{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 1 236 0 76 0 0 0 2 0 0 0 0 0 0 1 }{CSTYLE "2D Comment" 2 18 "" 0 1 48 37 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 "" 0 21 "" 0 1 0 0 0 1 0 0 0 0 2 0 0 0 0 1 }{CSTYLE "" -1 256 "" 1 14 0 0 0 0 0 0 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 257 "" 1 14 0 0 0 0 0 0 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 258 "" 1 14 0 0 0 0 0 0 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 259 "" 1 14 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 24 0 0 0 0 0 0 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 262 "" 1 24 0 0 0 0 0 0 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 263 "" 1 14 0 0 0 0 0 0 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 264 "" 1 14 0 0 0 0 0 0 0 0 0 0 0 0 0 1 } {CSTYLE "" -1 265 "" 1 14 0 0 0 0 0 0 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 266 "" 1 14 0 0 0 0 0 0 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 267 "" 1 14 0 0 0 0 0 0 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 268 "" 1 14 0 0 0 0 0 0 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 269 "" 1 14 0 0 0 0 0 0 0 0 0 0 0 0 0 1 } {CSTYLE "" -1 270 "" 1 14 0 0 0 0 0 0 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 271 "" 1 14 0 0 0 0 0 0 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 272 "" 1 14 0 0 0 0 0 0 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 273 "" 1 14 0 0 0 0 0 0 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 274 "" 1 14 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 }{PSTYLE "Normal" -1 0 1 {CSTYLE "" -1 -1 "T imes" 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 Output" -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 }{PSTYLE "Maple Plot" -1 13 1 {CSTYLE "" -1 -1 "Times" 1 12 0 0 0 1 2 2 2 2 2 2 1 1 1 1 }3 1 0 0 0 0 1 0 1 0 2 2 0 1 }{PSTYLE "Normal " -1 256 1 {CSTYLE "" -1 -1 "Times" 1 12 0 0 0 1 2 1 2 2 2 2 1 1 1 1 } 1 1 0 0 0 0 1 0 1 0 2 2 0 1 }} {SECT 0 {EXCHG {PARA 4 "" 0 "" {TEXT 261 14 "Ejercicios de " }}{PARA 4 "" 0 "" {TEXT 262 55 "(7) M\351todos de RUNGE-KUTTA impl\355citos y \+ semi-impl\355citos" }}{PARA 4 "" 0 "" {TEXT -1 0 "" }}{PARA 4 "" 0 "" {TEXT 260 56 "Ejercicio 07-08 (del EXAMEN EXTRAORDINARIO DE 15JUL09) " }}{PARA 4 "" 0 "" {TEXT -1 75 "Consid\351rese la familia de m\351tod os impl\355citos de RUNGE-KUTTA con dos etapas " }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 4 "" 0 "" {TEXT 263 15 " 0 | " } {XPPEDIT 18 0 "alpha;" "6#%&alphaG" }{TEXT 264 12 " - " } {XPPEDIT 18 0 "alpha;" "6#%&alphaG" }{TEXT 274 2 " " }}{PARA 4 "" 0 " " {TEXT 265 15 " 2 | " }{XPPEDIT 18 0 "alpha;" "6#%&alphaG" }{TEXT 275 14 " 2 - " }{XPPEDIT 18 0 "alpha;" "6#%&alphaG" }} {PARA 4 "" 0 "" {TEXT -1 12 " ---------" }{TEXT 256 24 "------------ ------------" }}{PARA 4 "" 0 "" {TEXT 257 16 " | " } {XPPEDIT 18 0 "1/4;" "6#*&\"\"\"F$\"\"%!\"\"" }{TEXT 258 12 " \+ " }{XPPEDIT 18 0 "3/4;" "6#*&\"\"$\"\"\"\"\"%!\"\"" }{TEXT 259 1 " \+ " }}{PARA 4 "" 0 "" {TEXT -1 81 "a) B\372squese el mayor orden alcanza ble por los miembros de esta familia, indicando" }}{PARA 4 "" 0 "" {TEXT -1 16 "los valores de " }{XPPEDIT 18 0 "alpha;" "6#%&alphaG" } {TEXT -1 26 " para los que se consigue" }}{PARA 4 "" 0 "" {TEXT -1 40 "(desde aqu\355 es Ejercicio del cap\355tulo 8)" }}{PARA 4 "" 0 "" {TEXT -1 69 "b) Calc\372lese la funci\363n de estabilidad del m\351tod o en el caso general." }}{PARA 4 "" 0 "" {TEXT -1 25 "c) B\372squese \+ un valor de " }{XPPEDIT 18 0 "alpha" "6#%&alphaG" }{TEXT -1 95 " para \+ el que el correspondiente m\351todo sea\nA-estable, probando, adem\341 s, dicha A-estabilidad. " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "restart:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 26 "interface(la beling=false):" }}}{EXCHG {PARA 0 "" 0 "" {MPLTEXT 0 21 37 "# desarrol lo de la verdadera solucion" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "#y:=unapply(y(x),x):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 24 "#f:=unapply(f(x,y),x,y):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "f0:=f(x,y(x)):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 44 "f1:=s ubs(diff(y(x),x)=f(x,y(x)),diff(f0,x)):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 44 "f2:=subs(diff(y(x),x)=f(x,y(x)),diff(f1,x)):" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 44 "f3:=subs(diff(y(x),x)=f(x,y( x)),diff(f2,x)):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 43 "f0:=sub s(\{y(x)=y0,x=x0\},f0):f0:=expand(f0);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#f0G-%\"fG6$%#x0G%#y0G" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 43 "f1:=subs(\{y(x)=y0,x=x0\},f1):f1:=expand(f1);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#f1G,&--&%\"DG6#\"\"\"6#%\"fG6$%#x0G%#y0GF+*&--& F)6#\"\"#F,F.F+-F-F.F+F+" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 43 "f2:=subs(\{y(x)=y0,x=x0\},f2):f2:=expand(f2);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#f2G,,--&%\"DG6$\"\"\"F+6#%\"fG6$%#x0G%#y0GF+*(\"\"#F +--&F)6$F+F2F,F.F+-F-F.F+F+*&--&F)6$F2F2F,F.F+)F7F2F+F+*&--&F)6#F2F,F. F+--&F)6#F+F,F.F+F+*&)F?F2F+F7F+F+" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 43 "f3:=subs(\{y(x)=y0,x=x0\},f3):f3:=expand(f3);" }} {PARA 12 "" 1 "" {XPPMATH 20 "6#>%#f3G,8--&%\"DG6%\"\"\"F+F+6#%\"fG6$% #x0G%#y0GF+*(\"\"$F+--&F)6%F+F+\"\"#F,F.F+-F-F.F+F+*(F2F+--&F)6%F+F7F7 F,F.F+)F8F7F+F+*(F2F+--&F)6$F+F7F,F.F+--&F)6#F+F,F.F+F+**\"\"&F+F@F+-- &F)6#F7F,F.F+F8F+F+*&--&F)6%F7F7F7F,F.F+)F8F2F+F+**F2F+F8F+--&F)6$F7F7 F,F.F+FDF+F+**\"\"%F+FUF+FJF+F>F+F+*&FJF+--&F)6$F+F+F,F.F+F+*&)FJF7F+F DF+F+*&)FJF2F+F8F+F+" }}}{EXCHG {PARA 0 "" 0 "" {MPLTEXT 0 21 23 "# de sarrollo del m\351todo" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 57 "k 10:=unapply(f(x0,y0+alpha*h*kp10(h)-alpha*h*kp20(h)),h);" }}{PARA 11 " " 1 "" {XPPMATH 20 "6#>%$k10Gf*6#%\"hG6\"6$%)operatorG%&arrowGF(-%\"fG 6$%#x0G,(%#y0G\"\"\"*(%&alphaGF29$F2-%%kp10G6#F5F2F2*(F4F2F5F2-%%kp20G F8F2!\"\"F(F(F(" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 65 "k20:=una pply(f(x0+2*h,y0+alpha*h*kp10(h)+(2-alpha)*h*kp20(h)),h);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%$k20Gf*6#%\"hG6\"6$%)operatorG%&arrowGF(-%\"f G6$,&%#x0G\"\"\"*&\"\"#F19$F1F1,(%#y0GF1*(%&alphaGF1F4F1-%%kp10G6#F4F1 F1*(,&F3F1F8!\"\"F1F4F1-%%kp20GF;F1F1F(F(F(" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 32 "k100:=k10(0):k100:=expand(k100);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%%k100G-%\"fG6$%#x0G%#y0G" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 32 "k200:=k20(0):k200:=expand(k200);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%%k200G-%\"fG6$%#x0G%#y0G" }}}{EXCHG {PARA 0 "> \+ " 0 "" {MPLTEXT 1 0 35 "Fi0:=expand((1/4)*k100+(3/4)*k200);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%$Fi0G-%\"fG6$%#x0G%#y0G" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "k11:=D(k10):" }}}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 12 "k21:=D(k20):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 66 "k110:=subs(\{kp10(0)=k100,kp20(0)=k200\},k11(0)):k110:=expand( k110);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%%k110G\"\"!" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 66 "k210:=subs(\{kp10(0)=k100,kp20(0)=k 200\},k21(0)):k210:=expand(k210);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#> %%k210G,&*&\"\"#\"\"\"--&%\"DG6#F(6#%\"fG6$%#x0G%#y0GF(F(*(F'F(--&F,6# F'F.F0F(-F/F0F(F(" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 35 "Fi1:=e xpand((1/4)*k110+(3/4)*k210);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%$Fi 1G,&*&#\"\"$\"\"#\"\"\"--&%\"DG6#F*6#%\"fG6$%#x0G%#y0GF*F**&F'F**&--&F .6#F)F0F2F*-F1F2F*F*F*" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "k 12:=D(k11):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "k22:=D(k21): " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 98 "k120:=subs(\{D(kp10)(0) =k110,D(kp20)(0)=k210,kp10(0)=k100,kp20(0)=k200\},k12(0)):k120:=expand (k120);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%%k120G,&**\"\"%\"\"\"--&% \"DG6#\"\"#6#%\"fG6$%#x0G%#y0GF(%&alphaGF(--&F,6#F(F/F1F(!\"\"**F'F()F )F.F(F4F(-F0F1F(F9" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 98 "k220: =subs(\{D(kp10)(0)=k110,D(kp20)(0)=k210,kp10(0)=k100,kp20(0)=k200\},k2 2(0)):k220:=expand(k220);" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#>%%k220G, 0*&\"\"%\"\"\"--&%\"DG6$F(F(6#%\"fG6$%#x0G%#y0GF(F(*(\"\")F(--&F,6$F( \"\"#F.F0F(-F/F0F(F(*(F'F(--&F,6$F9F9F.F0F()F:F9F(F(*(F4F(--&F,6#F9F.F 0F(--&F,6#F(F.F0F(F(*(F4F()FBF9F(F:F(F(**F'F(FBF(%&alphaGF(FFF(!\"\"** F'F(FKF(FMF(F:F(FN" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 35 "Fi2:= expand((1/4)*k120+(3/4)*k220);" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#>%$F i2G,0**\"\"%\"\"\"--&%\"DG6#\"\"#6#%\"fG6$%#x0G%#y0GF(%&alphaGF(--&F,6 #F(F/F1F(!\"\"**F'F()F)F.F(F4F(-F0F1F(F9*&\"\"$F(--&F,6$F(F(F/F1F(F(*( \"\"'F(--&F,6$F(F.F/F1F(FF(--&F,6$F.F.F/F1F()F " 0 "" {MPLTEXT 1 0 47 "cond1a:=coeff(Fi0,f(x0,y0))=coeff(f0,f(x0,y0));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%'cond1aG/\"\"\"F&" }}}{EXCHG {PARA 0 "" 0 "" {MPLTEXT 0 21 29 "# condiciones para el orden 2" }}}{EXCHG {PARA 0 "> \+ " 0 "" {MPLTEXT 1 0 65 "cond2a:=coeff(Fi1,D[1](f)(x0,y0))=coeff((1/2)* f1,D[1](f)(x0,y0));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%'cond2aG/#\" \"$\"\"##\"\"\"F(" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 97 "cond2b :=coeff(coeff(Fi1,D[2](f)(x0,y0)),f(x0,y0))=coeff(coeff((1/2)*f1,D[2]( f)(x0,y0)),f(x0,y0));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%'cond2bG/# \"\"$\"\"##\"\"\"F(" }}}{EXCHG {PARA 0 "" 0 "" {MPLTEXT 0 21 55 "s\363 lo se obtiene orden 1 y eso para cualquier valor de " }{XPPEDIT 18 0 "alpha;" "6#%&alphaG" }{MPLTEXT 0 21 5 " " }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {MPLTEXT 0 21 33 "# funcion de estabilidad general " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "restart:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 26 "interface(labeling=false):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 19 "f:=(x,y)->lambda*y;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"fGf*6$%\"xG%\"yG6\"6$%)operatorG%&arrowGF)*&%'lambdaG\"\"\"9 %F/F)F)F)" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 55 "ka1:=unapply(f (x0,y0+alpha*h*kp1(h)-alpha*h*kp2(h)),h);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%$ka1Gf*6#%\"hG6\"6$%)operatorG%&arrowGF(*&%'lambdaG\" \"\",(%#y0GF.*(%&alphaGF.9$F.-%$kp1G6#F3F.F.*(F2F.F3F.-%$kp2GF6F.!\"\" F.F(F(F(" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 63 "ka2:=unapply(f( x0+2*h,y0+alpha*h*kp1(h)+(2-alpha)*h*kp2(h)),h);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%$ka2Gf*6#%\"hG6\"6$%)operatorG%&arrowGF(*&%'lambdaG\" \"\",(%#y0GF.*(%&alphaGF.9$F.-%$kp1G6#F3F.F.*(,&\"\"#F.F2!\"\"F.F3F.-% $kp2GF6F.F.F.F(F(F(" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 99 "test :=solve(\{k1=subs(\{kp1(h)=k1,kp2(h)=k2\},ka1(h)),k2=subs(\{kp1(h)=k1, kp2(h)=k2\},ka2(h))\},\{k1,k2\});" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#> %%testG<$/%#k1G,$**%'lambdaG\"\"\"%#y0GF+,&F+!\"\"*(\"\"#F+F*F+%\"hGF+ F+F+,(F+F+*(F0F+F*F+F1F+F.**F0F+)F*F0F+)F1F0F+%&alphaGF+F+F.F./%#k2G*( F*F+F,F+F2F." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 54 "k1:=subs(te st,k1);k2:=subs(test,k2);simplify(k1+3*k2);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#k1G,$**%'lambdaG\"\"\"%#y0GF(,&F(!\"\"*(\"\"#F(F'F(% \"hGF(F(F(,(F(F(*(F-F(F'F(F.F(F+**F-F()F'F-F()F.F-F(%&alphaGF(F(F+F+" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#k2G*(%'lambdaG\"\"\"%#y0GF',(F'F' *(\"\"#F'F&F'%\"hGF'!\"\"**F+F')F&F+F')F,F+F'%&alphaGF'F'F-" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,$*,\"\"#\"\"\"%'lambdaGF&%#y0GF&,&F%!\"\"*& F'F&%\"hGF&F&F&,(F&F&*(F%F&F'F&F,F&F***F%F&)F'F%F&)F,F%F&%&alphaGF&F&F *F*" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 37 "y1:=expand(y0+h*((1/ 4)*k1+(3/4)*k2));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#y1G,(%#y0G\"\" \"**%\"hGF'%'lambdaGF'F&F',(F'F'*(\"\"#F'F*F'F)F'!\"\"**F-F')F*F-F')F) F-F'%&alphaGF'F'F.F'*,F-F.F*F-F&F'F+F.F)F-F." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 36 "y1:=collect(subs(lambda=z/h,y1),y0);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#y1G*&,(\"\"\"F'*&%\"zGF',(F'F'*&\"\"#F'F) F'!\"\"*(F,F')F)F,F'%&alphaGF'F'F-F'*(F,F-F)F,F*F-F-F'%#y0GF'" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 57 "r:=unapply(collect(simplify( y1/y0),z),z):r_general:=r(z);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%*r_ generalG,$*(\"\"#!\"\",(F'\"\"\"*&,&*&\"\"%F*%&alphaGF*F*F*F(F*)%\"zGF 'F*F**&F'F*F1F*F(F*,(F*F**&F'F*F1F*F(*(F'F*F0F*F/F*F*F(F*" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {MPLTEXT 0 21 25 "# parece oportuno tomar " }{XPPEDIT 18 0 "alpha = 1/4;" "6#/%&alphaG*&\"\"\"F&\"\"%!\"\"" }}}{EXCHG {PARA 0 "> \+ " 0 "" {MPLTEXT 1 0 45 "alpha:=1/4;num:=numer(r(z));den:=denom(r(z)); " }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%&alphaG#\"\"\"\"\"%" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%$numG,&\"\"#\"\"\"*&F&F'%\"zGF'!\"\"" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#>%$denG,(\"\"#\"\"\"*&\"\"%F'%\"zGF'! \"\"*$)F*F&F'F'" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 41 "z:=x+I*y :assume(x::real):assume(y::real):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 56 "numr:=Re(num);numi:=Im(num);denr:=Re(den);deni:=Im(de n);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%%numrG,&\"\"#\"\"\"*&F&F'%#x| irGF'!\"\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%%numiG,$*&\"\"#\"\"\"% #y|irGF(!\"\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%%denrG,*\"\"#\"\"\" *&\"\"%F'%#x|irGF'!\"\"*$)F*F&F'F'*$)%#y|irGF&F'F+" }}{PARA 11 "" 1 " " {XPPMATH 20 "6#>%%deniG,&*&\"\"%\"\"\"%#y|irGF(!\"\"*(\"\"#F(%#x|irG F(F)F(F(" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 48 "simplify(numr^2 +numi^2);simplify(denr^2+deni^2);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#, *\"\"%\"\"\"*&\"\")F%%#x|irGF%!\"\"*&F$F%)F(\"\"#F%F%*&F$F%)%#y|irGF,F %F%" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,4\"\"%\"\"\"*&\"#;F%%#x|irGF%! \"\"*&\"#?F%)F(\"\"#F%F%*&\"#7F%)%#y|irGF-F%F%*&\"\")F%)F(\"\"$F%F)*(F 3F%F(F%F0F%F)*$)F(F$F%F%*(F-F%F,F%F0F%F%*$)F1F$F%F%" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 45 "borde:=simplify(numr^2+numi^2-denr^2-deni ^2);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%&bordeG,2*&\"\")\"\"\"%#x|ir GF(F(*&\"#;F()F)\"\"#F(!\"\"*&F'F()%#y|irGF-F(F.*&F'F()F)\"\"$F(F(*(F' F(F)F(F0F(F(*$)F)\"\"%F(F.*(F-F(F,F(F0F(F.*$)F1F8F(F." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "with(plots):" }}}{EXCHG {PARA 0 "> \+ " 0 "" {MPLTEXT 1 0 56 "implicitplot(borde=0,x=-40..40,y=-40..40, grid refine=2);" 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Se trata del m\351todo" }}{PARA 4 "" 0 "" {TEXT 267 1 " " }} {PARA 4 "" 0 "" {TEXT 273 14 " 0 | " }{XPPEDIT 18 0 "1/4" "6# *&\"\"\"F$\"\"%!\"\"" }{TEXT 278 7 " - " }{XPPEDIT 18 0 "1/4" "6#* &\"\"\"F$\"\"%!\"\"" }}{PARA 4 "" 0 "" {TEXT 270 15 " 2 | " }{XPPEDIT 18 0 "1/4" "6#*&\"\"\"F$\"\"%!\"\"" }{TEXT 279 6 " " } {XPPEDIT 18 0 "5/4;" "6#*&\"\"&\"\"\"\"\"%!\"\"" }{TEXT 280 3 " " }} {PARA 4 "" 0 "" {TEXT -1 12 " ---------" }{TEXT 268 10 "----------" }}{PARA 4 "" 0 "" {TEXT 269 14 " | " }{XPPEDIT 18 0 "1/4;" "6#*&\"\"\"F$\"\"%!\"\"" }{TEXT 271 6 " " }{XPPEDIT 18 0 "3/4;" " 6#*&\"\"$\"\"\"\"\"%!\"\"" }{TEXT 272 1 " " }{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 }