 "" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 13 "start:=r(-1);" }}{PARA 11 "
" 1 "" {XPPMATH 20 "6#>%&startG7$#!\"\"\"\"#*$\"\"$#\"\"\"F(" }}}
{EXCHG {PARA 0 "" 0 "" {TEXT 260 20 "-- Definer slutpunkt" }{MPLTEXT 
1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 11 "slut:=r(1);" }}
{PARA 11 "" 1 "" {XPPMATH 20 "6#>%%slutG7$#\"\"\"\"\"#*$\"\"$F&" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 44 "phi_start:=subs(x=start[1],y
=start[2], phi);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%*phi_startG,&-%'
arctanG6#,$*(\"\"#!\"\"\"\"$#\"\"\"F+\"\"%F.F,F/*&F0F/F-F.F," }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 41 "phi_slut:=subs(x=slut[1],y=s
lut[2], phi);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%)phi_slutG,&-%'arct
anG6#,$*(\"\"#!\"\"\"\"$#\"\"\"F+\"\"%F.F/F/*&F0F/F-F.F," }}}{EXCHG 
{PARA 0 "" 0 "" {TEXT -1 24 "Kurveintegralet er alts\345" }{MPLTEXT 1 
0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 34 "C:=simplify(phi_sl
ut - phi_start);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"CG,$*(\"\"#\"
\"\"\"\"$!\"\"%#PiGF(F(" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "
" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> \+
" 0 "" {MPLTEXT 1 0 0 "" }}}}{MARK "1 0 0" 26 }{VIEWOPTS 1 1 0 1 1 
1803 1 1 1 1 }{PAGENUMBERS 0 1 2 33 1 1 }