{VERSION 6 0 "IBM INTEL NT" "6.0" } {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 Comment" 2 18 "" 0 1 0 0 0 0 0 0 0 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 } {CSTYLE "" -1 256 "" 1 18 0 0 0 0 0 0 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 257 "" 1 24 0 0 0 0 0 0 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 258 "" 1 24 0 0 0 0 0 0 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 259 "" 1 18 0 0 0 0 0 0 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 260 "" 1 18 0 0 0 0 0 0 0 0 0 0 0 0 0 1 } {CSTYLE "" -1 261 "" 1 18 0 0 0 0 0 0 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 262 "" 1 18 0 0 0 0 0 0 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 263 "" 1 18 0 0 0 0 0 0 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 264 "" 1 18 0 0 0 0 0 0 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 265 "" 1 18 0 0 0 0 0 0 0 0 0 0 0 0 0 1 } {CSTYLE "" -1 266 "" 0 18 0 0 0 0 0 0 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 267 "" 0 18 0 0 0 0 0 0 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 268 "" 1 18 0 0 0 0 0 0 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 269 "" 0 18 0 0 0 0 0 0 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 270 "" 0 18 0 0 0 0 0 0 0 0 0 0 0 0 0 1 } {CSTYLE "" -1 271 "" 1 18 0 0 0 0 0 0 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 272 "" 1 18 0 0 0 0 0 0 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 273 "" 1 18 0 0 0 0 0 0 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 274 "" 1 18 0 0 0 0 0 0 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 275 "" 1 14 0 0 0 0 0 0 0 0 0 0 0 0 0 1 } {CSTYLE "" -1 276 "" 1 14 0 0 0 0 0 0 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 277 "" 1 14 0 0 0 0 0 0 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 278 "" 1 14 0 0 0 0 0 0 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 279 "" 1 14 0 0 0 0 0 0 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 280 "" 1 14 0 0 0 0 0 0 0 0 0 0 0 0 0 1 } {CSTYLE "" -1 281 "" 1 14 0 0 0 0 0 0 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 282 "" 1 14 0 0 0 0 0 0 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 283 "" 1 14 0 0 0 0 0 0 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 284 "" 0 18 0 0 0 0 0 0 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 285 "" 0 18 0 0 0 0 0 0 0 0 0 0 0 0 0 1 } {CSTYLE "" -1 286 "" 0 18 0 0 0 0 0 0 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 287 "" 0 18 0 0 0 0 0 0 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 288 "" 0 18 0 0 0 0 0 0 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 289 "" 1 14 0 0 0 0 0 0 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 290 "" 1 14 0 0 0 0 0 0 0 0 0 0 0 0 0 1 } {CSTYLE "" -1 291 "" 1 14 0 0 0 0 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 "Heading 2" -1 4 1 {CSTYLE "" -1 -1 "Times" 1 14 0 0 0 1 2 1 2 2 2 2 1 1 1 1 }1 1 0 0 4 4 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 }{PSTYLE "Maple O utput" -1 12 1 {CSTYLE "" -1 -1 "Times" 1 12 0 0 0 1 2 2 2 2 2 2 1 1 1 1 }1 3 0 0 0 0 1 0 1 0 2 2 0 1 }} {SECT 0 {EXCHG {PARA 4 "" 0 "" {TEXT 257 14 "Ejercicios de " }}{PARA 4 "" 0 "" {TEXT 258 41 "(4) Estimaci\363n del error y cambio de paso" }}{PARA 4 "" 0 "" {TEXT -1 0 "" }}{PARA 4 "" 0 "" {TEXT 256 50 "Ejerci cio 04-06 (del EXAMEN ORDINARIO DE 19ENE12)" }}{PARA 4 "" 0 "" {TEXT -1 79 "\nLa idea es construir un par encajado RK2(3) empleando un m \341ximo de 3 etapas. " }}{PARA 4 "" 0 "" {TEXT -1 61 "Se quiere que e l m\351todo de orden 3 sea el dado por el tablero" }}{PARA 4 "" 0 "" {TEXT 275 14 " 0 | " }}{PARA 4 "" 0 "" {TEXT 276 6 " " } {XPPEDIT 18 0 "2/3;" "6#*&\"\"#\"\"\"\"\"$!\"\"" }{TEXT 277 12 " | \+ " }{XPPEDIT 18 0 "2/3;" "6#*&\"\"#\"\"\"\"\"$!\"\"" }{TEXT 278 1 " " }}{PARA 4 "" 0 "" {TEXT 279 6 " " }{XPPEDIT 18 0 "2/3;" "6# *&\"\"#\"\"\"\"\"$!\"\"" }{TEXT 289 9 " | " }{XPPEDIT 18 0 "-1/3 ;" "6#,$*&\"\"\"F%\"\"$!\"\"F'" }{TEXT 290 11 " 1" }}{PARA 0 "" 0 "" {TEXT -1 13 " ---------" }{TEXT 282 26 "------------------- -------" }}{PARA 4 "" 0 "" {TEXT 280 21 " | " } {XPPEDIT 18 0 "1/4;" "6#*&\"\"\"F$\"\"%!\"\"" }{TEXT 291 9 " \+ " }{XPPEDIT 18 0 "1/2;" "6#*&\"\"\"F$\"\"#!\"\"" }{TEXT 281 8 " \+ " }{XPPEDIT 18 0 "1/4;" "6#*&\"\"\"F$\"\"%!\"\"" }{TEXT 283 3 " " } }{PARA 4 "" 0 "" {TEXT -1 72 "Compru\351bese que, limit\341ndonos a la s 3 etapas del m\351todo anterior, no es " }}{PARA 4 "" 0 "" {TEXT -1 65 "posible conseguir completar el par encajado que buscamos, o sea, \+ " }}{PARA 4 "" 0 "" {TEXT -1 66 "que no es posible encontrar un m\351t odo de orden 2 que sea adecuado." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "restart:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 26 "interface(labeling=false):" }}}{EXCHG {PARA 4 "" 0 "" {TEXT -1 37 "El m\351todo de el orden 3 del enunciado" }{MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "y1:=f(x,y(x));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#y1G-%\"fG6$%\"xG-%\"yG6#F(" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 37 "y2:=subs(diff(y(x),x)=y1,diff(y1,x));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#y2G,&--&%\"DG6#\"\"\"6#%\"fG6$%\"xG-%\"yG 6#F/F+*&--&F)6#\"\"#F,F.F+-F-F.F+F+" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 37 "y3:=subs(diff(y(x),x)=y1,diff(y2,x));" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#>%#y3G,*--&%\"DG6$\"\"\"F+6#%\"fG6$%\"xG-%\"yG6#F/ F+*&--&F)6$F+\"\"#F,F.F+-F-F.F+F+*&,&F4F+*&--&F)6$F8F8F,F.F+F9F+F+F+F9 F+F+*&--&F)6#F8F,F.F+,&--&F)6#F+F,F.F+*&FBF+F9F+F+F+F+" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 28 "Y1:=subs(\{y(x)=y0,x=x0\},y1);" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#>%#Y1G-%\"fG6$%#x0G%#y0G" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 28 "Y2:=subs(\{y(x)=y0,x=x0\},y2);" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#>%#Y2G,&--&%\"DG6#\"\"\"6#%\"fG6$%#x0G %#y0GF+*&--&F)6#\"\"#F,F.F+-F-F.F+F+" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 28 "Y3:=subs(\{y(x)=y0,x=x0\},y3);" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#>%#Y3G,*--&%\"DG6$\"\"\"F+6#%\"fG6$%#x0G%#y0GF+*&--&F)6 $F+\"\"#F,F.F+-F-F.F+F+*&,&F2F+*&--&F)6$F6F6F,F.F+F7F+F+F+F7F+F+*&--&F )6#F6F,F.F+,&--&F)6#F+F,F.F+*&F@F+F7F+F+F+F+" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "k1_:=f(x0,y0);" }}{PARA 11 "" 1 "" {XPPMATH 20 " 6#>%$k1_G-%\"fG6$%#x0G%#y0G" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 34 "k2_:=f(x0+(2/3)*h,y0+(2/3)*h*k1_);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%$k2_G-%\"fG6$,&%#x0G\"\"\"*(\"\"#F*\"\"$!\"\"%\"hGF*F*,&%#y0GF **&#F,F-F**&F/F*-F&6$F)F1F*F*F*" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 41 "k3_:=f(x0+(2/3)*h,y0+(-1/3)*h*k1_+h*k2_);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%$k3_G-%\"fG6$,&%#x0G\"\"\"*(\"\"#F*\"\"$!\"\"%\"hGF*F *,(%#y0GF**&#F*F-F**&F/F*-F&6$F)F1F*F*F.*&F/F*-F&6$F(,&F1F**&#F,F-F*F4 F*F*F*F*" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "k1_0:=subs(h=0, k1_);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%%k1_0G-%\"fG6$%#x0G%#y0G" } }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "k2_0:=subs(h=0,k2_);" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#>%%k2_0G-%\"fG6$%#x0G%#y0G" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "k3_0:=subs(h=0,k3_);" }}{PARA 11 " " 1 "" {XPPMATH 20 "6#>%%k3_0G-%\"fG6$%#x0G%#y0G" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "k11:=diff(k1_,h);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%$k11G\"\"!" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "k21:=diff(k2_,h);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%$k21G,&*&# \"\"#\"\"$\"\"\"--&%\"DG6#F*6#%\"fG6$,&%#x0GF**(F(F*F)!\"\"%\"hGF*F*,& %#y0GF**&F'F**&F7F*-F16$F4F9F*F*F*F*F**&F'F**&--&F.6#F(F0F2F*F " 0 "" {MPLTEXT 1 0 17 "k31:=diff(k3_,h);" }} {PARA 12 "" 1 "" {XPPMATH 20 "6#>%$k31G,&*&#\"\"#\"\"$\"\"\"--&%\"DG6# F*6#%\"fG6$,&%#x0GF**(F(F*F)!\"\"%\"hGF*F*,(%#y0GF**&#F*F)F**&F7F*-F16 $F4F9F*F*F6*&F7F*-F16$F3,&F9F**&F'F*F " 0 "" {MPLTEXT 1 0 20 "k110:=subs(h=0,k11); " }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%%k110G\"\"!" }}}{EXCHG {PARA 0 " > " 0 "" {MPLTEXT 1 0 20 "k210:=subs(h=0,k21);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%%k210G,&*&#\"\"#\"\"$\"\"\"--&%\"DG6#F*6#%\"fG6$%#x0G %#y0GF*F**&F'F**&--&F.6#F(F0F2F*-F1F2F*F*F*" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "k310:=subs(h=0,k31);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%%k310G,&*&#\"\"#\"\"$\"\"\"--&%\"DG6#F*6#%\"fG6$%#x0G%#y0GF*F* *&F'F**&--&F.6#F(F0F2F*-F1F2F*F*F*" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "k12:=diff(k11,h);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6# >%$k12G\"\"!" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "k22:=diff(k 21,h);" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#>%$k22G,(*&#\"\"%\"\"*\"\"\" --&%\"DG6$F*F*6#%\"fG6$,&%#x0GF**(\"\"#F*\"\"$!\"\"%\"hGF*F*,&%#y0GF** &#F6F7F**&F9F*-F16$F4F;F*F*F*F*F**&F'F**&--&F.6$F*F6F0F2F*F?F*F*F**&F= F**&,&*&F=F*FCF*F**&F=F**&--&F.6$F6F6F0F2F*F?F*F*F*F*F?F*F*F*" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "k32:=diff(k31,h);" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#>%$k32G,**&#\"\"%\"\"*\"\"\"--&%\"DG6$F*F*6# %\"fG6$,&%#x0GF**(\"\"#F*\"\"$!\"\"%\"hGF*F*,(%#y0GF**&#F*F7F**&F9F*-F 16$F4F;F*F*F8*&F9F*-F16$F3,&F;F**&#F6F7F*F>F*F*F*F*F*F**&FFF**&--&F.6$ F*F6F0F2F*,(*&#F*F7F*F?F*F8FBF**&F9F*,&*&FFF*--&F.6#F*F0FCF*F**&FFF**& --&F.6#F6F0FCF*F?F*F*F*F*F*F*F*F**&,&*&FFF*FIF*F**&--&F.6$F6F6F0F2F*FM F*F*F*FMF*F**&-FZF2F*,(*&#F(F7F*FSF*F**&FcoF*FXF*F**&F9F*,(*&F'F*-F,FC F*F**&F'F**&-FJFCF*F?F*F*F**&FFF**&,&*&FFF*F[pF*F**&FFF**&-F\\oFCF*F?F *F*F*F*F?F*F*F*F*F*F*F*" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 20 " k120:=subs(h=0,k12);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%%k120G\"\"! " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "k220:=subs(h=0,k22);" } }{PARA 11 "" 1 "" {XPPMATH 20 "6#>%%k220G,(*&#\"\"%\"\"*\"\"\"--&%\"DG 6$F*F*6#%\"fG6$%#x0G%#y0GF*F**&F'F**&--&F.6$F*\"\"#F0F2F*-F1F2F*F*F**& #F;\"\"$F**&,&*&F>F*F7F*F**&F>F**&--&F.6$F;F;F0F2F*F " 0 "" {MPLTEXT 1 0 20 "k320:=subs(h=0,k32);" } }{PARA 12 "" 1 "" {XPPMATH 20 "6#>%%k320G,**&#\"\"%\"\"*\"\"\"--&%\"DG 6$F*F*6#%\"fG6$%#x0G%#y0GF*F**&F'F**&--&F.6$F*\"\"#F0F2F*-F1F2F*F*F**& #F;\"\"$F**&,&*&F>F*F7F*F**&F>F**&--&F.6$F;F;F0F2F*F " 0 "" {MPLTEXT 1 0 47 "Fi_0:=expand((1/4)*k1_0+(1 /2)*k2_0+(1/4)*k3_0);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%%Fi_0G-%\"f G6$%#x0G%#y0G" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 48 "cond1a:=co eff(Y1,f(x0,y0))=coeff(Fi_0,f(x0,y0));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%'cond1aG/\"\"\"F&" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 260 27 "con diciones para el orden 2" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 47 "Fi10:=expand((1/4)*k110+(1/2)*k210+(1/4)*k310);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%%Fi10G,&*&#\"\"\"\"\"#F(--&%\"DG6#F(6#%\"fG6$%#x0G%#y 0GF(F(*&F'F(*&--&F-6#F)F/F1F(-F0F1F(F(F(" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 66 "cond2a:=(1/2)*coeff(Y2,D[1](f)(x0,y0))=coeff(Fi10,D[1 ](f)(x0,y0));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%'cond2aG/#\"\"\"\" \"#F&" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 98 "cond2b:=(1/2)*coef f(coeff(Y2,D[2](f)(x0,y0)),f(x0,y0))=coeff(coeff(Fi10,D[2](f)(x0,y0)), f(x0,y0));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%'cond2bG/#\"\"\"\"\"#F &" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 261 28 "condiciones para el orden 3 " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 47 "Fi20:=expand((1/4)*k12 0+(1/2)*k220+(1/4)*k320);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%%Fi20G, ,*&#\"\"\"\"\"$F(--&%\"DG6$F(F(6#%\"fG6$%#x0G%#y0GF(F(*&#\"\"#F)F(*&-- &F-6$F(F6F/F1F(-F0F1F(F(F(*&F'F(*&--&F-6$F6F6F/F1F()F " 0 "" {MPLTEXT 1 0 76 "cond3a:=(1/6)*coeff(Y3,D[1,1](f)(x0 ,y0))=(1/2)*coeff(Fi20,D[1,1](f)(x0,y0));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%'cond3aG/#\"\"\"\"\"'F&" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 108 "cond3b:=(1/6)*coeff(coeff(Y3,D[1,2](f)(x0,y0)),f(x0, y0))=(1/2)*coeff(coeff(Fi20,D[1,2](f)(x0,y0)),f(x0,y0));" }}{PARA 11 " " 1 "" {XPPMATH 20 "6#>%'cond3bG/#\"\"\"\"\"$F&" }}}{EXCHG {PARA 0 "> \+ " 0 "" {MPLTEXT 1 0 112 "cond3c:=(1/6)*coeff(coeff(Y3,D[2,2](f)(x0,y0) ),f(x0,y0)^2)=(1/2)*coeff(coeff(Fi20,D[2,2](f)(x0,y0)),f(x0,y0)^2);" } }{PARA 11 "" 1 "" {XPPMATH 20 "6#>%'cond3cG/#\"\"\"\"\"'F&" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 116 "cond3d:=(1/6)*coeff(coeff(Y3,D[2]( f)(x0,y0)),D[1](f)(x0,y0))=(1/2)*coeff(coeff(Fi20,D[2](f)(x0,y0)),D[1] (f)(x0,y0));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%'cond3dG/#\"\"\"\"\" 'F&" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 108 "cond3e:=(1/6)*coeff (coeff(Y3,D[2](f)(x0,y0)^2),f(x0,y0))=(1/2)*coeff(coeff(Fi20,D[2](f)(x 0,y0)^2),f(x0,y0));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%'cond3eG/#\" \"\"\"\"'F&" }}}{EXCHG {PARA 4 "" 0 "" {TEXT -1 30 "M\351todo de orden 2 con 2 etapas" }{MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "y1:=f(x,y(x));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%# y1G-%\"fG6$%\"xG-%\"yG6#F(" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 37 "y2:=subs(diff(y(x),x)=y1,diff(y1,x));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#y2G,&--&%\"DG6#\"\"\"6#%\"fG6$%\"xG-%\"yG6#F/F+*&--& F)6#\"\"#F,F.F+-F-F.F+F+" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 37 "y3:=subs(diff(y(x),x)=y1,diff(y2,x));" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#>%#y3G,*--&%\"DG6$\"\"\"F+6#%\"fG6$%\"xG-%\"yG6#F/F+*&--&F)6$F+ \"\"#F,F.F+-F-F.F+F+*&,&F4F+*&--&F)6$F8F8F,F.F+F9F+F+F+F9F+F+*&--&F)6# F8F,F.F+,&--&F)6#F+F,F.F+*&FBF+F9F+F+F+F+" }}}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 28 "Y1:=subs(\{y(x)=y0,x=x0\},y1);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#Y1G-%\"fG6$%#x0G%#y0G" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 28 "Y2:=subs(\{y(x)=y0,x=x0\},y2);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#Y2G,&--&%\"DG6#\"\"\"6#%\"fG6$%#x0G%#y0GF+*&--&F)6# \"\"#F,F.F+-F-F.F+F+" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 28 "Y3: =subs(\{y(x)=y0,x=x0\},y3);" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#>%#Y3G, *--&%\"DG6$\"\"\"F+6#%\"fG6$%#x0G%#y0GF+*&--&F)6$F+\"\"#F,F.F+-F-F.F+F +*&,&F2F+*&--&F)6$F6F6F,F.F+F7F+F+F+F7F+F+*&--&F)6#F6F,F.F+,&--&F)6#F+ F,F.F+*&F@F+F7F+F+F+F+" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "k 1_:=f(x0,y0);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%$k1_G-%\"fG6$%#x0G% #y0G" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 34 "k2_:=f(x0+(2/3)*h,y 0+(2/3)*h*k1_);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%$k2_G-%\"fG6$,&%# x0G\"\"\"*(\"\"#F*\"\"$!\"\"%\"hGF*F*,&%#y0GF**&#F,F-F**&F/F*-F&6$F)F1 F*F*F*" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "k1_0:=subs(h=0,k1 _);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%%k1_0G-%\"fG6$%#x0G%#y0G" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "k2_0:=subs(h=0,k2_);" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#>%%k2_0G-%\"fG6$%#x0G%#y0G" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "k11:=diff(k1_,h);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%$k11G\"\"!" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "k21:=diff(k2_,h);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%$k21G,& *&#\"\"#\"\"$\"\"\"--&%\"DG6#F*6#%\"fG6$,&%#x0GF**(F(F*F)!\"\"%\"hGF*F *,&%#y0GF**&F'F**&F7F*-F16$F4F9F*F*F*F*F**&F'F**&--&F.6#F(F0F2F*F " 0 "" {MPLTEXT 1 0 20 "k110:=subs(h=0,k11); " }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%%k110G\"\"!" }}}{EXCHG {PARA 0 " > " 0 "" {MPLTEXT 1 0 20 "k210:=subs(h=0,k21);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%%k210G,&*&#\"\"#\"\"$\"\"\"--&%\"DG6#F*6#%\"fG6$%#x0G %#y0GF*F**&F'F**&--&F.6#F(F0F2F*-F1F2F*F*F*" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "k12:=diff(k11,h);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%$k12G\"\"!" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "k22:=dif f(k21,h);" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#>%$k22G,(*&#\"\"%\"\"*\" \"\"--&%\"DG6$F*F*6#%\"fG6$,&%#x0GF**(\"\"#F*\"\"$!\"\"%\"hGF*F*,&%#y0 GF**&#F6F7F**&F9F*-F16$F4F;F*F*F*F*F**&F'F**&--&F.6$F*F6F0F2F*F?F*F*F* *&F=F**&,&*&F=F*FCF*F**&F=F**&--&F.6$F6F6F0F2F*F?F*F*F*F*F?F*F*F*" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "k120:=subs(h=0,k12);" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#>%%k120G\"\"!" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "k220:=subs(h=0,k22);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%%k220G,(*&#\"\"%\"\"*\"\"\"--&%\"DG6$F*F*6#%\"fG6$%#x 0G%#y0GF*F**&F'F**&--&F.6$F*\"\"#F0F2F*-F1F2F*F*F**&#F;\"\"$F**&,&*&F> F*F7F*F**&F>F**&--&F.6$F;F;F0F2F*F " 0 "" {MPLTEXT 1 0 34 "Fi_0:=expand(b[1]*k1_0+b[2]*k2_0);" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#>%%Fi_0G,&*&&%\"bG6#\"\"\"F*-%\"fG6$%# x0G%#y0GF*F**&&F(6#\"\"#F*F+F*F*" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 48 "cond1a:=coeff(Y1,f(x0,y0))=coeff(Fi_0,f(x0,y0));" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#>%'cond1aG/\"\"\",&&%\"bG6#F&F&&F)6#\" \"#F&" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 263 27 "condiciones para el ord en 2" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 34 "Fi10:=expand(b[1]*k 110+b[2]*k210);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%%Fi10G,&*&#\"\"# \"\"$\"\"\"*&&%\"bG6#F(F*--&%\"DG6#F*6#%\"fG6$%#x0G%#y0GF*F*F**&F'F**( F,F*--&F2F.F4F6F*-F5F6F*F*F*" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 66 "cond2a:=(1/2)*coeff(Y2,D[1](f)(x0,y0))=coeff(Fi10,D[1](f)(x0,y0) );" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%'cond2aG/#\"\"\"\"\"#,$*&#F(\" \"$F'&%\"bG6#F(F'F'" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 98 "cond 2b:=(1/2)*coeff(coeff(Y2,D[2](f)(x0,y0)),f(x0,y0))=coeff(coeff(Fi10,D[ 2](f)(x0,y0)),f(x0,y0));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%'cond2bG /#\"\"\"\"\"#,$*&#F(\"\"$F'&%\"bG6#F(F'F'" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 265 27 "soluciones para el orden 2 " }}}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 54 "soluciones2:=allvalues(solve(\{cond1a,cond2a,cond2b \}));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%,soluciones2G<$/&%\"bG6#\" \"\"#F*\"\"%/&F(6#\"\"##\"\"$F," }}}{EXCHG {PARA 0 "" 0 "" {TEXT 264 59 "como quedan las condiciones para el orden 3 con ese m\351todo " }} }{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 34 "Fi20:=expand(b[1]*k120+b[2] *k220);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%%Fi20G,(*&#\"\"%\"\"*\"\" \"*&&%\"bG6#\"\"#F*--&%\"DG6$F*F*6#%\"fG6$%#x0G%#y0GF*F*F**&#\"\")F)F* *(F,F*--&F36$F*F/F5F7F*-F6F7F*F*F**&F'F**(F,F*--&F36$F/F/F5F7F*)FBF/F* F*F*" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 101 "cond3a:=(1/6)*coef f(Y3,D[1,1](f)(x0,y0))=(1/2)*coeff(Fi20,D[1,1](f)(x0,y0));subs(solucio nes2,cond3a);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%'cond3aG/#\"\"\"\" \"',$*&#\"\"#\"\"*F'&%\"bG6#F,F'F'" }}{PARA 11 "" 1 "" {XPPMATH 20 "6# /#\"\"\"\"\"'F$" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 133 "cond3b: =(1/6)*coeff(coeff(Y3,D[1,2](f)(x0,y0)),f(x0,y0))=(1/2)*coeff(coeff(Fi 20,D[1,2](f)(x0,y0)),f(x0,y0));subs(soluciones2,cond3b);" }}{PARA 11 " " 1 "" {XPPMATH 20 "6#>%'cond3bG/#\"\"\"\"\"$,$*&#\"\"%\"\"*F'&%\"bG6# \"\"#F'F'" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/#\"\"\"\"\"$F$" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 137 "cond3c:=(1/6)*coeff(coeff(Y 3,D[2,2](f)(x0,y0)),f(x0,y0)^2)=(1/2)*coeff(coeff(Fi20,D[2,2](f)(x0,y0 )),f(x0,y0)^2);subs(soluciones2,cond3c);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%'cond3cG/#\"\"\"\"\"',$*&#\"\"#\"\"*F'&%\"bG6#F,F'F'" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/#\"\"\"\"\"'F$" }}}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 141 "cond3d:=(1/6)*coeff(coeff(Y3,D[2](f)(x0,y0)),D[1]( f)(x0,y0))=(1/2)*coeff(coeff(Fi20,D[2](f)(x0,y0)),D[1](f)(x0,y0));subs (soluciones2,cond3d);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%'cond3dG/# \"\"\"\"\"'\"\"!" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/#\"\"\"\"\"'\"\"! " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 133 "cond3e:=(1/6)*coeff(co eff(Y3,D[2](f)(x0,y0)^2),f(x0,y0))=(1/2)*coeff(coeff(Fi20,D[2](f)(x0,y 0)^2),f(x0,y0));subs(soluciones2,cond3e);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%'cond3eG/#\"\"\"\"\"'\"\"!" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/#\"\"\"\"\"'\"\"!" }}}{EXCHG {PARA 4 "" 0 "" {TEXT 266 52 "evidentemente el m\351todo de orden 2 que hemos buscado" } {TEXT 268 1 " " }}{PARA 4 "" 0 "" {TEXT 267 55 "no es adecuado para fo rmar un par encajado (anula 3 de " }}{PARA 4 "" 0 "" {TEXT 269 52 "los 5 coeficientes del t\351rmino principal del error)." }}{PARA 4 "" 0 " " {TEXT 270 53 "Buscamos un m\351todo m\341s adecuado entre los de 3 e tapas" }}}{EXCHG {PARA 4 "" 0 "" {TEXT -1 56 "M\351todo de el orden 2 \+ con las tres etapas del otro m\351todo" }{MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "y1:=f(x,y(x));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#y1G-%\"fG6$%\"xG-%\"yG6#F(" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 37 "y2:=subs(diff(y(x),x)=y1,diff(y1,x));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#y2G,&--&%\"DG6#\"\"\"6#%\"fG6$%\"xG-%\"yG 6#F/F+*&--&F)6#\"\"#F,F.F+-F-F.F+F+" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 37 "y3:=subs(diff(y(x),x)=y1,diff(y2,x));" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#>%#y3G,*--&%\"DG6$\"\"\"F+6#%\"fG6$%\"xG-%\"yG6#F/ F+*&--&F)6$F+\"\"#F,F.F+-F-F.F+F+*&,&F4F+*&--&F)6$F8F8F,F.F+F9F+F+F+F9 F+F+*&--&F)6#F8F,F.F+,&--&F)6#F+F,F.F+*&FBF+F9F+F+F+F+" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 28 "Y1:=subs(\{y(x)=y0,x=x0\},y1);" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#>%#Y1G-%\"fG6$%#x0G%#y0G" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 28 "Y2:=subs(\{y(x)=y0,x=x0\},y2);" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#>%#Y2G,&--&%\"DG6#\"\"\"6#%\"fG6$%#x0G %#y0GF+*&--&F)6#\"\"#F,F.F+-F-F.F+F+" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 28 "Y3:=subs(\{y(x)=y0,x=x0\},y3);" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#>%#Y3G,*--&%\"DG6$\"\"\"F+6#%\"fG6$%#x0G%#y0GF+*&--&F)6 $F+\"\"#F,F.F+-F-F.F+F+*&,&F2F+*&--&F)6$F6F6F,F.F+F7F+F+F+F7F+F+*&--&F )6#F6F,F.F+,&--&F)6#F+F,F.F+*&F@F+F7F+F+F+F+" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "k1_:=f(x0,y0);" }}{PARA 11 "" 1 "" {XPPMATH 20 " 6#>%$k1_G-%\"fG6$%#x0G%#y0G" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 34 "k2_:=f(x0+(2/3)*h,y0+(2/3)*h*k1_);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%$k2_G-%\"fG6$,&%#x0G\"\"\"*(\"\"#F*\"\"$!\"\"%\"hGF*F*,&%#y0GF **&#F,F-F**&F/F*-F&6$F)F1F*F*F*" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 40 "k3_:=f(x0+(2/3)*h,y0-(1/3)*h*k1_+h*k2_);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%$k3_G-%\"fG6$,&%#x0G\"\"\"*(\"\"#F*\"\"$!\"\"%\"hGF*F *,(%#y0GF**&#F*F-F**&F/F*-F&6$F)F1F*F*F.*&F/F*-F&6$F(,&F1F**&#F,F-F*F4 F*F*F*F*" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "k1_0:=subs(h=0, k1_);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%%k1_0G-%\"fG6$%#x0G%#y0G" } }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "k2_0:=subs(h=0,k2_);" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#>%%k2_0G-%\"fG6$%#x0G%#y0G" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "k3_0:=subs(h=0,k3_);" }}{PARA 11 " " 1 "" {XPPMATH 20 "6#>%%k3_0G-%\"fG6$%#x0G%#y0G" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "k11:=diff(k1_,h);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%$k11G\"\"!" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "k21:=diff(k2_,h);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%$k21G,&*&# \"\"#\"\"$\"\"\"--&%\"DG6#F*6#%\"fG6$,&%#x0GF**(F(F*F)!\"\"%\"hGF*F*,& %#y0GF**&F'F**&F7F*-F16$F4F9F*F*F*F*F**&F'F**&--&F.6#F(F0F2F*F " 0 "" {MPLTEXT 1 0 17 "k31:=diff(k3_,h);" }} {PARA 12 "" 1 "" {XPPMATH 20 "6#>%$k31G,&*&#\"\"#\"\"$\"\"\"--&%\"DG6# F*6#%\"fG6$,&%#x0GF**(F(F*F)!\"\"%\"hGF*F*,(%#y0GF**&#F*F)F**&F7F*-F16 $F4F9F*F*F6*&F7F*-F16$F3,&F9F**&F'F*F " 0 "" {MPLTEXT 1 0 20 "k110:=subs(h=0,k11); " }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%%k110G\"\"!" }}}{EXCHG {PARA 0 " > " 0 "" {MPLTEXT 1 0 20 "k210:=subs(h=0,k21);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%%k210G,&*&#\"\"#\"\"$\"\"\"--&%\"DG6#F*6#%\"fG6$%#x0G %#y0GF*F**&F'F**&--&F.6#F(F0F2F*-F1F2F*F*F*" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "k310:=subs(h=0,k31);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%%k310G,&*&#\"\"#\"\"$\"\"\"--&%\"DG6#F*6#%\"fG6$%#x0G%#y0GF*F* *&F'F**&--&F.6#F(F0F2F*-F1F2F*F*F*" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "k12:=diff(k11,h);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6# >%$k12G\"\"!" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "k22:=diff(k 21,h);" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#>%$k22G,(*&#\"\"%\"\"*\"\"\" --&%\"DG6$F*F*6#%\"fG6$,&%#x0GF**(\"\"#F*\"\"$!\"\"%\"hGF*F*,&%#y0GF** &#F6F7F**&F9F*-F16$F4F;F*F*F*F*F**&F'F**&--&F.6$F*F6F0F2F*F?F*F*F**&F= F**&,&*&F=F*FCF*F**&F=F**&--&F.6$F6F6F0F2F*F?F*F*F*F*F?F*F*F*" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "k32:=diff(k31,h);" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#>%$k32G,**&#\"\"%\"\"*\"\"\"--&%\"DG6$F*F*6# %\"fG6$,&%#x0GF**(\"\"#F*\"\"$!\"\"%\"hGF*F*,(%#y0GF**&#F*F7F**&F9F*-F 16$F4F;F*F*F8*&F9F*-F16$F3,&F;F**&#F6F7F*F>F*F*F*F*F*F**&FFF**&--&F.6$ F*F6F0F2F*,(*&#F*F7F*F?F*F8FBF**&F9F*,&*&FFF*--&F.6#F*F0FCF*F**&FFF**& --&F.6#F6F0FCF*F?F*F*F*F*F*F*F*F**&,&*&FFF*FIF*F**&--&F.6$F6F6F0F2F*FM F*F*F*FMF*F**&-FZF2F*,(*&#F(F7F*FSF*F**&FcoF*FXF*F**&F9F*,(*&F'F*-F,FC F*F**&F'F**&-FJFCF*F?F*F*F**&FFF**&,&*&FFF*F[pF*F**&FFF**&-F\\oFCF*F?F *F*F*F*F?F*F*F*F*F*F*F*" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 20 " k120:=subs(h=0,k12);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%%k120G\"\"! " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "k220:=subs(h=0,k22);" } }{PARA 11 "" 1 "" {XPPMATH 20 "6#>%%k220G,(*&#\"\"%\"\"*\"\"\"--&%\"DG 6$F*F*6#%\"fG6$%#x0G%#y0GF*F**&F'F**&--&F.6$F*\"\"#F0F2F*-F1F2F*F*F**& #F;\"\"$F**&,&*&F>F*F7F*F**&F>F**&--&F.6$F;F;F0F2F*F " 0 "" {MPLTEXT 1 0 20 "k320:=subs(h=0,k32);" } }{PARA 12 "" 1 "" {XPPMATH 20 "6#>%%k320G,**&#\"\"%\"\"*\"\"\"--&%\"DG 6$F*F*6#%\"fG6$%#x0G%#y0GF*F**&F'F**&--&F.6$F*\"\"#F0F2F*-F1F2F*F*F**& #F;\"\"$F**&,&*&F>F*F7F*F**&F>F**&--&F.6$F;F;F0F2F*F " 0 "" {MPLTEXT 1 0 44 "Fi_0:=expand(b[1]*k1_0+b[2 ]*k2_0+b[3]*k3_0);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%%Fi_0G,(*&&%\" bG6#\"\"\"F*-%\"fG6$%#x0G%#y0GF*F**&&F(6#\"\"#F*F+F*F**&&F(6#\"\"$F*F+ F*F*" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 48 "cond1a:=coeff(Y1,f( x0,y0))=coeff(Fi_0,f(x0,y0));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%'co nd1aG/\"\"\",(&%\"bG6#F&F&&F)6#\"\"#F&&F)6#\"\"$F&" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 272 27 "condiciones para el orden 2" }}}{EXCHG {PARA 0 " > " 0 "" {MPLTEXT 1 0 44 "Fi10:=expand(b[1]*k110+b[2]*k210+b[3]*k310); " }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%%Fi10G,**&#\"\"#\"\"$\"\"\"*&&% \"bG6#F(F*--&%\"DG6#F*6#%\"fG6$%#x0G%#y0GF*F*F**&F'F**(F,F*--&F2F.F4F6 F*-F5F6F*F*F**&F'F**&&F-6#F)F*F/F*F*F**&F'F**(FAF*F;F*F>F*F*F*" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 66 "cond2a:=(1/2)*coeff(Y2,D[1]( f)(x0,y0))=coeff(Fi10,D[1](f)(x0,y0));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%'cond2aG/#\"\"\"\"\"#,&*&#F(\"\"$F'&%\"bG6#F(F'F'*&F+F'&F.6#F, F'F'" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 98 "cond2b:=(1/2)*coeff (coeff(Y2,D[2](f)(x0,y0)),f(x0,y0))=coeff(coeff(Fi10,D[2](f)(x0,y0)),f (x0,y0));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%'cond2bG/#\"\"\"\"\"#,& *&#F(\"\"$F'&%\"bG6#F(F'F'*&F+F'&F.6#F,F'F'" }}}{EXCHG {PARA 0 "" 0 " " {TEXT 274 27 "soluciones para el orden 2 " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 54 "soluciones2:=allvalues(solve(\{cond1a,cond2a,cond2 b\}));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%,soluciones2G<%/&%\"bG6#\" \"\"#F*\"\"%/&F(6#\"\"#,&#\"\"$F,F*&F(6#F3!\"\"/F4F4" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 273 59 "como quedan las condiciones para el orden 3 co n ese m\351todo " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 44 "Fi20:=e xpand(b[1]*k120+b[2]*k220+b[3]*k320);" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#>%%Fi20G,2*&#\"\"%\"\"*\"\"\"*&&%\"bG6#\"\"#F*--&%\"DG6$F*F*6#%\"fG 6$%#x0G%#y0GF*F*F**&#\"\")F)F**(F,F*--&F36$F*F/F5F7F*-F6F7F*F*F**&F'F* *(F,F*--&F36$F/F/F5F7F*)FBF/F*F*F**&F'F**&&F-6#\"\"$F*F0F*F*F**&F;F**( FLF*F>F*FBF*F*F**&F'F**(FLF*FEF*FIF*F*F**&#F(FNF**(FLF*--&F3F.F5F7F*-- &F36#F*F5F7F*F*F**&FTF**(FLF*)FVF/F*FBF*F*F*" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 101 "cond3a:=(1/6)*coeff(Y3,D[1,1](f)(x0,y0))=(1/2)* coeff(Fi20,D[1,1](f)(x0,y0));subs(soluciones2,cond3a);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%'cond3aG/#\"\"\"\"\"',&*&#\"\"#\"\"*F'&%\"bG6#F, F'F'*&F+F'&F/6#\"\"$F'F'" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/#\"\"\"\" \"'F$" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 133 "cond3b:=(1/6)*coe ff(coeff(Y3,D[1,2](f)(x0,y0)),f(x0,y0))=(1/2)*coeff(coeff(Fi20,D[1,2]( f)(x0,y0)),f(x0,y0));subs(soluciones2,cond3b);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%'cond3bG/#\"\"\"\"\"$,&*&#\"\"%\"\"*F'&%\"bG6#\"\"#F' F'*&F+F'&F/6#F(F'F'" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/#\"\"\"\"\"$F$ " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 137 "cond3c:=(1/6)*coeff(co eff(Y3,D[2,2](f)(x0,y0)),f(x0,y0)^2)=(1/2)*coeff(coeff(Fi20,D[2,2](f)( x0,y0)),f(x0,y0)^2);subs(soluciones2,cond3c);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%'cond3cG/#\"\"\"\"\"',&*&#\"\"#\"\"*F'&%\"bG6#F,F'F'* &F+F'&F/6#\"\"$F'F'" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/#\"\"\"\"\"'F$ " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 141 "cond3d:=(1/6)*coeff(co eff(Y3,D[2](f)(x0,y0)),D[1](f)(x0,y0))=(1/2)*coeff(coeff(Fi20,D[2](f)( x0,y0)),D[1](f)(x0,y0));subs(soluciones2,cond3d);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%'cond3dG/#\"\"\"\"\"',$*&#\"\"#\"\"$F'&%\"bG6#F-F'F' " }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/#\"\"\"\"\"',$*&#\"\"#\"\"$F%&%\" bG6#F+F%F%" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 133 "cond3e:=(1/6 )*coeff(coeff(Y3,D[2](f)(x0,y0)^2),f(x0,y0))=(1/2)*coeff(coeff(Fi20,D[ 2](f)(x0,y0)^2),f(x0,y0));subs(soluciones2,cond3e);" }}{PARA 11 "" 1 " " {XPPMATH 20 "6#>%'cond3eG/#\"\"\"\"\"',$*&#\"\"#\"\"$F'&%\"bG6#F-F'F '" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/#\"\"\"\"\"',$*&#\"\"#\"\"$F%&% \"bG6#F+F%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 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}} {EXCHG {PARA 4 "" 0 "" {TEXT 284 65 "Ocurre lo mismo que antes: no es \+ posible encontrar ning\372n m\351todo " }}{PARA 4 "" 0 "" {TEXT 285 66 "de orden 2 que no anule al menos 3 de los coeficientes del t\351rm ino" }}{PARA 4 "" 0 "" {TEXT 286 73 "principal del error. Por lo tanto , limit\341ndose a las 3 etapas del m\351todo " }}{PARA 4 "" 0 "" {TEXT 287 66 "del enunciado, no es posible completar el par con ning \372n m\351todo de" }}{PARA 4 "" 0 "" {TEXT 288 7 "orden 2" }{TEXT -1 0 "" }}}}{MARK "0 3 0" 15 }{VIEWOPTS 1 1 0 3 4 1802 1 1 1 1 } {PAGENUMBERS 0 1 2 33 1 1 }