F. Multivariables

Ixqflrqhv gh Yduldv Yduldeohv
Mxqh Dploor
63237233

Frqwhqlgr
4 Ixqflrqhv Uhdohv gh Yduldv Yduldeohv
414 Ghqlflrqhv 1 1 1 1 1 1 1 1 1 1 1 1 1 1
415 Uhsuhvhqwdflöq Juäfd 1 1 1 1 1 1 1 1
41514 Ixqflrqhv gh grv yduldeohv 1 1
41515 Ixqflrqhv gh wuhv yduldeohv 1 1
5 Oðplwhv | Frqwlqxlgdg
514 Oðplwhv 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
515 Oðplwhv Gluhfflrqdohv 1 1 1 1 1 1 1 1
516Frqwlqxlgdg 1 1 1 1 1 1 1 1 1 1 1 1 1
517 Ixqflrqhv gh Wuhv r Päv Yduldeohv

1
1
1
1

1
1
1
1
1
1
1
1

1
1
1
1
1
1
1
1

1
1
1
1
1
1
1
1

1
1
1
1
1
1
1
1

1
1
1
1
1
1
1
1

1
1
1
1
1
1
1
1

1
1
1
1
1
1
1
1

1
1
1
1
1
1
1
1

1
1
1
1
1
1
1
1

1
1
1
1
1
1
1
1

1
1
1
1
1
1
1
1

1
1
1
1
1
1
1
1

11
1
1
1
1
1
1

1
1
1
1

5
5
6
6
7

1
1
1
1

7
7
8
9
:

6 Ghulydgdv Sdufldohv
;
614 Ixqflrqhv gh Grv Yduldeohv 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 ;
615 Ghulydgdv Sdufldohv gh Rughq Vxshulru 1 1 1 1 1 1 1 1 1 1 1 1 1 43
616 Ixqflrqhv gh Wuhv r Päv Yduldeohv 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 44
7 Glihuhqfldelolgdg
44
714 Ixqflrqhv gh Grv Yduldeohv 1 1 1 1 1 1 1 11 1 1 1 1 1 1 1 1 1 1 1 45
715 Ixqflrqhv gh Wuhv r Päv Yduldeohv 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 47
8 Uhjod gh od Fdghqd
814 Uhjod gh od Fdghqd sdud grv Yduldeohv 1 1 1 1 1 1 1 1 1 1 1 1 1
815 Irupd Jhqhudo gh od Uhjod gh od Fdghqd 1 1 1 1 1 1 1 1 1 1 1 1
816 Ghulydflöq Lpsoðflwd 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1

49
49
4:
4;

9 Ghulydgdv Gluhfflrqdohv1 Judglhqwh
914Ghulydgdv Gluhfflrqdohv 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
915 Yhfwru Judglhqwh 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
916 Ixqflrqhv gh Wuhv Yduldeohv 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1

54
54
55
57

: Pä{lprv | Pðqlprv
59
:14 Sxqwrv Fuðwlfrv | H{wuhprv 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 59
:15 Hvwxglr gh Pä{lprv | Pðqlprv 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 5;

4; Pxowlsolfdgruhv gh Odjudqjh
;14 Sureohpdv frq xqd Frqglflöq gh Oljdgxud 1 1
;1414 Pìwrgr gh Odjudqjh 1 1 1 1 1 1 1 1 1 1
;1415 Ixqgdphqwr gho Pìwrgr gh Odjudqjh 1
;15 Sureohpdv frq Grv r Päv Frqg1 gh Oljdgxud
;1514 Pìwrgr gh Odjudqjh 1 1 1 1 1 1 1 1 1 1
;1515 Ixqgdphqwr gho Pìwrgr gh Odjudqjh 1

4
414

1
1
1
1
1
1

1
1
1
1
1
1

1
1
1
1
1
1

1
1
1
1
1
11
1
1
1
1
1

1
1
1
1
1
1

1
1
1
1
1
1

1
1
1
1
1
1

1
1
1
1
1
1

5<
5<
5<
63
64
64
65

Ixqflrqhv Uhdohv gh Yduldv Yduldeohv
Ghqlflrqhv

H{lvwhq pdjqlwxghv txh ghshqghq gh grv r päv pdjqlwxghv lqghshqglhqwhv1
Sru hmhpsor/ ho äuhd gh xq uhfwäqjxor ghshqgh gh od orqjlwxg gh fdgd xqr
gh vxv odgrv/ ho yroxphq gh xq sdudohohsðshgr uhfwdqjxodu ghshqgh ghod
orqjlwxg gh fdgd xqd gh vxv dulvwdv/ hwf1 Hv sru hoor qhfhvdulr frqvlghudu
xq qxhyr wlsr gh ixqflrqhv fx|dv hqwudgdv hvwìq frqvwlwxlgdv sru grv r päv
ydoruhv1
Ghqlflöq 4 Vh oodpd ixqflöq uhdo gh ?0yduldeohv d wrgd dsolfdflöq
frq ydoruhv uhdohv fx|r grplqlr vhd xq frqmxqwr ( gho hvsdflr hxfoðghr ?0
glphqvlrqdo U? 1 Hv ghflu vh wudwd gh xq surfhvr s txh dvljqd d fdgd ?0wxsod
r yhfwru gh ?frpsrqhqwhv uhdohv/ ' E%Q/    /%? / xq qýphur uhdo +/ hv0
fulelìqgrvh
+ ' s E%Q/    /%? 
r hq qrwdflöq yhfwruldo
+ ' s E 
Odv frpsrqhqwhv %Qc    c %? gho yhfwru vh frqrfhq frpr yduldeohv lqgh0
shqglhqwhv | ho qýphur uhdo + frpr yduldeoh ghshqglhqwh1
Hq ho fdvr gh ixqflrqhv gh grv yduldeohv/ hv ghflu sdud ? ' 2c vh dfrvwxp0
eud hvfulelu
5 ' s E%c +

5

hq yh} gh + ' sE% c %2 Sdud ixqflrqhv gh wuhv yduldeohv/ ? ' c vh hvfuleh
 ' s E%c +c 5 
hq yh} gh + ' s E% c %2c % 1
Or plvpr txh hq odv ixqflrqhv gh xqd yduldeoh odv ixqflrqhv gh yduldv
yduldeohv sxhghq ghqluvh phgldqwh xqd h{suhvlöq vlpeöolfd txh odv frqwhqjd
r phgldqwh xq dojrulwpr1 Sru hmhpsor/ od h{suhvlöq
s E%c + ' %2 n +2
ghqh xqd ixqflöq gh grv yduldeohv od fxdo uhsuhvhqwd ho fxdgudgr...