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{SECT 0 {PARA 18 "" 0 "" {TEXT -1 35 "Minicurso de Introducci\363n a M
aple V" }}{PARA 19 "" 0 "" {TEXT 286 27 "Addlink Software Cient\355fic
o" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }
{TEXT 256 12 "Observaci\363n:" }}{PARA 0 "" 0 "" {TEXT -1 369 "En este
 Minicurso de Introducci\363n a Maple V, hemos usado para la notaci
\363n habitual de Maple para la introducci\363n de los distintos coman
dos. No debemos olvidar, que podr\355amos introducir gran parte de los
 comandos, expresiones y acciones haciendo uso de las paletas, men\372
s contextuales y el editor matem\341tico; o bien, mostrar los inputs e
n formato tradicional matem\341tico." }}{PARA 0 "" 0 "" {TEXT -1 0 "" 
}}{SECT 1 {PARA 0 "" 0 "" {TEXT 318 33 "CUANDO USE MAPLE V NO OLVIDE Q
UE:" }}{PARA 16 "" 0 "" {TEXT -1 67 "Cuando entre un comando mediante \+
notaci\363n Maple, no olvide colocar " }{TEXT 306 1 ";" }{TEXT -1 3 " \+
o " }{TEXT 307 1 ":" }{TEXT -1 21 " al final. El uso de " }{TEXT 308 
1 ":" }{TEXT -1 19 " suprime el output." }}{PARA 16 "" 0 "" {TEXT -1 
70 "La ayuda sobre cualquier comando es disponible desde el prompt usa
ndo " }{TEXT 303 7 "?t\363pico" }{TEXT -1 24 " o bien dentro del men
\372 " }{TEXT 304 4 "Help" }{TEXT -1 17 ", con el submen\372 " }{TEXT 
305 12 "Topic Search" }{TEXT -1 1 "." }}{PARA 16 "" 0 "" {TEXT -1 99 "
Maple distingue entre may\372sculas y min\355sculas; por lo tanto, val
or y VALOR son variables distintas." }}{PARA 16 "" 0 "" {TEXT -1 39 "L
as l\355neas de comentario comienzan por " }{TEXT 302 1 "#" }{TEXT -1 
52 ". Estas l\355neas son ignoradas por el kernel de Maple." }}{PARA 
16 "" 0 "" {TEXT -1 57 "Para la carga de ficheros debemos usar comilla
s simples: " }{TEXT 301 19 "'nombre de fichero'" }{TEXT -1 1 "." }}
{PARA 16 "" 0 "" {TEXT -1 11 "El comando " }{TEXT 300 7 "restart" }
{TEXT 309 0 "" }{TEXT -1 154 " borra toda la memoria de Maple. Si nos \+
perdemos en medio de una sesi\363n de Maple podemos: o bien salir y in
iciar de nuevo Maple V, o bien usar el comando " }{TEXT 310 7 "restart
" }{TEXT -1 1 "." }}{PARA 16 "" 0 "" {TEXT -1 12 "El operador " }
{TEXT 311 1 "%" }{TEXT -1 36 " permite recuperar el \372ltimo output.
" }}{PARA 16 "" 0 "" {TEXT -1 27 "El operador de producto es " }{TEXT 
312 1 "*" }{TEXT -1 70 ". A*B permite multiplicar A por B; AB no reali
za el producto esperado." }}{PARA 16 "" 0 "" {TEXT -1 68 "Maple dispon
e de un interfaz de documentos m\372ltiples. Los distintos " }{TEXT 
313 10 "worksheets" }{TEXT -1 21 " hacen uso del mismo " }{TEXT 314 6 
"kernel" }{TEXT -1 239 ". Esto significa que si en un determinado work
sheet x toma el valor 5, dentro de la misma sesi\363n cualquier otro w
orksheet supondr\341 que el valor de x es 5. Si no se desea trabajar c
on worksheets que compartan el mismo kernel debe usarse la " }{TEXT 
315 16 "versi\363n paralela" }{TEXT -1 46 " de Maple. Para ello selecc
ionaremos el icono " }{TEXT 316 23 "Parallel Server Maple V" }{TEXT 
-1 13 " en lugar de " }{TEXT 317 18 "Maple V Release 5." }{TEXT -1 
113 "1 dentro de la carpeta Maple V Release 5.1. (o ejecutaremos Maple
 con wmaple32.exe -km p en lugar de wmaple32.exe" }}}{PARA 0 "" 0 "" 
{TEXT -1 0 "" }}{SECT 1 {PARA 3 "" 0 "" {TEXT -1 18 "C\341lculos Num
\351ricos" }}{SECT 1 {PARA 4 "" 0 "" {TEXT -1 7 "Enteros" }}{PARA 0 "
" 0 "" {TEXT -1 53 "Maple V puede ser usado como una potente calculado
ra:" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 9 "32*12^13;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"1/.8sDy
BM" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 92 "Ad
em\341s, Maple V incorpora un gran n\372mero de funciones para trabaja
r con enteros, incluyendo:" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 
15 "" 0 "" {TEXT -1 19 "Aritm\351tica modular:" }}{EXCHG {PARA 0 "> " 
0 "" {MPLTEXT 1 0 9 "25 mod 3;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"\"
\"" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 15 "" 0 "" {TEXT -1 10 "F
actorial:" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 5 "200!;" }}{PARA 
12 "" 1 "" {XPPMATH 20 "6#\"bbl++++++++++++++++++++++++?ZP(*QqB'*yAA#*
yhze3q^B1C.</>.E-mo&zbSd7KSK!Rd2CCCvF`[HGuAJT'=HLSDSUm^9iXC#R%*))pRPsJ
j2FdGY86$*HG&\\iE>10rjU-zUwDI)Q'>*Q@@xT!Ri%)>,%G/.#HM.M'*\\%fVCLDu%HjK
<(oxf8&Hi]=KR@jBb.0zkt'yl)y" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 
15 "" 0 "" {TEXT -1 34 "Descomposici\363n en factores primos:" }}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 11 "ifactor(%);" }}{PARA 12 "" 
1 "" {XPPMATH 20 "6#*hp)-%!G6#\"\"#\"$(>\"\"\")-F&6#\"\"$\"#(*F*)-F&6#
\"\"&\"#\\F*)-F&6#\"\"(\"#KF*)-F&6#\"#6\"#>F*)-F&6#\"#8\"#;F*)-F&6#\"#
<F=F*)-F&6#F>\"#5F*)-F&6#\"#B\"\")F*)-F&6#\"#H\"\"'F*)-F&6#\"#JFUF*)-F
&6#\"#PF3F*)-F&6#\"#T\"\"%F*)-F&6#\"#VF\\oF*)-F&6#\"#ZF\\oF*)-F&6#\"#`
F.F*)-F&6#\"#fF.F*)-F&6#\"#hF.F*)-F&6#\"#nF(F*)-F&6#\"#rF(F*)-F&6#\"#t
F(F*)-F&6#\"#zF(F*)-F&6#\"#$)F(F*)-F&6#\"#*)F(F*)-F&6#F/F(F*-F&6#\"$,
\"\"\"\"-F&6#\"$.\"F_r-F&6#\"$2\"F_r-F&6#\"$4\"F_r-F&6#\"$8\"F_r-F&6#
\"$F\"F_r-F&6#\"$J\"F_r-F&6#\"$P\"F_r-F&6#\"$R\"F_r-F&6#\"$\\\"F_r-F&6
#\"$^\"F_r-F&6#\"$d\"F_r-F&6#\"$j\"F_r-F&6#\"$n\"F_r-F&6#\"$t\"F_r-F&6
#\"$z\"F_r-F&6#\"$\"=F_r-F&6#\"$\">F_r-F&6#\"$$>F_r-F&6#F)F_r-F&6#\"$*
>F_r" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 15 "" 0 "" {TEXT -1 20 
"Tests de primalidad:" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 13 "isp
rime(157);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#%%trueG" }}}{PARA 0 "" 
0 "" {TEXT -1 0 "" }}}{SECT 1 {PARA 4 "" 0 "" {TEXT -1 10 "Racionales
" }}{PARA 0 "" 0 "" {TEXT -1 208 "Una de las principales virtudes de M
aple V es el c\341lculo simb\363lico racional: podemos trabajar con ra
cionales e irracionales sin necesidad de tener que remitirnos a aproxi
maciones num\351ricas (en coma flotante)." }}{PARA 0 "" 0 "" {TEXT -1 
0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 10 "1/2 + 2/3;" }}{PARA 
11 "" 1 "" {XPPMATH 20 "6##\"\"(\"\"'" }}}{PARA 0 "" 0 "" {TEXT -1 0 "
" }}{PARA 0 "" 0 "" {TEXT -1 65 "Maple V autom\341ticamente se encarga
 de simplificar las fracciones:" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 4 "2/4;" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6##\"\"\"\"\"#" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 
0 "" 0 "" {TEXT -1 79 "Tambi\351n la manipulaci\363n de n\372meros irr
acionales se realiza de manera simb\363lica:" }}{PARA 0 "" 0 "" {TEXT 
-1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "sqrt(2);" }}{PARA 
11 "" 1 "" {XPPMATH 20 "6#*$-%%sqrtG6#\"\"#\"\"\"" }}}{EXCHG {PARA 0 "
> " 0 "" {MPLTEXT 1 0 30 "(2^30)/(3^20)*sqrt(2)+sqrt(8);" }}{PARA 11 "
" 1 "" {XPPMATH 20 "6#,$*$-%%sqrtG6#\"\"#\"\"\"#\"+E1JZ!)\"+,Wy'[$" }}
}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{SECT 1 {PARA 4 "" 0 "" {TEXT -1 9 "
Decimales" }}{PARA 0 "" 0 "" {TEXT -1 194 "A pesar que Maple V es un S
istema de C\341lculo Simb\363lico (y por lo tanto se trabaja de manera
 exacta), podemos obtener aproximaciones num\351ricas de cualquier val
or. El l\355mite es de 500.000 d\355gitos." }}{PARA 0 "" 0 "" {TEXT 
-1 65 "Para obtener dichas aproximaciones decimales usaremos el comand
o " }{TEXT 258 5 "evalf" }{TEXT -1 1 "." }}{PARA 0 "" 0 "" {TEXT -1 0 
"" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 9 "evalf(%);" }}{PARA 11 "
" 1 "" {XPPMATH 20 "6#$\"+V(GRE$!\"*" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 11 "evalf(7/6);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"+nm
mm6!\"*" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 
34 "Podemos manipular constantes como " }{XPPEDIT 18 0 "Pi;" "6#%#PiG
" }{TEXT -1 61 "  de manera simb\363lica o a partir de aproximaciones \+
num\351ricas:" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 
0 "" {MPLTEXT 1 0 3 "Pi;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#%#PiG" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "evalf(Pi,200);" }}{PARA 12 "
" 1 "" {XPPMATH 20 "6#$\"cw?QI\\&*[HiW'fb5@&Q>q-TG]u6\"[G\"3%f`sJAe]&4
Y%Q4ZmI#G8l3[@)z1<@MD[.G')**3iG1k\"yI#fW\\(4#e5v$*Rpr>%)G]zKQVEYQKz*e`
EfTJ!$*>" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 
119 "Cuando intervienen expresiones decimales dentro de los inputs, lo
s outputs obtenidos tambi\351n son expresiones decimales:" }}{PARA 0 "
" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "1.0/5.
3;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"+`Cz')=!#5" }}}{EXCHG {PARA 
0 "> " 0 "" {MPLTEXT 1 0 8 "sin(.2);" }}{PARA 11 "" 1 "" {XPPMATH 20 "
6#$\"+3Lp')>!#5" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" 
{TEXT -1 167 "Maple V puede calcular valores num\351ricos tanto para l
as funciones elementales como para funciones m\341s especiales (y obte
ner expresiones decimales cuando lo deseeemos):" }}{PARA 0 "" 0 "" 
{TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 10 "sin(2*Pi);" 
}}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"\"!" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 7 "exp(2);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#-%$expG6#\"
\"#" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 9 "evalf(%);" }}{PARA 
11 "" 1 "" {XPPMATH 20 "6#$\"+*4c!*Q(!\"*" }}}{PARA 0 "" 0 "" {TEXT 
-1 0 "" }}}{SECT 1 {PARA 4 "" 0 "" {TEXT -1 9 "Complejos" }}{PARA 0 "
" 0 "" {TEXT -1 77 "Maple V trabaja con n\372meros imaginarios. En par
ticular, la unidad imaginaria " }{XPPEDIT 18 0 "sqrt(-1);" "6#-%%sqrtG
6#,$\"\"\"!\"\"" }{TEXT -1 32 " es representada por el s\355mbolo " }
{TEXT 257 1 "I" }{TEXT -1 1 ":" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "(2+5*I)+(1-I);" }}{PARA 11 "
" 1 "" {XPPMATH 20 "6#,&\"\"$\"\"\"%\"IG\"\"%" }}}{EXCHG {PARA 0 "> " 
0 "" {MPLTEXT 1 0 14 "(1+I)/(3-2*I);" }}{PARA 11 "" 1 "" {XPPMATH 20 "
6#,&#\"\"\"\"#8F%%\"IG#\"\"&F&" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}
{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{SECT 1 {PARA 3 "" 0 "" {TEXT -1 19 "
C\341lculos Simb\363licos" }}{SECT 1 {PARA 4 "" 0 "" {TEXT -1 39 "Mani
pulaci\363n de expresiones polin\363micas" }}{PARA 0 "" 0 "" {TEXT -1 
184 "La verdadera virtud de Maple (como Sistema de Computaci\363n Alge
braica) se encuentra en el \341rea del c\341lculo simb\363lico, donde \+
es capaz de trabajar con indeterminadas de manera matem\341tica:" }}
{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 
8 "(1+x)^2;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#*$),&%\"xG\"\"\"F'F'\"
\"#\"\"\"" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT 
-1 82 "Maple V trabaja de manera matem\341tica y autom\341tica con las
 expresiones polin\363micas:" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "(1+x)+(3-2*x);" }}{PARA 11 "
" 1 "" {XPPMATH 20 "6#,&\"\"%\"\"\"%\"xG!\"\"" }}}{PARA 0 "" 0 "" 
{TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 125 "Disponemos de miles de f
unciones para la manipulaci\363n de expresiones simb\363licas. A conti
nuaci\363n podemos ver algunos ejemplos:" }}{PARA 0 "" 0 "" {TEXT -1 
0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 16 "expand((1+x)^2);" }}
{PARA 11 "" 1 "" {XPPMATH 20 "6#,(*$)%\"xG\"\"#\"\"\"\"\"\"F&F'F)F)" }
}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 10 "factor(%);" }}{PARA 11 "" 
1 "" {XPPMATH 20 "6#*$),&%\"xG\"\"\"F'F'\"\"#\"\"\"" }}}{EXCHG {PARA 
0 "> " 0 "" {MPLTEXT 1 0 15 "diff(sin(x),x);" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#-%$cosG6#%\"xG" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 
0 11 "sum(n^2,n);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,(*$)%\"nG\"\"$\"
\"\"#\"\"\"F'*$)F&\"\"#F(#!\"\"F-F&#F*\"\"'" }}}{EXCHG {PARA 0 "> " 0 
"" {MPLTEXT 1 0 23 "rem(x^3+x+1,x^2+x+1,x);" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#,&\"\"#\"\"\"%\"xGF%" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 22 "series(sin(x),x=0,10);" }}{PARA 11 "" 1 "" {XPPMATH 
20 "6#+/%\"xG\"\"\"\"\"\"#!\"\"\"\"'\"\"$#F%\"$?\"\"\"&#F(\"%S]\"\"(#F
%\"'!)GO\"\"*-%\"OG6#F%\"#5" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}
{SECT 1 {PARA 4 "" 0 "" {TEXT -1 38 "Manipulaci\363n algebraica de exp
resiones" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 
189 "Maple V proporciona al usuario un potente entorno para simplifica
ci\363n de expresiones. En particular, hace uso de distintas identidad
es trigonom\351tricas para la simplificaci\363n de expresiones:" }}
{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 
59 "simplify(cos(x)^5+sin(x)^4+2*cos(x)^2-2*sin(x)^2-cos(2*x));" }}
{PARA 11 "" 1 "" {XPPMATH 20 "6#,&*$)-%$cosG6#%\"xG\"\"&\"\"\"\"\"\"*$
)F&\"\"%F+F," }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" 
{TEXT -1 85 "Para simplificar expresiones algebraicas racionales, pode
mos usar tambi\351n el comando " }{TEXT 267 6 "normal" }{TEXT -1 1 ".
" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 
1 0 32 "normal((x^3-y^3)/(x^2+x-y-y^2));" }}{PARA 11 "" 1 "" {XPPMATH 
20 "6#*&,(*$)%\"xG\"\"#\"\"\"\"\"\"*&%\"yGF*F'F*F**$)F,F(F)F*F),(F'F*F
*F*F,F*!\"\"" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" 
{TEXT -1 11 "El comando " }{TEXT 268 7 "convert" }{TEXT -1 221 " permi
te al usuario transformar una determinada expresi\363n a otro tipo de \+
formato. En particular, podemos transformar una expresi\363n racional \+
a una expresi\363n equivalente en forma de suma de distintas expresion
es racionales:" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 
0 "" {MPLTEXT 1 0 33 "expr:=(a*x^2+b)/(x*(-3*x^2-x+4));" }}{PARA 11 "
" 1 "" {XPPMATH 20 "6#>%%exprG*&,&*&%\"aG\"\"\")%\"xG\"\"#\"\"\"F)%\"b
GF)F-*&F+\"\"\",(*$F*F-!\"$F+!\"\"\"\"%F)\"\"\"!\"\"" }}}{EXCHG {PARA 
0 "> " 0 "" {MPLTEXT 1 0 24 "convert(expr,parfrac,x);" }}{PARA 11 "" 
1 "" {XPPMATH 20 "6#,(*&%\"bG\"\"\"%\"xG!\"\"#\"\"\"\"\"%*&,&%\"aG\"#;
F%\"\"*F&,&F'\"\"$F+F*F(#!\"\"\"#G*&,&F.F*F%F*F&,&F'F*F4F*F(#F4\"\"(" 
}}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 110 "Con e
l mismo comando podemos transformar una expresi\363n trigonom\351trica
 a su equivalente en formato exponencial:" }}{PARA 0 "" 0 "" {TEXT -1 
0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "convert(cot(x),exp);
" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#*&*&%\"IG\"\"\",&*$)-%$expG6#*&F%
\"\"\"%\"xGF.\"\"#F&F.F.F.F.F&,&F(F.!\"\"F.!\"\"" }}}}{SECT 1 {PARA 4 
"" 0 "" {TEXT -1 24 "Resoluci\363n de ecuaciones" }}{PARA 0 "" 0 "" 
{TEXT -1 31 "Es conveniente usar el comando " }{TEXT 260 7 "restart" }
{TEXT -1 185 " al comienzo de una sesi\363n, o cuando vayamos a involu
crarnos dentro de una misma sesi\363n en c\341lculos que no est\341n r
elacionados con las variables o expresiones definidas con anterioridad
." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 9 "?restart;" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 
"" 0 "" {TEXT -1 15 "Con el comando " }{TEXT 259 7 "restart" }{TEXT 
-1 93 " eliminamos de la memoria del kernel cualquier definici\363n o \+
asignaci\363n que hayamos realizado." }}{PARA 0 "" 0 "" {TEXT -1 0 "" 
}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "restart;" }}}{PARA 0 "" 0 "
" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 57 "Para resolver ecuacione
s algebraicas usaremos el comando " }{TEXT 261 5 "solve" }{TEXT -1 1 "
:" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 21 "solve(a*x^2+b*x+c,x);" }}{PARA 11 "" 1 "" {XPPMATH 
20 "6$,$*&,&%\"bG!\"\"*$-%%sqrtG6#,&*$)F&\"\"#\"\"\"\"\"\"*&%\"aGF1%\"
cGF1!\"%F0F1F0F3!\"\"#F1F/,$*&,&F&F'F(F'F0F3F6F7" }}}{PARA 0 "" 0 "" 
{TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT 262 12 "Observaci\363n:" }{TEXT 
-1 60 " Maple V asume que la ecuaci\363n contenida dentro del comando \+
" }{TEXT 263 5 "solve" }{TEXT -1 236 " est\341 igualada a 0, si no se \+
indica lo contrario. Si Maple V devuelve la ecuaci\363n sin resolver, \+
esto no significa que la ecuaci\363n no tenga soluci\363n, sino que Ma
ple V no ha sido capaz de determinarla con el comando que le hemos ind
icado." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 95 
"Con el mismo comando, Maple V puede resolver sistemas de ecuaciones y
 sistemas de inecuaciones:" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 31 "solve(\{x+2*y=3,y+1/x=1\},\{x,y\});
" }}{PARA 11 "" 1 "" {XPPMATH 20 "6$<$/%\"xG!\"\"/%\"yG\"\"#<$/F(#\"\"
\"F)/F%F)" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 36 "solve(\{x^2*y^
2=0,x-y=1,x<>0\},\{x,y\});" }}{PARA 11 "" 1 "" {XPPMATH 20 "6$<$/%\"xG
\"\"\"/%\"yG\"\"!F#" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "
" {TEXT -1 25 "En ocasiones, el comando " }{TEXT 264 5 "solve" }{TEXT 
-1 23 " devuelve la expresi\363n " }{TEXT 265 7 "Root_Of" }{TEXT -1 
221 ". Con esta expresi\363n representamos de manera simb\363lica el c
onjunto de ra\355ces de ciertas ecuaciones de una variable. Si queremo
s obtener todos los valores (mediante una aproximaci\363n num\351rica)
 podemos hacer uso del comando " }{TEXT 266 9 "allvalues" }{TEXT -1 1 
":" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 19 "solve(x^5-2*x+2,x);" }}{PARA 11 "" 1 "" {XPPMATH 20 "
6#-%'RootOfG6#,(*$)%#_ZG\"\"&\"\"\"\"\"\"F)!\"#\"\"#F," }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 13 "allvalues(%);" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6'$!+7,Vk8!\"*,&$!+\\ggH>!#5\"\"\"%\"IG$!+uv\"*o7F%,&F'F*
F+$\"+uv\"*o7F%,&$\"+4mv^()F)F*F+$!+c8A>NF),&F2F*F+$\"+c8A>NF)" }}}
{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{SECT 1 {PARA 4 "" 0 "" {TEXT -1 17 "
Sumas y productos" }}{PARA 0 "" 0 "" {TEXT -1 85 "Maple V es capaz de \+
calcular sumas finitas y series, y productos finitos e infinitos:" }}
{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 
11 "Sum(k^2,k);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#-%$SumG6$*$)%\"kG\"
\"#\"\"\"F(" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 9 "value(%);" }}
{PARA 11 "" 1 "" {XPPMATH 20 "6#,(*$)%\"kG\"\"$\"\"\"#\"\"\"F'*$)F&\"
\"#F(#!\"\"F-F&#F*\"\"'" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 24 "
sum(1/k!,k=0..infinity);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#-%$expG6#
\"\"\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "Product(k^2,k=1..
4);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#-%(ProductG6$*$)%\"kG\"\"#\"\"
\"/F(;\"\"\"\"\"%" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 9 "value(%
);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"$w&" }}}{PARA 0 "" 0 "" {TEXT 
-1 0 "" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{SECT 0 {PARA 3 "" 0 "" 
{TEXT -1 13 "Visualizaci\363n" }}{PARA 0 "" 0 "" {TEXT -1 227 "Maple V
 permite realizar gr\341ficos bidimensionales y tridimensionales. Adem
\341s, podemos representar ecuaciones expl\355citas, impl\355citas, pa
ram\351tricas y conjuntos de datos. Tambi\351n podemos representar fun
ciones con discontinuidades." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "restart;" }}}{PARA 0 "" 0 "" 
{TEXT -1 0 "" }}{SECT 0 {PARA 4 "" 0 "" {TEXT -1 11 "Gr\341ficos 2D" }
}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{SECT 1 {PARA 5 "" 0 "" {TEXT -1 16 "
Simples Gr\341ficos" }}{PARA 0 "" 0 "" {TEXT -1 45 "Para generar gr
\341ficos 2D usaremos el comando " }{TEXT 269 4 "plot" }{TEXT -1 1 ".
" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 
1 0 27 "plot(sin(x),x=-2*Pi..2*Pi);" }}{PARA 13 "" 1 "" {GLPLOT2D 400 
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0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 276 "Para modificar los \+
gr\341ficos, podemos usar el men\372 contextual que aparece al pulsar \+
el bot\363n derecho del rat\363n o bien al pulsar sobre la ventana gr
\341fica mediante los botones que aparecen en el men\372 de gr\341fico
s. Tambi\351n podemos indicar las distintas opciones dentro del comand
o " }{TEXT 270 4 "plot" }{TEXT -1 1 "." }}{PARA 0 "" 0 "" {TEXT -1 0 "
" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 15 "?plot[options];" }}}
{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{SECT 1 {PARA 5 "" 0 "" {TEXT -1 30 "
Funciones con Discontinuidades" }}{PARA 0 "" 0 "" {TEXT -1 105 "Para i
ndicar a Maple que la funci\363n que vamos a representar presenta disc
ontinuidades usaremos la opci\363n " }{TEXT 271 12 "discont=true" }
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{PARA 4 "" 0 "" {TEXT -1 23 "Composici\363n de Gr\341ficos" }}{PARA 0 
"" 0 "" {TEXT -1 13 "Los comandos " }{TEXT 273 7 "display" }{TEXT -1 
3 " y " }{TEXT 274 9 "display3d" }{TEXT -1 49 " permiten la creaci\363
n de composici\363n de gr\341ficos." }}{PARA 0 "" 0 "" {TEXT -1 243 "C
uando asignamos un nombre a un gr\341fico, se omite el gr\341fico (deb
emos utilizar en lugar de punto y coma, dos puntos para omitir el outp
ut que muestra la estructura del gr\341fico). Para representar el gr
\341fico asignado hay que utilizar el comando " }{TEXT 276 7 "display
" }{TEXT -1 3 " o " }{TEXT 275 9 "display3d" }{TEXT -1 92 ". El uso de
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ntos gr\341ficos." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 ">
 " 0 "" {MPLTEXT 1 0 12 "with(plots);" }}{PARA 12 "" 1 "" {XPPMATH 20 
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"" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 165 "En este primer e
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7$Fh]lF[bl7$F[^lF[bl7$F^^lF[bl7$F*F[bl7$Fb^lF[bl7$Fe^lF[bl7$Fh^lF[bl7$
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7$F_dlF[bl7$FbdlF[bl7$FedlF[bl7$FhdlF[bl7$F[elF[bl7$F^elF[bl7$FaelF[bl
7$FdelF[bl7$FgelF[bl7$FjelF[bl7$F]flF[bl7$F`flF[bl7$FcflF[bl7$FfflF[bl
7$FiflF[bl7$F\\glF[bl7$F_glF[bl7$FbglF[bl7$FeglF[bl7$FhglF[bl7$F[hlF[b
l7$F^hlF[bl7$FahlF[bl7$FdhlF[bl7$FghlF[bl7$FjhlF[bl7$F]ilF[bl7$F`ilF[b
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<Ficl7$F?Ficl7$FBFicl7$FEFicl7$FHFicl7$FKFicl7$FNFicl7$FQFicl7$FTFicl7
$FWFicl7$FZFicl7$FgnFicl7$FjnFicl7$F]oFicl7$F`oFicl7$FcoFicl7$FfoFicl7
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cl7$FaqFicl7$FdqFicl7$FgqFicl7$FjqFicl7$F]rFicl7$F`rFicl7$FcrFicl7$Ffr
Ficl7$FirFicl7$F\\sFicl7$F_sFicl7$FbsFicl7$FesFicl7$FhsFicl7$F[tFicl7$
F^tFicl7$FatFicl7$FdtFicl7$FgtFicl7$FjtFicl7$F]uFicl7$F`uFicl7$FcuFicl
7$FfuFicl7$FiuFicl7$F\\vFicl7$F_vFicl7$FbvFicl7$FevFicl7$FhvFicl7$F[wF
icl7$F^wFicl7$FawFicl7$FdwFicl7$FgwFicl7$FjwFicl7$F]xFicl7$F`xFicl7$Fc
xFicl7$FfxFicl7$FixFicl7$F\\yFicl7$F_yFicl7$FbyFicl7$FeyFicl7$FhyFicl7
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e\\lFicl7$Fi\\lFicl7$F\\]lFicl7$F_]lFicl7$Fb]lFicl7$Fe]lFicl7$Fh]lFicl
7$F[^lFicl7$F^^lFicl7$F*Ficl7$Fb^lFicl7$Fe^lFicl7$Fh^lFicl7$F[_lFicl7$
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7$FbdlFicl7$FedlFicl7$FhdlFicl7$F[elFicl7$F^elFicl7$FaelFicl7$FdelFicl
7$FgelFicl7$FjelFicl7$F]flFicl7$F`flFicl7$FcflFicl7$FfflFicl7$FiflFicl
7$F\\glFicl7$F_glFicl7$FbglFicl7$FeglFicl7$FhglFicl7$F[hlFicl7$F^hlFic
l7$FahlFicl7$FdhlFicl7$FghlFicl7$FjhlFicl7$F]ilFicl7$F`ilFicl7$FcilFic
l7$FfilFicl7$FiilFicl7$F\\jlFicl7$F_jlFicl7$FbjlFicl7$FejlFicl7$FhjlFi
cl7$F[[mFicl7$F^[mFicl7$Fa[mFicl7$Fd[mFicl7$Fg[mFicl7$Fj[mFicl7$F]\\mF
icl7$F`\\mFicl7$Fc\\mFicl7$Ff\\mFicl7$Fi\\mFicl7$F\\]mFicl7$F_]mFicl7$
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m-F$6&7ew7$F(Fgel7$F,Fgel7$F0Fgel7$F3Fgel7$F6Fgel7$F9Fgel7$F<Fgel7$F?F
gel7$FBFgel7$FEFgel7$FHFgel7$FKFgel7$FNFgel7$FQFgel7$FTFgel7$FWFgel7$F
ZFgel7$FgnFgel7$FjnFgel7$F]oFgel7$F`oFgel7$FcoFgel7$FfoFgel7$FioFgel7$
F\\pFgel7$F_pFgel7$FbpFgel7$FepFgel7$FhpFgel7$F[qFgel7$F^qFgel7$FaqFge
l7$FdqFgel7$FgqFgel7$FjqFgel7$F]rFgel7$F`rFgel7$FcrFgel7$FfrFgel7$FirF
gel7$F\\sFgel7$F_sFgel7$FbsFgel7$FesFgel7$FhsFgel7$F[tFgel7$F^tFgel7$F
atFgel7$FdtFgel7$FgtFgel7$FjtFgel7$F]uFgel7$F`uFgel7$FcuFgel7$FfuFgel7
$FiuFgel7$F\\vFgel7$F_vFgel7$FbvFgel7$FevFgel7$FhvFgel7$F[wFgel7$F^wFg
el7$FawFgel7$FdwFgel7$FgwFgel7$FjwFgel7$F]xFgel7$F`xFgel7$FcxFgel7$Ffx
Fgel7$FixFgel7$F\\yFgel7$F_yFgel7$FbyFgel7$FeyFgel7$FhyFgel7$F[zFgel7$
F^zFgel7$FazFgel7$FdzFgel7$FgzFgel7$FjzFgel7$F][lFgel7$F`[lFgel7$Fc[lF
gel7$Ff[lFgel7$Fi[lFgel7$F\\\\lFgel7$F_\\lFgel7$Fb\\lFgel7$Fe\\lFgel7$
Fi\\lFgel7$F\\]lFgel7$F_]lFgel7$Fb]lFgel7$Fe]lFgel7$Fh]lFgel7$F[^lFgel
7$F^^lFgel7$F*Fgel7$Fb^lFgel7$Fe^lFgel7$Fh^lFgel7$F[_lFgel7$F^_lFgel7$
Fa_lFgel7$Fd_lFgel7$Fg_lFgel7$Fj_lFgel7$F]`lFgel7$F``lFgel7$Fc`lFgel7$
Ff`lFgel7$Fi`lFgel7$F\\alFgel7$F_alFgel7$FbalFgel7$FealFgel7$FhalFgel7
$F[blFgel7$F^blFgel7$FablFgel7$FdblFgel7$FgblFgel7$FjblFgel7$F]clFgel7
$F`clFgel7$FcclFgel7$FfclFgel7$FiclFgel7$F\\dlFgel7$F_dlFgel7$FbdlFgel
7$FedlFgel7$FhdlFgel7$F[elFgel7$F^elFgel7$FaelFgel7$FdelFgel7$FgelFgel
7$FjelFgel7$F]flFgel7$F`flFgel7$FcflFgel7$FfflFgel7$FiflFgel7$F\\glFge
l7$F_glFgel7$FbglFgel7$FeglFgel7$FhglFgel7$F[hlFgel7$F^hlFgel7$FahlFge
l7$FdhlFgel7$FghlFgel7$FjhlFgel7$F]ilFgel7$F`ilFgel7$FcilFgel7$FfilFge
l7$FiilFgel7$F\\jlFgel7$F_jlFgel7$FbjlFgel7$FejlFgel7$FhjlFgel7$F[[mFg
el7$F^[mFgel7$Fa[mFgel7$Fd[mFgel7$Fg[mFgel7$Fj[mFgel7$F]\\mFgel7$F`\\m
Fgel7$Fc\\mFgel7$Ff\\mFgel7$Fi\\mFgel7$F\\]mFgel7$F_]mFgel7$Fb]mFgel7$
Fe]mFgel7$Fh]mFgel7$F[^mFgel7$F^^mFgel7$Fa^mFgel7$Fd^mFgel7$Fg^mFgel7$
Fj^mFgel7$F]_mFgel7$F`_mFgel7$Fc_mFgel7$Ff_mFgel7$Fi_mFgel7$F\\`mFgel7
$F_`mFgel7$Fb`mFgel7$Fe`mFgel7$Fh`mFgel7$F[amFgelF]amFcamFfam-F$6&7ew7
$F(Fegl7$F,Fegl7$F0Fegl7$F3Fegl7$F6Fegl7$F9Fegl7$F<Fegl7$F?Fegl7$FBFeg
l7$FEFegl7$FHFegl7$FKFegl7$FNFegl7$FQFegl7$FTFegl7$FWFegl7$FZFegl7$Fgn
Fegl7$FjnFegl7$F]oFegl7$F`oFegl7$FcoFegl7$FfoFegl7$FioFegl7$F\\pFegl7$
F_pFegl7$FbpFegl7$FepFegl7$FhpFegl7$F[qFegl7$F^qFegl7$FaqFegl7$FdqFegl
7$FgqFegl7$FjqFegl7$F]rFegl7$F`rFegl7$FcrFegl7$FfrFegl7$FirFegl7$F\\sF
egl7$F_sFegl7$FbsFegl7$FesFegl7$FhsFegl7$F[tFegl7$F^tFegl7$FatFegl7$Fd
tFegl7$FgtFegl7$FjtFegl7$F]uFegl7$F`uFegl7$FcuFegl7$FfuFegl7$FiuFegl7$
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l7$FdwFegl7$FgwFegl7$FjwFegl7$F]xFegl7$F`xFegl7$FcxFegl7$FfxFegl7$FixF
egl7$F\\yFegl7$F_yFegl7$FbyFegl7$FeyFegl7$FhyFegl7$F[zFegl7$F^zFegl7$F
azFegl7$FdzFegl7$FgzFegl7$FjzFegl7$F][lFegl7$F`[lFegl7$Fc[lFegl7$Ff[lF
egl7$Fi[lFegl7$F\\\\lFegl7$F_\\lFegl7$Fb\\lFegl7$Fe\\lFegl7$Fi\\lFegl7
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7$F*Fegl7$Fb^lFegl7$Fe^lFegl7$Fh^lFegl7$F[_lFegl7$F^_lFegl7$Fa_lFegl7$
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7$FhdlFegl7$F[elFegl7$F^elFegl7$FaelFegl7$FdelFegl7$FgelFegl7$FjelFegl
7$F]flFegl7$F`flFegl7$FcflFegl7$FfflFegl7$FiflFegl7$F\\glFegl7$F_glFeg
l7$FbglFegl7$FeglFegl7$FhglFegl7$F[hlFegl7$F^hlFegl7$FahlFegl7$FdhlFeg
l7$FghlFegl7$FjhlFegl7$F]ilFegl7$F`ilFegl7$FcilFegl7$FfilFegl7$FiilFeg
l7$F\\jlFegl7$F_jlFegl7$FbjlFegl7$FejlFegl7$FhjlFegl7$F[[mFegl7$F^[mFe
gl7$Fa[mFegl7$Fd[mFegl7$Fg[mFegl7$Fj[mFegl7$F]\\mFegl7$F`\\mFegl7$Fc\\
mFegl7$Ff\\mFegl7$Fi\\mFegl7$F\\]mFegl7$F_]mFegl7$Fb]mFegl7$Fe]mFegl7$
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$Fb`mFegl7$Fe`mFegl7$Fh`mFegl7$F[amFeglF]amFcamFfam-F$6&7ew7$F(Fcil7$F
,Fcil7$F0Fcil7$F3Fcil7$F6Fcil7$F9Fcil7$F<Fcil7$F?Fcil7$FBFcil7$FEFcil7
$FHFcil7$FKFcil7$FNFcil7$FQFcil7$FTFcil7$FWFcil7$FZFcil7$FgnFcil7$FjnF
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bpFcil7$FepFcil7$FhpFcil7$F[qFcil7$F^qFcil7$FaqFcil7$FdqFcil7$FgqFcil7
$FjqFcil7$F]rFcil7$F`rFcil7$FcrFcil7$FfrFcil7$FirFcil7$F\\sFcil7$F_sFc
il7$FbsFcil7$FesFcil7$FhsFcil7$F[tFcil7$F^tFcil7$FatFcil7$FdtFcil7$Fgt
Fcil7$FjtFcil7$F]uFcil7$F`uFcil7$FcuFcil7$FfuFcil7$FiuFcil7$F\\vFcil7$
F_vFcil7$FbvFcil7$FevFcil7$FhvFcil7$F[wFcil7$F^wFcil7$FawFcil7$FdwFcil
7$FgwFcil7$FjwFcil7$F]xFcil7$F`xFcil7$FcxFcil7$FfxFcil7$FixFcil7$F\\yF
cil7$F_yFcil7$FbyFcil7$FeyFcil7$FhyFcil7$F[zFcil7$F^zFcil7$FazFcil7$Fd
zFcil7$FgzFcil7$FjzFcil7$F][lFcil7$F`[lFcil7$Fc[lFcil7$Ff[lFcil7$Fi[lF
cil7$F\\\\lFcil7$F_\\lFcil7$Fb\\lFcil7$Fe\\lFcil7$Fi\\lFcil7$F\\]lFcil
7$F_]lFcil7$Fb]lFcil7$Fe]lFcil7$Fh]lFcil7$F[^lFcil7$F^^lFcil7$F*Fcil7$
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$FablFcil7$FdblFcil7$FgblFcil7$FjblFcil7$F]clFcil7$F`clFcil7$FcclFcil7
$FfclFcil7$FiclFcil7$F\\dlFcil7$F_dlFcil7$FbdlFcil7$FedlFcil7$FhdlFcil
7$F[elFcil7$F^elFcil7$FaelFcil7$FdelFcil7$FgelFcil7$FjelFcil7$F]flFcil
7$F`flFcil7$FcflFcil7$FfflFcil7$FiflFcil7$F\\glFcil7$F_glFcil7$FbglFci
l7$FeglFcil7$FhglFcil7$F[hlFcil7$F^hlFcil7$FahlFcil7$FdhlFcil7$FghlFci
l7$FjhlFcil7$F]ilFcil7$F`ilFcil7$FcilFcil7$FfilFcil7$FiilFcil7$F\\jlFc
il7$F_jlFcil7$FbjlFcil7$FejlFcil7$FhjlFcil7$F[[mFcil7$F^[mFcil7$Fa[mFc
il7$Fd[mFcil7$Fg[mFcil7$Fj[mFcil7$F]\\mFcil7$F`\\mFcil7$Fc\\mFcil7$Ff
\\mFcil7$Fi\\mFcil7$F\\]mFcil7$F_]mFcil7$Fb]mFcil7$Fe]mFcil7$Fh]mFcil7
$F[^mFcil7$F^^mFcil7$Fa^mFcil7$Fd^mFcil7$Fg^mFcil7$Fj^mFcil7$F]_mFcil7
$F`_mFcil7$Fc_mFcil7$Ff_mFcil7$Fi_mFcil7$F\\`mFcil7$F_`mFcil7$Fb`mFcil
7$Fe`mFcil7$Fh`mFcil7$F[amFcilF]amFcamFfam-F$6&7ew7$F(Fa[m7$F,Fa[m7$F0
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FKFa[m7$FNFa[m7$FQFa[m7$FTFa[m7$FWFa[m7$FZFa[m7$FgnFa[m7$FjnFa[m7$F]oF
a[m7$F`oFa[m7$FcoFa[m7$FfoFa[m7$FioFa[m7$F\\pFa[m7$F_pFa[m7$FbpFa[m7$F
epFa[m7$FhpFa[m7$F[qFa[m7$F^qFa[m7$FaqFa[m7$FdqFa[m7$FgqFa[m7$FjqFa[m7
$F]rFa[m7$F`rFa[m7$FcrFa[m7$FfrFa[m7$FirFa[m7$F\\sFa[m7$F_sFa[m7$FbsFa
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{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{SECT 1 {PARA 3 "" 0 "" {TEXT -1 21 "
Paquetes espec\355ficos." }}{SECT 1 {PARA 4 "" 0 "" {TEXT -1 14 "\301l
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"" {MPLTEXT 1 0 8 "restart;" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{SECT 
1 {PARA 5 "" 0 "" {TEXT -1 12 "Introducci\363n" }}{PARA 0 "" 0 "" 
{TEXT -1 218 "Maple V proporciona al usuario un amplio abanico de paqu
etes especiales relacionados con Estad\355stica, Teor\355a de N\372mer
os, Teor\355a de Grafos... y uno especialmente dise\361ado para la ens
e\361anza de An\341lisis a los estudiantes." }}{PARA 0 "" 0 "" {TEXT 
-1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 56 "Existen distintos procedimiento
s para cargar un paquete:" }}{PARA 15 "" 0 "" {TEXT -1 55 "Carga de to
das las funciones contenidas en el paquete: " }{TEXT 277 21 "with(nomb
re_paquete);" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "with(stats);
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" {TEXT -1 0 "" }}{PARA 15 "" 0 "" {TEXT -1 40 "Carga de algunas funci
ones del paquete: " }{TEXT 278 49 "with(nombre_paquete,rutina1,rutina2
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ls,odeadvisor);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#7#%+odeadvisorG" }}
}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 15 "" 0 "" {TEXT -1 43 "Carga y
 uso (a la vez) de una sola rutina: " }{TEXT 279 28 "nombre_paquete[ru
tina](...);" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 40 "finance[cashf
lows]([100, 200, 50], 0.1);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"+s3k
PH!\"(" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 
147 "Uno de los paquetes m\341s usados es el paquete de \341lgebra lin
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0 "> " 0 "" {MPLTEXT 1 0 13 "with(linalg);" }}{PARA 7 "" 1 "" {TEXT 
-1 32 "Warning, new definition for norm" }}{PARA 7 "" 1 "" {TEXT -1 
33 "Warning, new definition for trace" }}{PARA 12 "" 1 "" {XPPMATH 20 
"6#7^r%.BlockDiagonalG%,GramSchmidtG%,JordanBlockG%)LUdecompG%)QRdecom
pG%*WronskianG%'addcolG%'addrowG%$adjG%(adjointG%&angleG%(augmentG%(ba
cksubG%%bandG%&basisG%'bezoutG%,blockmatrixG%(charmatG%)charpolyG%)cho
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ibonacciG%+forwardsubG%*frobeniusG%*gausselimG%*gaussjordG%(geneqnsG%*
genmatrixG%%gradG%)hadamardG%(hermiteG%(hessianG%(hilbertG%+htranspose
G%)ihermiteG%*indexfuncG%*innerprodG%)intbasisG%(inverseG%'ismithG%*is
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%)linsolveG%'mataddG%'matrixG%&minorG%(minpolyG%'mulcolG%'mulrowG%)mul
tiplyG%%normG%*normalizeG%*nullspaceG%'orthogG%*permanentG%&pivotG%*po
tentialG%+randmatrixG%+randvectorG%%rankG%(ratformG%$rowG%'rowdimG%)ro
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ectorG%*wronskianG" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{SECT 1 {PARA 
5 "" 0 "" {TEXT -1 23 "Operaciones Matriciales" }}{PARA 0 "" 0 "" 
{TEXT -1 191 "Un array es una generealizaci\363n de la estructura matr
icial de datos. La conversi\363n entre arrays y matrices es autom\341t
ica; por ello, cuando creamos un array podemos utilizarlo como una mat
riz." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 56 "D
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280 5 "array" }{TEXT -1 1 "." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 50 "M1:=array([[1/2,-1/3,2],[-5,
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" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#-%'matrixG6#7%7%#\"\"\"\"\"##!\"\"
\"\"$F*7%!\"&#\"#9F-\"\"*7%\"\"!\"#6#F/\"\"'" }}}{EXCHG {PARA 0 "> " 
0 "" {MPLTEXT 1 0 10 "evalm(M1);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#-%
'matrixG6#7%7%#\"\"\"\"\"##!\"\"\"\"$F*7%!\"&#\"#9F-\"\"*7%\"\"!\"#6#F
/\"\"'" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 
44 "Para calcular la inversa tenemos el comando " }{TEXT 283 7 "invers
e" }{TEXT -1 1 ":" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 ">
 " 0 "" {MPLTEXT 1 0 12 "inverse(M1);" }}{PARA 11 "" 1 "" {XPPMATH 20 
"6#-%'matrixG6#7%7%#\"%_=\"%\")G#!$\"RF*#\"$A#F*7%#\"#vF*#\"#:\"%id#\"
$h#F*7%#\"$!**F*#\"#**F*#!#7F*" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}
{PARA 0 "" 0 "" {TEXT -1 103 "Definimos a continuaci\363n una matriz c
on valores simb\363licos. En esta ocasi\363n nos serviremos del comand
o " }{TEXT 284 6 "matrix" }{TEXT -1 46 " con una variaci\363n sobre la
 sintaxis habitual:" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 
"> " 0 "" {MPLTEXT 1 0 58 "M2:=matrix(3,3,[1/2,0,-2,sin(theta),1,phi^2
,0,phi-1,3/4]);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#M2G-%'matrixG6#7
%7%#\"\"\"\"\"#\"\"!!\"#7%-%$sinG6#%&thetaGF+*$)%$phiGF,\"\"\"7%F-,&F6
F+!\"\"F+#\"\"$\"\"%" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 
"" {TEXT -1 57 "Para multiplicar las matrices M1 y M2 tenemos el coman
do " }{TEXT 285 8 "multiply" }{TEXT -1 15 " o el operador:" }}{PARA 0 
"" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "M3:=
multiply(M1,M2);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#M3G-%'matrixG6#
7%7%,&#\"\"\"\"\"%F,-%$sinG6#%&thetaG#!\"\"\"\"$,&#!\"(F4F,%$phiG\"\"#
,&#F,F9F,*$)F8F9\"\"\"F27%,&#!\"&F9F,F.#\"#9F4,&#!#8F4F,F8\"\"*,&#\"#n
F-F,F<FC7%,$F.\"#6,&#\"#r\"\"'F,F8#FBFR,&#FB\"\")F,F<FN" }}}{PARA 0 "
" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 49 "Calculemos el dete
rminante de esta \372ltima matriz:" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "det(M3);" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#,,#!%\")G\"#[\"\"\"*$)%$phiG\"\"#\"\"\"#F%\"#O*$)F*\"\"
$F,#\"%\")GF.-%$sinG6#%&thetaG#F%\"\"**&F4F'F*F'#F3F9" }}}{PARA 0 "" 
0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 116 "El paquete linalg c
ontiene definiciones de matrices especiales como la matriz de Hilbert \+
o la matriz de Vandermonde:" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 10 "hilbet(4);" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#-%'hilbetG6#\"\"%" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 25 "vandermonde([s,t,u,v,w]);" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#-%'matrixG6#7'7'\"\"\"%\"sG*$)F)\"\"#\"\"\"*$)F)\"\"$F-
*$)F)\"\"%F-7'F(%\"tG*$)F5F,F-*$)F5F0F-*$)F5F3F-7'F(%\"uG*$)F=F,F-*$)F
=F0F-*$)F=F3F-7'F(%\"vG*$)FEF,F-*$)FEF0F-*$)FEF3F-7'F(%\"wG*$)FMF,F-*$
)FMF0F-*$)FMF3F-" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{SECT 1 {PARA 5 
"" 0 "" {TEXT -1 24 "Operaciones con Vectores" }}{PARA 0 "" 0 "" 
{TEXT -1 120 "Veamos a continuaci\363n algunos de los comandos para la
 creaci\363n y manipulaci\363n de vectores dentro del entorno de Maple
 V:" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 20 "v1:=vector([1,1,1]);" }}{PARA 11 "" 1 "" {XPPMATH 20 
"6#>%#v1G-%'vectorG6#7%\"\"\"F)F)" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 20 "v2:=vector([1,0,0]);" }}{PARA 11 "" 1 "" {XPPMATH 20 
"6#>%#v2G-%'vectorG6#7%\"\"\"\"\"!F*" }}}{PARA 0 "" 0 "" {TEXT -1 0 "
" }}{PARA 0 "" 0 "" {TEXT -1 65 "Calculemos el \341ngulo determinado p
or los dos vectores anteriores:" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 13 "angle(v1,v2);" }}{PARA 11 "
" 1 "" {XPPMATH 20 "6#-%'arccosG6#,$*$-%%sqrtG6#\"\"$\"\"\"#\"\"\"F+" 
}}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 87 "Tambi
\351n podemos calcular el producto escalar y el producto vectorial de \+
ambos vectores:" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> \+
" 0 "" {MPLTEXT 1 0 15 "dotprod(v1,v2);" }}{PARA 11 "" 1 "" {XPPMATH 
20 "6#\"\"\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "crossprod(v
1,v2);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#-%'vectorG6#7%\"\"!\"\"\"!\"
\"" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 182 "C
uando los elementos del vector son funciones, tenemos la posibilidad d
e manipular de la misma manera todos los elementos del vector, de la m
isma manera que har\355amos con una funci\363n:" }}{PARA 0 "" 0 "" 
{TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 51 "diff_vector:
=vector([sin(x),cos(x),sin(x)*cos(x)]);" }}{PARA 11 "" 1 "" {XPPMATH 
20 "6#>%,diff_vectorG-%'vectorG6#7%-%$sinG6#%\"xG-%$cosGF+*&F)\"\"\"F-
F0" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 24 "map(diff,diff_vector,
x);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#-%'vectorG6#7%-%$cosG6#%\"xG,$-
%$sinGF)!\"\",&*$)F'\"\"#\"\"\"\"\"\"*$)F,F2F3F." }}}{PARA 0 "" 0 "" 
{TEXT -1 0 "" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{SECT 1 {PARA 4 "" 
0 "" {TEXT -1 21 "C\341lculo Infinitesimal" }}{PARA 0 "" 0 "" {TEXT 
-1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "restart;" }}}{PARA 
0 "" 0 "" {TEXT -1 0 "" }}{SECT 1 {PARA 5 "" 0 "" {TEXT -1 7 "L\355mit
es" }}{PARA 0 "" 0 "" {TEXT -1 77 "Calculemos el l\355mite de una func
i\363n racional cuando x se aproxima al valor 1." }}{PARA 0 "" 0 "" 
{TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 37 "f:=(x^2-2*x+
1)/(x^4+3*x^3-7*x^2+x+2);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"fG*&,
(*$)%\"xG\"\"#\"\"\"\"\"\"F)!\"#F,F,F+,,*$)F)\"\"%F+F,*$)F)\"\"$F+F4F'
!\"(F)F,F*F,!\"\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 13 "Limit(
f,x=1);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#-%&LimitG6$*&,(*$)%\"xG\"\"
#\"\"\"\"\"\"F*!\"#F-F-F,,,*$)F*\"\"%F,F-*$)F*\"\"$F,F5F(!\"(F*F-F+F-!
\"\"/F*F-" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 9 "value(%);" }}
{PARA 11 "" 1 "" {XPPMATH 20 "6##\"\"\"\"\")" }}}{PARA 0 "" 0 "" 
{TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 112 "Cuando el l\355mite en u
n punto no se encuentra definido, siempre podemos recurrir al c\341lcu
lo de l\355mites laterales:" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 21 "limit(tan(x),x=Pi/2);" }}{PARA 11 "
" 1 "" {XPPMATH 20 "6#%*undefinedG" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 26 "limit(tan(x),x=Pi/2,left);" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#%)infinityG" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 
27 "limit(tan(x),x=Pi/2,right);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,$%
)infinityG!\"\"" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{SECT 1 {PARA 5 "
" 0 "" {TEXT -1 24 "Derivaci\363n e Integraci\363n" }}{PARA 0 "" 0 "" 
{TEXT -1 98 "Maple V, como manipulador algebraico, permite calcular de
rivadas e integrales de manera simb\363lica:" }}{PARA 0 "" 0 "" {TEXT 
-1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "diff(sin(x)*x,x);
" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,&*&-%$cosG6#%\"xG\"\"\"F(F)F)-%$s
inGF'F)" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "int(cos(x),x);" 
}}{PARA 11 "" 1 "" {XPPMATH 20 "6#-%$sinG6#%\"xG" }}}{EXCHG {PARA 0 ">
 " 0 "" {MPLTEXT 1 0 20 "int(sin(x),x=0..Pi);" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#\"\"#" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 
"" {TEXT -1 104 "Ahora podemos derivar una expresi\363n, integrar el r
esultado y comparar la expresi\363n inicial con la final:" }}{PARA 0 "
" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "f:=x*
sin(a*x)+b*x^2;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"fG,&*&%\"xG\"\"
\"-%$sinG6#*&%\"aG\"\"\"F'F.F.F.*&%\"bGF.)F'\"\"#F(F." }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "df:=diff(f,x);" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#>%#dfG,(-%$sinG6#*&%\"aG\"\"\"%\"xGF+F+*(F,\"\"\"-%$cos
GF(F+F*F.F+*&%\"bGF+F,F.\"\"#" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 
0 10 "int(df,x);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,(*&-%$cosG6#*&%\"
aG\"\"\"%\"xGF*\"\"\"F)!\"\"!\"\"*&,&F%F**(F)F,F+F,-%$sinGF'F*F*F,F)F-
F**&%\"bGF*)F+\"\"#F,F*" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "
simplify(%);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,&*&%\"xG\"\"\"-%$sinG
6#*&%\"aG\"\"\"F%F,F,F,*&%\"bGF,)F%\"\"#F&F," }}}{PARA 0 "" 0 "" 
{TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 38 "Podemos realizar integral
es definidas:" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 
0 "" {MPLTEXT 1 0 15 "int(df,x=1..2);" }}{PARA 11 "" 1 "" {XPPMATH 20 
"6#,(-%$sinG6#,$%\"aG\"\"#F)%\"bG\"\"$-F%6#F(!\"\"" }}}{PARA 0 "" 0 "
" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 41 "E incluso integrales mu
cho m\341s complejas:" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 
0 "> " 0 "" {MPLTEXT 1 0 13 "f:=exp(-x^2);" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#>%\"fG-%$expG6#,$*$)%\"xG\"\"#\"\"\"!\"\"" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 9 "Int(f,x);" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#-%$IntG6$-%$expG6#,$*$)%\"xG\"\"#\"\"\"!\"\"F," }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 9 "value(%);" }}{PARA 11 "" 1 "
" {XPPMATH 20 "6#,$*&-%%sqrtG6#%#PiG\"\"\"-%$erfG6#%\"xG\"\"\"#F.\"\"#
" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 89 "En c
aso que Maple V no sepa resolver simb\363licamente la integral, podemo
s usar el comando " }{TEXT 287 5 "evalf" }{TEXT -1 40 " para obtener u
na aproximaci\363n num\351rica." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 22 "int(exp(-x^3),x=0..1);" }}
{PARA 11 "" 1 "" {XPPMATH 20 "6#-%$intG6$-%$expG6#,$*$)%\"xG\"\"$\"\"
\"!\"\"/F,;\"\"!\"\"\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 9 "ev
alf(%);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"+@=6v!)!#5" }}}{PARA 0 "
" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 24 "Estudiemos otro ej
emplo:" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 19 "f:=exp(-a*t)*ln(t);" }}{PARA 11 "" 1 "" {XPPMATH 20 "
6#>%\"fG*&-%$expG6#,$*&%\"aG\"\"\"%\"tGF,!\"\"F,-%#lnG6#F-F," }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 21 "int(f,t=0..infinity);" }}
{PARA 6 "" 1 "" {TEXT -1 68 "Definite integration: Can't determine if \+
the integral is convergent." }}{PARA 6 "" 1 "" {TEXT -1 30 "Need to kn
ow the sign of --> a" }}{PARA 6 "" 1 "" {TEXT -1 57 "Will now try inde
finite integration and then take limits." }}{PARA 11 "" 1 "" {XPPMATH 
20 "6#-%&limitG6$,$*&,**&-%$expG6#,$*&%\"aG\"\"\"%\"tGF0!\"\"F0-%#lnG6
#F1F0F0-%#EiG6$F0F.F0%&gammaGF0-F46#F/F0\"\"\"F/!\"\"F2/F1%)infinityG
" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 135 "Vem
os c\363mo la soluci\363n simb\363lica consiste en un l\355mite, cuyo \+
valor final depende de los distintos valores que puede tomar el par
\341metro " }{TEXT 288 1 "a" }{TEXT -1 53 ". Si asumimos ciertas condi
ciones sobre el par\341metro " }{TEXT 289 1 "a" }{TEXT -1 45 ", podemo
s obtener una expresi\363n m\341s concreta:" }}{PARA 0 "" 0 "" {TEXT 
-1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "assume(a>0);" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 21 "int(f,t=0..infinity);" }}
{PARA 11 "" 1 "" {XPPMATH 20 "6#,&*&-%#lnG6#%#a|irG\"\"\"F(!\"\"!\"\"*
&%&gammaGF)F(F*F+" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" 
{TEXT 291 12 "Observaci\363n:" }{TEXT -1 38 " El s\355mbolo ~ indica q
ue el par\341metro " }{TEXT 290 1 "a" }{TEXT -1 104 " tiene en su memo
ria ciertas suposiciones. Para eliminar las posibles suposiciones que \+
tenga el s\355mbolo " }{TEXT 292 1 "a" }{TEXT -1 18 " debemos escribir
:" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 7 "a:='a';" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"aGF$" }
}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{SECT 1 {PARA 5 "" 0 "" {TEXT -1 
24 "Ecuaciones Diferenciales" }}{PARA 0 "" 0 "" {TEXT -1 85 "Maple V p
uede resolver ecuaciones diferenciales ordinarias simb\363lica y num
\351ricamente:" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 
0 "" {MPLTEXT 1 0 26 "dsolve(diff(y(x),x)=y(x));" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#/-%\"yG6#%\"xG*&%$_C1G\"\"\"-%$expGF&F*" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 44 "edsist:=diff(y(x),x)=z(x),diff(z(x)
,x)=y(x);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%'edsistG6$/-%%diffG6$-%
\"yG6#%\"xGF--%\"zGF,/-F(6$F.F-F*" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 43 "dsolve(\{edsist,y(0)=0,z(0)=1\},\{y(x),z(x)\});" }}
{PARA 11 "" 1 "" {XPPMATH 20 "6#<$/-%\"yG6#%\"xG,&-%$expGF'#\"\"\"\"\"
#-F+6#,$F(!\"\"#F2F./-%\"zGF',&F/F,F*F," }}}{PARA 0 "" 0 "" {TEXT -1 
0 "" }}{PARA 0 "" 0 "" {TEXT -1 25 "Las opciones del comando " }{TEXT 
293 6 "dsolve" }{TEXT -1 147 " permiten especificar tres posibles meto
dolog\355as para resolver ecuaciones diferenciales: m\351todos num\351
ricos, m\351todos de series y m\351todos de Laplace:" }}{PARA 0 "" 0 "
" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 64 "ecuac:=\{d
iff(y(t),t)=x(t)+y(t),diff(x(t),t)=y(t),x(0)=2,y(0)=1\};" }}{PARA 11 "
" 1 "" {XPPMATH 20 "6#>%&ecuacG<&/-%%diffG6$-%\"yG6#%\"tGF-,&-%\"xGF,
\"\"\"F*F1/-F(6$F/F-F*/-F06#\"\"!\"\"#/-F+F7F1" }}}{EXCHG {PARA 0 "> \+
" 0 "" {MPLTEXT 1 0 47 "result:=dsolve(ecuac,\{x(t),y(t)\},type=numeri
c);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%'resultGR6#%(rkf45_xG6'%\"iG%
(rkf45_sG%)outpointG%#r1G%#r2G6#%aoCopyright~(c)~1993~by~the~Universit
y~of~Waterloo.~All~rights~reserved.G6\"C&>8&-%&evalfG6#9$@$52-%$absG6#
,$F3!\"\"-F<6#,&&%,loc_controlG6#\"\"#\"\"\"F3F?4-%'memberG6$&FD6#\"\"
'<*F?FG!\"#FF$FG\"\"!$F?FR$FPFR$FFFRC%>FD-%%copyG6#=F06#;FG\"#LE\\[lB
\"#EFR\"#IFR\"\"($FG!\"*\"#@FQ\"#?FU\"#9FR\"#BFR\"\"$FR\"#5FR\"\")\"&+
+$\"#FFR\"#:FR\"#DFR\"#GFR\"#8FR\"#AFRFFFR\"#7FR\"#KFR\"#<FR\"\"%$FG!
\")FGFF\"#HFR\"#;FR\"\"*\"%+5\"#=FR\"#JFRFNFGFhnFR\"#CFR\"#6FR\"\"&Fap
\"#>FR>%'loc_y0G-FY6#=F06#;FGFFE\\[l#FFFQFGFU>%'loc_y1G-FY6#=F0FbqE\\[
l!@$0F;FRC$>&FD6#FcoF3@%1%'DigitsG-%'evalhfG6#FcrC$>8%-%*traperrorG6#-
Fer6#-%=dsolve/numeric_solnall_rkf45G6,%&loc_FG-%$varG6#FD-Fds6#F^q-Fd
s6#Ffq-Fds6#%'loc_F1G-Fds6#%'loc_F2G-Fds6#%'loc_F3G-Fds6#%'loc_F4G-Fds
6#%'loc_F5G-Fds6#%)loc_workG@$/Fir%*lasterrorGC%>8'-%+searchtextG6$.Fe
r-%(convertG6$-%#opG6$FG7#Fir%%nameG>8(-Fcu6$.%)hardwareGFfu@%50FauFR0
F_vFR-F`s6,FbsFDF^qFfqF\\tF_tFbtFetFhtF[u-%&ERRORG6#FirFhv7$/%\"tGF7-%
$seqG6$/&%$ordG6#,&8$FGFGFG&F^q6#Fhw/FhwFcqF06%FDF^qFfqF0" }}}{PARA 0 
"" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 188 "El resultado es \+
un procedimiento de Maple (es decir, una funci\363n implementada con l
enguaje de programaci\363n de Maple) que puede ser representado gr\341
ficamente o evaluado en puntos concretos:" }}{PARA 0 "" 0 "" {TEXT -1 
0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 10 "result(0);" }}{PARA 
11 "" 1 "" {XPPMATH 20 "6#7%/%\"tG\"\"!/-%\"xG6#F%$\"\"#F&/-%\"yGF*$\"
\"\"F&" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 10 "result(1);" }}
{PARA 11 "" 1 "" {XPPMATH 20 "6#7%/%\"tG\"\"\"/-%\"xG6#F%$\"1X[C*oo@e&
!#:/-%\"yGF*$\"1%z5r8\"*o#yF-" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 
0 7 "result;" }}{PARA 11 "" 1 "" {TEXT -1 0 "" }}}{PARA 0 "" 0 "" 
{TEXT -1 0 "" }}}{SECT 1 {PARA 5 "" 0 "" {TEXT -1 21 "Desarrollos de T
aylor" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 8 "restart;" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "
" 0 "" {TEXT -1 81 "Vamos a calcular la aproximaci\363n de Taylor de o
rden 6 en x = 0 de cierta funci\363n:" }}{PARA 0 "" 0 "" {TEXT -1 0 "
" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 19 "f:=sin(4*x)*cos(x);" }}
{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"fG*&-%$sinG6#,$%\"xG\"\"%\"\"\"-%$
cosG6#F*F," }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 21 "fs1:=taylor(f
,x=0,6);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%$fs1G++%\"xG\"\"%\"\"\"#
!#Q\"\"$\"\"$#\"$@%\"#I\"\"&-%\"OG6#\"\"\"\"\"'" }}}{PARA 0 "" 0 "" 
{TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 69 "Podemos comparar la funci
\363n inicial con la aproximaci\363n gr\341ficamente:" }}{PARA 0 "" 0 
"" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 93 "plot(\{f,
convert(fs1,polynom)\},x=-1..1,-2..2,title=`sin(4x) cos(x) vs. Desarro
llo de Taylor`);" }}{PARA 13 "" 1 "" {GLPLOT2D 400 300 300 {PLOTDATA 
2 "6'-%'CURVESG6$7in7$$!\"\"\"\"!$\"1cj,L8-*3%!#;7$$!1nmm;p0k&*F-$\"1G
Gwz(zFk$F-7$$!1LL$3<XZ=*F-$\"1jY\"\\N@33$F-7$$!1nmmT%p\"e()F-$\"1d#=!*
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"" }}{PARA 0 "" 0 "" {TEXT -1 78 "El orden del desarrollo de Taylor pu
ede especificarse como opci\363n del comando " }{TEXT 294 6 "taylor" }
{TEXT -1 34 " o bien usando la variable global " }{TEXT 295 5 "Order" 
}{TEXT -1 89 ". Cambiaremos el orden, y estudiaremos c\363mo var\355a \+
el gr\341fico con esta nueva aproximaci\363n:" }}{PARA 0 "" 0 "" 
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