asignacion hasta derivadas parciales

FDOFXOR 440P
Krmd gh Sureohpdv
Ghulydgdv Sdufldohv
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Grplqlrv/ Fxuydv | Vxshuflhv gh Qlyho
41 Lqglfdu ho wlsr gh vxshuflh | uhsuhvhqwduod hvtxhpäwlfdphqwh
+d, b%2 n +2 n S5 2 ' b
+e, e%2 n e+2 5 2 ' e
+f, +2 n 5 2 %2 ' 
+g, 5 2 %2 +2 ' 
+h, +2 %2 ' 5
+i, +2 n 5 2 ' %2
+j, %2 n e5 2 ' S
+k, +5 ' 
+l, 5 ' E%2 n +2
+m, %2 5 2 +2 ' 
+n, 5 2 %2 + 2 ' b
+o, S+2 n b5 2 e%2 ' f
51 Ghwhuplqdu xqd hfxdflöq gh od vxshuflh rewhqlgd do jludu od fxuyd
douhghgru gho hmh f
4
+d, od uhfwd 5 ' 2+c + fc 5 f
+e, od sduäerod 5 '  n +2
+f, phgld holsvh 5 2 n 2+2 ' 
+g, ho fðufxor + 2 n E5 2 '  +Glylgluor hq grv sduwhv | rewhqhu grv
hfxdflrqhv/ uhvxowd xq wrur,
61 Ghwhuplqdu ho grplqlr gh odv vljxlhqwhv ixqflrqhv
s
e %2 +2

+e, s E%c + ' s
 2%2 +2
+d, s E%c + '
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+g, s E%c +c 5 ' *?E%+5
+f, s E%c + '
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71 Rewhqhu odv fxuydv gh qlyho gh odv vljxlhqwhv ixqflrqhv
+d, s E%c + ' % n +
+e, s E%c + ' e %2 +2
+f, s E%c + ' %2 +2
+g, s E%c + ' m%m n m+m
+h, s E%c + ' *?E%+
81 Rewhqhu odv vxshuflhv gh qlyho gh odv vljxlhqwhv ixqflrqhv
+d, s E%c +c 5 ' *?E%2 n +2 n 5 2
%2 + 2 5 2
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+f, s E%c +c 5 ' 5 %2 +2
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+h, s E%c +c 5 ' %2 n +2 5 2
5
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Oðplwhv | Frqwlqxlgdg
41 Rewhqhu orv oðplwhv vljxlhqwhv=
+d,
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E%c+ <Efcf
 n %2 n + 2
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51 Rewhqhu orv oðplwhv vljxlhqwhv=
+d,
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E%c+ Ecf
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61 Xvdu frrughqdgdv sroduhv sdud rewhqhu orv vljxlhqwhv oðplwhv=
+d,
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E%c+ Efcf
%+
%2 +2
%2 n +2
+e,
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E%c+<Efcf %2 n + 2
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+f,
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n +2
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t?E%2 n +2
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%2 n +2
71 Phgldqwh oðplwhv gluhfflrqdohv ghprvwudu txh qr h{lvwhq orv vljxlhqwhv
oðplwhv=
+d,
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2%+
n +2
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+e,
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81 Phgldqwh oðplwhv sru fdplqrv ghprvwudu txh qr h{lvwhq orv vljxlhqwhv
oðplwhv=
+d,
2%2+
E%c+ <Efcf %e n + 2
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+e,
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E%c+ <Efcf %
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91 Fdofxodu ho oðplwh phgldqwh ghvduuroor gh wd|oru=
t? %2 t? +2
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E%c+ <Efcf
%2 +2
:1 Rewhqhu orv oðplwhv vljxlhqwhv=
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E%c+c5 Efcfcf
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E%c+c5 Efcfcf
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Ghulydgdv Sdufldohv | Glihuhqfldelolgdg
41 Vhd
2
sE%c + ' e%+ Frpsuredu odv ljxdogdghv
|
s%+ ' s+%
s%%+ ' s%+% ' s+%% 51 Vhd
sE%c + ' %+
%2 +2
%2 n +2
sdud E%c + 9' Efc f | s Efc f ' f1
+d, Prvwudu txh s%Efc f ' s+ Efc f ' f1
+e, Fdofxodu s% | s+ hq xq sxqwr E%c + 9' Efc f1
+f, Prvwudu txh s%+ Efc f 9' s+% Efc f1
9
61 Hfxdflöq gh Odsodfh Od hfxdflöq
Y 2s
Y 2s
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Y%2 Y+2
Y5 2
vh frqrfh frpr hfxdflöq gh Odsodfh1 Suredu txh odv vljxlhqwhv ixq0
flrqhv vrq vroxflöq gh glfkd hfxdflöq=
+d, s E%c +c 5 ' E% @2 n E+ K2 2E5 S2
+e, s E%c +c 5 '
t
E% @2 n E+ K2 n E5 S2
t
+f, s E%c +c 5 ' *? E% @2 n E+ K2
71 Ghwhuplqdu ydoruhv gh @/ K | S wdohv txh
sE%c +c 5 ' t? @% t? K+ ULt S5
vhd vroxflöq gh od hfxdflöq gh Odsodfh1
81 Hfxdflöq gh Rqgdv Od hfxdflöq
2
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2Y s
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vh frqrfh frpr hfxdflöq gh rqgdv1 Suredu txh odv vljxlhqwhv ixqflrqhv
vrq vroxflöq gh glfkd hfxdflöq=
+d, s E%c | ' @ t?E% S| n K t?E% n S|
+e, s E%c | ' t? S| t? %
+f, s E%c | ' *?E@% n @S|EK% KS|
91 Fdofxodu od olqhdol}dflöq uE%c + gh s E%c + hq ho sxqwr txh vh lqglfd
+d, s E%c + ' ff 2f%2 f+2 (
+e, s E%c + ' %2 %+ n +2(
+f, s E%c + ' e3
E%2 n+2 +h, s E%c + ' % +(
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| ' E*2c *
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:1 Rewhqhu od olqhdol}dflöq gh s E%c +c 5 hq orv sxqwrv lqglfdgrv=
+d, s E%c +c 5 ' %+ n %5 n +5( ' Ec c 1
s
+e, s E%c +c 5 ' %2 n +2 n 5 2 ( ' Efc c f1
+f, s E%c +c 5 ' e3% t?E+ n 5(
+g, s E%c +c 5 ' @hU|@? %+5(
;1 Vhd
s E%c + '
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vl E%c + 9' Efc f(
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+d, Fdofxodu s% Efc f | s+ Efc f1
+e, Suredu txh s qr hv frqwlqxd ql glihuhqfldeoh hq Efc f1
<1 Vhd
s E%c + ' s
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n +2
%2
vl E%c + 9' Efc f(
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+d, Fdofxodu s% Efc f | s+ Efc f1
+e, Suredu txh s hv frqwlqxd shur qr glihuhqfldeoh hq Efc f1
Vhd
s E%c + ' s
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%+
n +2
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vl E%c + 9' Efc f(
s Efc f ' f
+d, Fdofxodu s% Efc f | s+ Efc f1
+e, Suredu txh s hv frqwlqxd | glihuhqfldeoh hq Efc f1
431 Xqd ixqflöq frq ghulydgdv sdufldohv frqwlqxdv hv glihuhqfldeoh shur
xqd ixqflöq sxhgh vhu glihuhqfldeoh | vxv ghulydgdv sdufldohv qr vhu
frqwlqxdv1 Vhd
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s E%c + ' E%2 n +2 t? s 2
% n +2
vl E%c + 9' Efc f( s Efc f ' f1
+d, Ghprvwudu txh s% Efc f ' s+ Efc f ' f1
+e, Frpsuredu od glihuhqfldelolgdg gh s hq Efc f1
;
+f, Fdofxodu od ghulydgd sdufldo s% hq fxdotxlhu rwur sxqwr E%c + 9' f
| frpsuredu txh glfkd ghulydgd qr hv frqwlqxd hq Efc f1
441 Vh ghvhd frqvwuxlu xq ghsövlwr gh irupd floðqgulfd gh udglr o ' 2 p |
dowxud ' p 1
+d, Hvwlpdu ho lqfuhphqwr gh yroxphq {T phgldqwh _T vl o vh lqfuh0
phqwd hq ffp | hq ffp1 ÁFxdo hv lqfuhphqwr hvwlpdgr gh
yroxphq hq wdqwr sru flhqwrB
+e, Vl o vh plgh frq xq huuru qr pd|ru txh ho 2I | frq xq huuru
qr pd|ru txh ho fDI/ hvwlpdu ho huuru hq wdqwr sru flhqwr txh vh
frphwh hq ho fäofxor gho yroxphq1
+f, Ghwhuplqdu xq fxdgudgr douhghgru gho sxqwr Eo ' 2c ' sdud
txh ho yroxphq yduðh hq phqrv gh f61
451 Wuhv uhvlvwruhv frq - ' ff/ -2 ' 2ff | - ' 2eD rkplrv vh frorfdq
hq xq flufxlwr frqhfwdgrv hq sdudohor1 Od uhvlvwhqfld htxlydohqwh gho
frqmxqwr ylhqh h{suhvdgd sru od iöupxod
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+e, Hvwlpdu xq pdujhq gh huuru hq orv uhvlvwruhv/ frq ho plvpr wdqwr
sru flhqwr hq orv wuhv/ sdud txh - qr fdpelh hq päv gh xq D sru
flhqwr1
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Uhjod gh fdghqd1 Ghulydflöq Lpsoðflwd
41 Vhdq
sE%c + ' E%2 n + 23*2 E n % n %2+ +2 *e
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+d, Rewhqhu od ghulydgd gh 8 E| ' s E%E|c +E| uhvshfwr d | phgldqwh
vxvwlwxflöq | ghulydflöq
+e, Rewhqhu od plvpd ghulydgd phgldqwh od uhjod gh od fdghqd1
51 Uhshwlu ho hmhuflflr dqwhulru frq
s E%c + ' ULtE%2+
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61 Vhdq
s E%c +c 5
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t?E|2e| t?E| ULt |
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+d, Rewhqhu od ghulydgd gh 8 E| ' s E%E|c +E|c 5E| uhvshfwr d | ph0
gldqwh vxvwlwxflöq | ghulydflöq
+e, Rewhqhu od plvpd ghulydgd phgldqwh od uhjod gh od fdghqd1
71 Vhd 5 ' sE%c + frq % ' o ULt w/ + ' o t? w1 Frpsuredu od vljxlhqwh
iöupxod txh dsduhfh hq whruðd gh fdpsrv hohfwurpdjqìwlfrv/
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81 Ghwhuplqdu orv ydoruhv gh 6 sdud orv fxdohv 5 ' s E+ n 6% hv vroxflöq
gh od hfxdflöq hq ghulydgdv sdufldohv
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Y 25
Y25
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91 Xqd ixqflöq s E%c + vh glfh krprjìqhd gh judgr ? vl
s E|%c |+ ' |? s E%c +
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+d, Ghprvwudu txh xqd ixqflöq krprjìqhd gh judgr ? vdwlvidfh od
vljxlhqwh hfxdflöq
%
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n+
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Y%
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+e, Frpsuredu txh od ixqflöq
s E%c + ' %D % +2 n 2%+e .+D
hv xqd ixqflöq krprjìqhd | txh vdwlvidfh od hfxdflöq dqwhulru1
:1 Hqfrqwudu phgldqwh ghulydflöq lpsoðflwd gh od hfxdflöq
s
s
s
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%n +n 5 ' odv ghulydgdv sulphudv | vhjxqgdv gh 5 uhvshfwr gh % h + hq ho sxqwr
Ec c 1
;1 Uhshwlu ho hmhuflflr dqwhulru frq od hfxdflöq
e5 t?E% n + n e+ t?E% n 5 n e% t?E+ n 5 ' f
| ho sxqwr EZc Zc Z1
<1 Lqglfdu orv sxqwrv hq orv txh od hfxdflöq
%e n +e n 5 2 n 2%5 2+5 n D ' f
ghqh lpsoðflwdphqwh xqd ixqflöq 5 ' }E%c + | fdofxodu vxv ghulydgdv
sulphudv1
431 Fdofxodu phgldqwh ghulydflöq lpsoðflwd gh odv hfxdflrqhv
2 n 2 n %2 n +2 n 5 2 ' f
2 n 2 2%+5 ' f
odv ghulydgdv sulphudv | vhjxqgdv gh | uhvshfwr gh %/ + | 51
44