C ap дежи D ivers s¦ip s de f¨()i (es)i де(dri)as La ecuaci щon de
Anuncio
! "#%$'&)(*#+&',./1- 032 $546$)7879$):<;>=?(@$A$'79B8( 2 ,C#ED / 7F$ 0 $):G&)#+HI- BJ(G: / # 0 BJ$'K8, / K); 2 # / K8,ML+$ 0 #%( 0 #%79$)K9,M$ 2 $ONP( 0 &), /RQ
0 $)$`7SD =T(G$OL+$ 0 #E$'-BJK8(@,M&)KJ#+#+:DU$ $ 0 BJ$ ,cb12 $)$ K90G7 / DV7AHG, 0 K #+D[G:M/$'7%DdWX#E&)7O,M:YNXI- -0G782,e& K8,M&)7]#+& 78Z@; 2 78$),MDU[G, $'2GB8/ Kf- #\#g=T&)(G,M:Y$]- :M#\K8$',M&)&)(*#@#+;@&'H@,.(G/1- $)0^7A2 & $OK94_K8$'$'787879H $):*#+HG$h#+K8#U$'&):M#$
2HG#+K9B8$a/?2GKJ# /30 ,C#+: $':%"0a#+HG2 :M#+&),M# / $ / ,e&kj*#+7l& I K / $ # /10 #+7'npo I# $qI 0G$):e2 :C#+7U$)7l:M#rNP( / &),.- /1$t0G2 4_$'7879$):
u1vxw<y>z{;G=T(G2 $%$'79BJ2 ( 2 ,C#+D / 76$ 0 0G$':|/ &f#E0iHI- B82 (G: / # 0 BJ$)/mK9/, / K'2 n 0 } 0 2 $)- 7XBJ$%K9$'0b?,M78#+2 K8$'D / 76[GK8$~b1$'DV$ 0 B80 $`#+/+:M0sL1( 2 0 #+7 / BJK8#+7
NP( 0 &), /10 $)7]79(G75HGK / HG,M$ 2 # 2 $'7)n
. %Uttq FUftAU q ' AqgAU q SF%
/+0 78, 2 $)K9$)D / 73:C#q$)&'(*#+&',./1- 0!2 $4_$)7978$):<;_& /10 7 / :M(@&),./+- 0 &'$ 0 BJK8# 2 #$ 0 y@n!}79& /R #ED / 7U# 2 $)D#+- 7
¡@¢
£x¤ E¥§y¦ £¨¤E¥©£ ª«
w ¦f¬ n ¦ z
} 7XBk#q$)&'(*#+&',./1- 0 j@,MH¨$)K8L+$ / D$'- B8K8,M&)#
B8,M$ 0 $ 2G/ 7h7 / :e(G&), /10 $'7g:M, 0 $f#+:eDV$ 0 BJ$3, 0G2 $)H¨$ 0G2 ,e$ 0 BJ$'7); ( 0 # 2 $l:C#E7
&'(*#+:e$)7%$'7`:M#V>#& /10G/ &), 2 #au>­®w<y1z~ng¯%$~BJ$'K8DU, 0 $'D / 7#+j / K8#l:C#d79$)L1( 0G2 #7 / :e(G&),f/1- 0 nh° K / H /10 $'D / 7( 0 #
7 / :M(@&),./+- 02 $:C#gN / K8DV#
£ w±y>zu>­®w±y>z*²­¡³ ´ w¶µ9zG·>µA«
w ¦f¬ n¹¸+z
"(G$'L /
w ¦f¬ n¾½1z
y¦ £ ¤ w±y>zº y¦ u ­ ¤ w±y>z ² ­i³ ´ wPµ9zG·1µ ¥»y¦ u>­Rw±y>z ´ w<y1z¼
£¨¤ w±y>zº¿u ­ ¤ w<y>z ² ­À³ ´ wPµ9zG·1µ ¥ ¸Tu ­ ¤ w<y1z ´ w<y>z ¥ u>­Rw<y>z ´ ¤ w<y1z«
w ¦f¬ nÂÁ>z
Ã5$)$'DVHG:M#+Äf# 0G2G/ $ 0 w ¦.¬ n ¦ zk;GHG(@$)79B / =T(G$3u>­®w±y>zO$)7A7 / :e(G&),f/1- 02 $$):e:C#@;
´ ¤ w±y>z{u1­Rw<y>z ¥ ´ w±y>zÅY¸Tu ­ ¤ w<y1z ¥»y¦ u>­Rw±y>zÇÆdª¼
¦.È1È
E¸ 1
$'79B / $'7);
ÉFÊËa)ÌÍ ÎÏкÑÓÒRÔ?Õ©Ö%Í.×SØÙÚ|ÑAÚÛÎÜÍÝËAÑ5ÚÞÖØsß%ÏàgÉFÍ~Ñ]à\Ø6ÚrÉFÍÝÐdÝÌÍ àÖÙ5Í~ÉFÊÚ
¤´ w<y>zºá»Å ¸?u>u ­R­ ¤ w±w±y>y>z z ¥ y¦ Æ ´ w±y>z¼
w´ ±y>zãâÛ${ämH Å á ² ­³ å ¸?u>u ­.­ ¤ wPwPµ9µ9z z ¥ ¦µmæ ·1µ Æ ¼
´ w±y>z¡${ä@HaçCáq: 0 u|­ è w<y>zSáé: 0 yEꩼ
$'7 2 $)&),eK);
îfó
î
w ¦f¬ n¹ô+z
´ w<y1zº ymu ­ è¦ w±y>z y¦ ë ¦ ¥ íîkì ïñð¨ò è y+è «
"#37 / :e(G&),f/1- 0 :M, 0 $f#E:MDU$ 0 BJ$%, 0G2 $'Hñ$ 0G2 ,M$ 0 BJ$`#lu>­®w<y1z5$'7A$ 0 B /10 &'$)7
w ¦f¬ n¾ö1z
õ`­Rw<y>zu1­®w<y>z ²­ ³ µku ·1­ è µ wPµ9z ¼
: / =?(@$`K9$)$'78&)K9,M[G,eD / 7]& / D /
î
'
î
ú
î
îü
õh­.w<y>zº¿u>­Rw±y>zh÷ø: 0 y ¥ íîJì ïñð¨ù è y è u>­.w<y>z@: 0 y ¥ íîkì ïñðñû è y¸þý è «
î
Ã5$)$'DVH@:C#+Ä)# 0G2G/ $ 0 :C#`$)&'(*#+&),f/1- 0l2 ,cNP$)K9$ 0 &',C#+:Fw ¦.¬ n ¦ z 2 $~BJ$)K9DV, 0 #+D / 7º: / 7º& / $'ÿ*&',M$ 0 B8$)75â è n°F#+K8#^$):e: / ;
0@/ Bk#+D / 7]=T(G$E¢
î
î
ü
¦y õ ­ ¤ w<y>z y¦ u ­ ¤ w<y1z@: 0 y ¥ y ¦ è u>­®w±y>z ¥ íîkì ïñð û è ¸ ¸ y¸þý è è ¸¦
î
î
ü
õ ­ ¤ w<y>zpu ­ ¤ w±y>z@: 0 y ¥ ¸Tu ­ ¤ w<y1z y¦ á©u>­Rw<y>z y ¦ è ¥ íîJì ïñð û è ¸ þw<¸ 3áÁ ¦ z y¸ ý è è «
/ DVH*#EKJ# 0G2@/ : / 7]& / $'ÿG&),M$ 0 BJ$)7 2 $H / BJ$ 0 &)î ,M#+7],ML1(G#+:M$'7 î 2 $`y@;*78$BJ,e$ 0 $:M#gK8$):M#+&),f/1- 02 $`K8$'&)(GK9K8$ 0 &),C#
û è î á û è è è á wXw á ¦¹z z è ¦ ¼ ¡¸l«
w ¦f¬ n +z
/ DV#+D / 7 û ­]ãm;G 0G/ BJ#+D / 7O=T(G$h7G/ - : / 0@/ 75, 0 BJ$'K8$)78# 0 : / 7I - 0@2 ,M&'$)7]H*#+K9$)7'n6} 0 B /+0 &)$'7
ûè ¦ ¼
û á ¦ á ¦ ¿á ¦
Á ¬ Á å ¦ ¥ ¸¨¦ æ «
î
îû wÝá z
w ¦f¬ n ¬ z
è w ¦¾z è å ¦ ¥§¸¦ ¥»½¦ ¥ !!®¥ ¦ æ «
Ò®Ô?Õ#"mÕ©ßÏÜàgÉFÍ~Ñ]àغÚÞÖØ%$\Êà'&ØÐ
¸E ¦
.
(*) "# $)D 79B8KJ#+&',.- $)7`NE#+- &),e: H / K`, 0@2 (G&)&',./1- 0 n/m(GH /10 ,e$ 0G2G/
&',M$'K9Bk# H*+-#E, KJ#0V ;GH /m22 $)D // 7]&f#+:e&)/1(G0 :M#+K
ð
û 2è 1!3Gè w ¥ ¦ z è wXw á 𠦹z z è 1 å ¦ ¥§¸¦ ¥ «)«f« ¦ æ á 4 w wXá ¥ ¦ z 1!3z576 è
¦ ¦ û 2è 1!3Gè á 4 w wÝá ¥ ¦ z 1!3z86 è å ¦ ¥ ¸¦ ¥ !!f¥ ¦ ¥ ¥ ¦ æ «
¦
¦
=T(G$d:M##EÿGK8DV#+&),f/1- 0 $)7
¥¦ ¦
=xn $+n 2 n
$'79BJ$K9$)79(G:eBJ# 2G/ ;mH /?2 $)D / 76$)78&'K8,e[G,MKO( 0 #g7 / :e(G&),f/1- 0 :e, 0 $)#+:MDU$ 0 BJ$A, 0@2 $)H¨$ 0G2 ,M$ 0 B8$ 2 $gu>­®w:9ñz6$ 0
:M#^N / K8/1DV0 #@¢
üy è
üy üy =
õh­.w<y>zº¿u>­.w<y>z ¥ w ¦ ¾z è ¸ ý á wY¸;¦ ¾z è å ¦ ¥»¸¦ æ ¸ ý ¥ w±½<¦ ¾z è å ¦ ¥§¸¦ ¥»½¦ æ ¸ ý á !! w ¦f¬ n È z
¦
> K*#R- ÿ*&f#+DU$ 0 B8$+¢
N0
x
#+- : / L>#+DU$ 0 BJ$E;E#E7 / &),C# 2 #+7#5:C#+7þNP( 0 &), /10 $)7 2 $AI- 0G2 ,M&'$)779(GHñ$'K8, / K8$'7u 1 w±y>z~;R78$'K*#5- H / 79,M[G:e$S$ 0 & /10 BJK8#+K
0
:M#g78$'L1( 0G2 #U7 / :e(G&),f/1- 0 ;@õ 1 w<y>z{n
@ AÞttA)Uq q B gDC
} $):&)#+H- B8(G: # B8$)K9, K';mb?,MD 7]=T(G$`:C#+7_NP( 0 &), /10 $)7 2 $`4_$'7879$):Ü78$HG(G$ 2 $ 0 K8$)H@K8$)79$ 0 Bk#EK\$ 0 :M#^N / K8DV#
, 0 0 BJ$)L+KJ#+: I / 0 / /
u 1 w<y>z ¸ ¦ E G² F $~ämH 4IH w<y 79$ '0 J á J Kz 6®· J «
L\#+L>#+D / 7O$':&f#+D^[G, /32 $bE#+K8,M#+[G:e$ J N
á M\; F 2 $hD /m2@/ =?(@$
u 1 w±y>z ¸ ¦ E ² F ${ämH 4 á H w±yº79$ 0 Méá M_Kz 6®· M «
?
F
¸E>¸
?$f#
ÉFÊËa)ÌÍ ÎÏкÑÓÒRÔ?Õ©Ö%Í.×SØÙÚ|ÑAÚÛÎÜÍÝËAÑ5ÚÞÖØsß%ÏàgÉFÍ~Ñ]à\Ø6ÚrÉFÍÝÐdÝÌÍ àÖÙ5Í~ÉFÊÚ
1/ 0 79, 2 '$ K8$'D / 75#Ej / KJ# ( 0 #UL1$ 0 $)K8#+:M,eÄf#+&',./1- 02 $`: / # 0 BJ$'K8, / K5#+:þHG:M# 0G/ & / DUHG:e$ 9/ ;m:C#gNP( 0 &',./1- 0
² PSR T ³ UWVYX<Z R T v Z \· [3«
Ow±y>zº Q
w ¦.¬ n ¦ 1z
/
} 0 B /+0 &)$'7
]
?$f#U# 2 $)D#+- 7
] [
w ®z R T v Z «
w ¦.¬ n ¦1¦ z
¤ E¥_^ è ] ª«
w ¦.¬ n ¦ ¸+z
/
£ w±y@¼[®z R T ³ U`VYX;Z ¼
2 $`D ?/ 2G/ ?= (@$
y è;a èy £ è ¥ y a £y ¥ y è £ ¿á a è [ £ è «
a
a
a
Ow<y>zO78#EBJ,e79N±#+&'$`:M#g$)&'(*#+&),f/1- 0Þ2 $`4_$)7978$):6wP[*# 9/ &),M$'K9BJ#+7]K8$'79BJK9,M&'&), /+0 $)7Jz~;
y+-è O ¤ +¥ y O ¤+¥ w<y+è6á ^ è{bz Oª«
(*) +-, . +/ 0 w .¦ ¬ n ¦ ÁTzk;
/+0 w .¦ ¬ n ¦ ¸1zk;
m,ºw ¦.¬ n ¦ ô+z678$`7J#EB8,M7XN±#+&)$E;*$ 0 B /10 &)$)7
h ² P Å y è a èy £ è ¥ y a £y ¥ w<y è á Ü^ è z £xÆ ] «
a
a
/
há ^ è ²QP £ ] á Q² P å a è [ £ è æ ]
a
£
á ^ è|² P £ ] ¥ ² P a [ ] ¤ á Åa £[ ] Ædcc P
c
a
a
á ^ è ²QP £ ] á ²QP £ ] ¤ E¥ Å £ ] ¤ á a c £[ ] Æ cc P
c
a
£
á² P £ w ] ¤ E¥G^ è ] z ¥ Å £ ] ¤ áea [ ] Æ cc P c «
a
h Å £ ] ¤ áea £[ ] Æ cc P «
a
c
c
c
c
w ¦.¬ n ¦ ½1z
w ¦.¬ n ¦ Á>z
w ¦.¬ n ¦ ô+z
Ò®Ô?Õ#"mÕ©ßÏÜàgÉFÍ~Ñ]àغÚÞÖØ%$\Êà'&ØÐ
¸E1½
° / K : / Bk# 0 B / f; O $)7 7 / :M(@&),./+- 0é2 $:C#q$'&)(*#E&),./+- 02 $
4_$)7978$':]78, £ a £hg a [
7 /102 $'78HGK9$)&',C#+[G:e$)73$ 0 $':
& /10 B / K 0G/U2 $, 0 BJ$'L1KJ#+&',./1- 0 â3n
=xn $+n 2 n
ð
ð
/m$)# 0 #+j / K8#Uy^i
9kji@l; [%m [ ¥ H [ è ; ð [ n pè orq n\} 0 $'79B8$`ð &)#+7 / ;
78$ 0 [%À78$ 0 [ & / 79'j [ è ¥ H & / 7 [ 79$ 0 j'[ è «
/+0 78, 2 $)K8# 0G2G/ :C##Eÿ*K8DV#+&',./1- 0 # 0 B8$)K9, / K'; sf$ 0 =T(_$]- H*#+KXBJ$ 2 $':GHG:C# 0G/ w<Ã5$t[1¼vuÇDw[®zÜB8$ 0 $'D / 7yx £ wY9¼[®zxR
x R Tz
x|{ }}7XB / $)7';¨[@(G78&)#+D / 7A( 0 & /10 B / K 0G/ âð Bk#+:þ=T(G$
UWVYX<Z
Ã5$>wÝá H 979$ 0 [Rzw 9& / 7 [ 79$ 0 'j [ è á { yá ~ «
} 7XBk#3& /10G2 ,M&),f/1- 0 $)=T(G,cbE#+:M$#
ð
79$ 0 'j [ è á { yá ~ 78,& / 7 [ ð js
¼
w ¦.¬ n ¦ ö1z
79$ 0 'j [ è á { ~ 78,& / 7 [
«
} 79& /R #+D / 75: / 7]& /10 B / K 0G/ 7 2 $, 0 B8$)L1K8#+&),f/1- 0 ¢
s2
c2
c1
−3π −π
2
−π
2
π
2
π
3π
2
s1
£ g [U7 $'78HGK9$)&',M[G:e$)7$ , ÿ ,cB ;¨a$'79Bk#ED 7$ & ,M&', $'7
/ [GK8$ $'79B 7& B K 7'; £ h
$2 2 $'/ ÿ 0 ,eK 2G/ 7/ 0 (G/1$'bE0 #+/75NP0G( / 0 &', /10 $)7);*a 7 / :Ma(@&), /+/10 0t$)7 2 2 $:C#g$'&)(*#E&),./+- 00 2 0 ,cNP$)0 K9$ 0 / &',C#+: 2 $`4_$)79/ 78$):<¢ 0 /10@2 /10
(*) \ m;h
;|#|y
ð
v
R T#z
R T ·\[U¼ 9kji
v n Kè Yw 9ñz ¦ ²QP
w .¦ ¬ n ¦ +z
E
UWVX;Z
Z
:
/10 78, 2 $)K8$'D / 7A$':&f#+7 / HG#+K9B8,M&)(@:C#+K ^ ;@ð :M# $~ämHGK8$'78,f/1- 0
|:w 9ñz¡
1 :w 9ñz ¥ 1 ¾Kè :w 9ñz
w ¦.¬ n .¦ ¬ z
¯%$Uw ¦.¬ n ¦ 1zk;
² PSR Tz U`VYX;Z R T v Z ;· [3¼
|:w 9ñz ¦ Q
E
& /10
¸E+Á
ÉFÊËa)ÌÍ ÎÏкÑÓÒRÔ?Õ©Ö%Í.×SØÙÚ|ÑAÚÛÎÜÍÝËAÑ5ÚÞÖØsß%ÏàgÉFÍ~Ñ]à\Ø6ÚrÉFÍÝÐdÝÌÍ àÖÙ5Í~ÉFÊÚ
s2
c
−π
0
° (G$'79B / =T(G$
π
s1
Gè R T 1 Z ¼
78$ 0 w ¥ ¸ Üz¡79$ 0 [U¼
:M#+7], 0 B8$)L1K8#+&), /10 $)7]7 / [GK9$h: / 7O78ð$'L1DU$ 0 B / 75b1$'K9B8,M&f#E:M$)7 2 $`â79$`# 0 (G:C# 0 $ 0 B8K8$`7fI- n/m$BJ,M$ 0 $$ 0 B /+0 &)$'7
² F R Tz U`VYX\£ R T 1 £ · J «
wY9ñz ¥ ¾èK w:9ñzº ¦ _
1
1
E
F
/?$`79,ML1(@$ 0 :C#+7]79,ML1(G,e$ 0 BJ$'75K8$):M#+&), /10 $'7]$ 0 BJK9$`:M#+7ONP( 0 &', /10 $)75&),e:øI - 0@2 K8,e&f#+76=?(@$hjG$'D / 7]$~ä@#+DU, 0 # 2@/ ¢
ð
w ¦.¬ n ¦.È z
u 1 ¸¦ ç 1 ð ¥ 1 ¾Kè ê ¼
õ 1 ¸ ¦ H ç 1 ¤á 1 ¾Kè ê ¼
w ¦.¬ n¹¸+1z
#U:M#g, 0 b1$'K87J#m;
ð
u ¥ H õ
¼
w ¦.¬ n¹¸ ¦ z
1
1
1
¾èK u á H õ
«
w ¦.¬ n¹¸1¸+z
1
1
1
R T 1 3
Z F
¢[
E
