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-1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "" 11 260 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 }1 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 } {PSTYLE "" 0 261 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 } 3 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "" 0 262 1 {CSTYLE "" -1 -1 " " 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 }3 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 } {PSTYLE "" 0 263 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 } 3 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }} {SECT 0 {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 256 "" 0 "" {TEXT 256 14 "ABC do Maple V" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 257 "" 0 " " {TEXT 258 9 "Ma To Fu " }}{PARA 259 "" 0 "" {TEXT 257 15 "LabMAC-UEM 1998" }}{PARA 258 "" 0 "" {TEXT 259 26 "(www.geocities.com/cnumap)" } }{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }} {PARA 0 "" 0 "" {TEXT 294 35 "This text is written in Portuguese." }} {PARA 0 "" 0 "" {TEXT 264 75 "Clique no \355cone [+] para abrir os Cap \355tulos e em [-] para fechar os mesmos." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{SECT 1 {PARA 3 "" 0 "" {TEXT -1 12 "Apresenta\347\343o" }} {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 1 "O" }{TEXT 261 1 " " }{TEXT -1 7 "Maple V" }{TEXT 260 1 " " }{TEXT -1 360 "\351 u m sistema de computa\347\343o alg\351brica bastante popular nos meios \+ acad\352micos e cient\355ficos. Similarmente ao sistema Mathematica, \+ \351 capaz de efetuar opera\347\365es simb\363licas e c\341lculos comp lexos de uma maneira simples e tamb\351m possui recursos para programa \347\343o. H\341 contudo algumas limita\347\365es para c\341lculos num \351ricos de grande porte, onde o Fortran continua a imperar. " }} {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 495 "Nestas n otas apresentamos apenas um pequeno tutorial dos comandos b\341sicos d o Maple V. O objetivo \351 tornar o leitor capaz de fazer c\341lculos \+ simples e programa\347\343o elementar, bem como plotar gr\341ficos 2D \+ e 3D. Esperamos que o leitor, ap\363s ter utilizado estas notas, sint a-se encorajado a explorar por si mesmo as outras possibilidades do Ma ple V. Os interessados em t\363picos avan\347ados tais como \301lgebra Linear, Equa\347\365es Diferencias, Progama\347\343o Linear ou Estat \355stica, poder\343o encontrar refer\352ncias e " }{TEXT 295 5 "links " }{TEXT -1 21 " no final do texto. " }}{PARA 0 "" 0 "" {TEXT -1 0 " " }}{PARA 0 "" 0 "" {TEXT -1 24 "Este texto \351 uma vers\343o " } {TEXT 263 12 "simplificada" }{TEXT -1 19 " e adaptada para a " }{TEXT 491 9 "Release 4" }{TEXT -1 424 " das notas de minicursos realizados p elo autor na Universidade Estadual de Maring\341 entre 1993 e 1997, e \+ no Laborat\363rio Nacional de Computa\347\343o Cient\355fica (LNCC/CNP q) em 1995. O autor aproveita para agradecer os professores Doherty An drade (Maring\341) e Jaime Mu\361oz Rivera (Rio de Janeiro) pelas suge st\365es e corre\347\365es apresentadas. O autor tamb\351m agradece a \+ hospitalidade do LNCC (Petr\363polis) onde estas notas foram preparada s. " }}{PARA 0 "" 0 "" {TEXT -1 1 " " }}{PARA 0 "" 0 "" {TEXT -1 22 "P etr\363polis, 18/12/98. " }}{PARA 0 "" 0 "" {TEXT -1 26 "(modificado e m 24/01/2000)" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{SECT 1 {PARA 3 "" 0 "" {TEXT -1 18 "1 Primeiros Passos" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT 262 156 "Nesta primeira parte, atrav\351s de e xemplos, discutiremos alguns comandos que s\343o absolutamente indispe ns\341veis. Toda instru\347\343o Maple inicia-se ap\363s o sinal ( " } {TEXT 386 1 ">" }{TEXT 387 25 ") e termina com o sinal (" }{TEXT 265 1 " " }{TEXT 383 1 ";" }{TEXT 267 1 " " }{TEXT 266 8 ") ou ( " } {TEXT 384 1 ":" }{TEXT 385 3 "). " }}{PARA 0 "" 0 "" {TEXT -1 0 "" }} {PARA 0 "" 0 "" {TEXT -1 70 "As opera\347\365es aritm\351ticas b\341si cas s\343o feitas com os seguintes s\355mbolos:" }}{PARA 0 "" 0 "" {TEXT 269 6 " +" }{TEXT -1 17 " (adi\347\343o) " }{TEXT 0 1 "-" }{TEXT -1 20 " (subtra\347\343o) " }{TEXT 0 1 "*" }{TEXT -1 24 " (multiplica\347\343o) " }{TEXT 0 1 "/" }{TEXT -1 18 " ( divis\343o) " }{TEXT 0 1 "^" }{TEXT -1 15 " (pot\352ncia\347 \343o)." }}{PARA 0 "" 0 "" {TEXT 268 169 "A multiplica\347\343o e divi s\343o s\343o efetuadas antes da adi\347\343o e subtra\347\343o e pot \352ncias s\343o efetuadas antes da multiplica\347\343o. Para evitar c onfus\365es podemos utilizar par\352nteses " }{TEXT 492 2 "()" }{TEXT 493 42 " para agrupar express\365es. Por\351m colchetes " }{TEXT 388 2 "[]" }{TEXT 273 10 " e chaves " }{TEXT 389 2 "\{\}" }{TEXT 390 40 " \+ n\343o devem ser utilizados para este fim." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT 275 18 "Opera\347\365es B\341sicas " } }{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 6 "5*3+9;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"#C" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 6 "3^2*2;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6# \"#=" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 19 "(11*4^5)/(-5+14*3); " }}{PARA 11 "" 1 "" {XPPMATH 20 "6##\"&k7\"\"#P" }}}{EXCHG {PARA 0 " " 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 70 "Vejamos o que acon tece quando esquecemos o sinal de ponto e v\355rgula ( " }{TEXT 270 1 ";" }{TEXT -1 3 " )." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 3 "2*3" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 0 " " }}{PARA 7 "" 1 "" {TEXT -1 50 "Warning, incomplete statement or miss ing semicolon" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 50 "O sistema reclama em azul dizendo que a instru\347\343 o " }{TEXT 494 3 "2*3" }{TEXT -1 99 " est\341 incompleta ou que falta \+ um ponto e v\355rgula. Neste caso devemos voltar e corrigir o problema . " }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT 276 23 "A Representa\347\343o Decimal" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 23 "Podemos usar o comando " }{TEXT 271 5 "evalf" }{TEXT -1 146 " (avaliar com ponto flutuante) para se obter uma representa\347 \343o decimal de um n\372mero. Normalmente, o sistema utiliza dez alga rismos significativos." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "evalf(176/47);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"+^3oWP!\"*" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 11 "25*sqrt(2);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,$*$\"\"##\"\"\"F %\"#D" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 9 "evalf(\");" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#$\"+0R`NN!\")" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 11 "As aspas ( " }{TEXT 393 1 "\"" }{TEXT -1 14 " ) significam " }{TEXT 272 13 "o valor acima " }{TEXT -1 59 ". Assim, no exemplo anterior, as aspas representam o v alor " }{XPPEDIT 18 0 "25*sqrt(2)" "*&\"#D\"\"\"-%%sqrtG6#\"\"#F$" } {TEXT -1 12 ". O comando " }{TEXT 392 4 "sqrt" }{TEXT -1 2 " (" } {TEXT 274 11 "square root" }{TEXT -1 61 ") \351 destinado para o c\341 lculo da raiz quadrada. A precis\343o do " }{TEXT 495 5 "evalf" } {TEXT -1 75 " pode ser modificada arbitrariamente. Abaixo veremos o va lor aproximado de " }{XPPEDIT 18 0 "Pi" "I#PiG6\"" }{TEXT -1 3 " ( " } {TEXT 391 2 "Pi" }{TEXT -1 36 " ) com 30 algarismos significativos." } }{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 13 "evalf(Pi,30);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"?G$QVEYQKz*e `EfTJ!#H" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT 277 25 "Atribuindo Letras e Nomes" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 155 "Nos trabalhos mais compl exos \351 importante podermos representar por letras express\365es com plicadas. No Maple esta representa\347\343o \351 feita atrav\351s do s \355mbolo ( " }{TEXT 395 2 ":=" }{TEXT -1 24 " ). A regra \351 simples : " }{TEXT 394 6 "A := B" }{TEXT -1 69 " significa que o lado direito (B) \351 a defini\347\343o do lado esquerdo (A)." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 16 "A1 := x*sqr t(7);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#A1G*&%\"xG\"\"\"\"\"(#F'\" \"#" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 5 "A1^2;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,$*$%\"xG\"\"#\"\"(" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT 278 21 "Opera\347\365es Simb\363licas " }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 120 "Uma das vantagens da computa\347\343o alg\351brica \351 \+ a capacidade de se fazer c\341lculos simb\363licos. Veremos a seguir o s comandos " }{TEXT 396 6 "expand" }{TEXT -1 14 " (expandir), " } {TEXT 397 6 "factor" }{TEXT -1 13 " (fatorar) e " }{TEXT 398 8 "simpli fy" }{TEXT -1 16 " (simplificar)." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }} }{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 32 "A2 := (x^3*y+x^3-y^4-y^3)/( y+1);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#A2G*&,**&%\"xG\"\"$%\"yG\" \"\"F+*$F(F)F+*$F*\"\"%!\"\"*$F*F)F/F+,&F*F+F+F+F/" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 13 "simplify(A2);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,&*$%\"yG\"\"$!\"\"*$%\"xGF&\"\"\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 15 "A3:=factor(A2);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>% #A3G*&,&%\"xG\"\"\"%\"yG!\"\"F(,(*$F'\"\"#F(*&F'F(F)F(F(*$F)F-F(F(" }} }{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 11 "expand(A3);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,&*$%\"yG\"\"$!\"\"*$%\"xGF&\"\"\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" } }{PARA 0 "" 0 "" {TEXT 281 19 "Fun\347\365es Elementares" }}{PARA 0 " " 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 101 "No Maple as fun\347\365es elementares j\341 est \343o pr\351-definidas, como por exemplo, as fun\347\365es trigonom \351tricas " }{TEXT 399 3 "sin" }{TEXT -1 9 " (seno), " }{TEXT 400 3 " cos" }{TEXT -1 14 " (cosseno) e " }{TEXT 401 3 "tan" }{TEXT -1 59 " ( tangente). A fun\347\343o logar\355tmo natural \351 representada por \+ " }{TEXT 402 2 "ln" }{TEXT -1 43 " e a fun\347\343o exponencial \351 r epresentada por " }{TEXT 403 3 "exp" }{TEXT -1 23 ". A constante de Eu ler " }{TEXT 279 1 "e" }{TEXT 280 1 " " }{TEXT -1 16 "\351 definida po r " }{TEXT 404 6 "exp(1)" }{TEXT -1 26 ". Vejamos alguns exemplos." } }{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "expand(cos(x+y));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,&*&-%$cosG 6#%\"xG\"\"\"-F&6#%\"yGF)F)*&-%$sinGF'F)-F/F+F)!\"\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "evalf(exp(1),25);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\":(Gg`BX!f%G=G=F!#C" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 13 "exp(ln(xyz));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#%$xy zG" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT 282 17 "Definindo Fun\347\365es " }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 86 "Vamos agora definir fun\347\365es. A maneira mais simples de se definir uma fun\347\343o \351 assim: " }} {PARA 262 "" 0 "" {TEXT 405 6 "f := (" }{TEXT 406 11 " vari\341veis " }{TEXT 407 6 ") -> (" }{TEXT 408 30 " express\343o contendo vari\341ve is " }{TEXT 409 1 ")" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 24 "f := x -> sin(x)*cos(x);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"fG:6#%\"xG6\"6$%)operatorG%&arrowGF(*&-%$sinG6 #9$\"\"\"-%$cosGF/F1F(F(" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 5 " f(z);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#*&-%$sinG6#%\"zG\"\"\"-%$cosG F&F(" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "f(Pi/4);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6##\"\"\"\"\"#" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 13 "g := exp + f;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\" gG,&%$expG\"\"\"%\"fGF'" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 6 "g (-x);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,&-%$expG6#,$%\"xG!\"\"\"\"\" *&-%$sinG6#F(F*-%$cosGF.F*F)" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 24 "h := (x,y) -> x^2-5*y^3;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\" hG:6$%\"xG%\"yG6\"6$%)operatorG%&arrowGF),&*$9$\"\"#\"\"\"*$9%\"\"$!\" &F)F)" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 7 "h(s,t);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,&*$%\"sG\"\"#\"\"\"*$%\"tG\"\"$!\"&" }}} {EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 94 "Fu n\347\365es definidas por duas ou mais express\365es podem ser definid as com o uso de procedimentos " }{TEXT 410 4 "proc" }{TEXT -1 76 ". V eremos um exemplo no Cap\355tulo 4 onde estudaremos a programa\347\343 o em Maple. " }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT 283 32 "Resolu\347\343o de Equa\347\365es e Sistemas" }} {PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" } }{PARA 0 "" 0 "" {TEXT -1 10 "O comando " }{TEXT 411 5 "solve" }{TEXT -1 107 " (resolver), serve para resolver equa\347\365es diversas. No e xemplo abaixo resolveremos uma equa\347\343o na vari\341vel " }{TEXT 284 1 "x" }{TEXT -1 2 ". " }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 23 "equa1 := x^3+3*x^2-4=0;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%&equa1G/,(*$%\"xG\"\"$\"\"\"*$F(\"\"#F)!\" %F*\"\"!" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 13 "solve(equa1);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6%\"\"\"!\"#F$" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 103 "Quando a equa\347 \343o possui mais de uma vari\341vel, \351 fundamental indicar ao sist ema a inc\363gnita do problema." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "equa2 := 2*x+y=0;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%&equa2G/,&%\"xG\"\"#%\"yG\"\"\"\"\"!" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 16 "solve(equa2, x);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,$%\"yG#!\"\"\"\"#" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 16 "solve(equa2, y);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,$%\"xG!\"#" }}}{EXCHG {PARA 260 "" 1 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 10 "O comando " }{TEXT 412 5 "solve" }{TEXT -1 57 " resolve tamb\351m equa\347\365es com ra\355zes complexas. A letra ( \+ " }{TEXT 413 1 "I" }{TEXT -1 57 " ) representa a unidade imagin\341ria dos n\372meros complexos." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 15 "solve(z^2+1,z);" }}{PARA 11 "" 1 " " {XPPMATH 20 "6$%\"IG,$F#!\"\"" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 13 "Se o comando " }{TEXT 414 5 "solve" }{TEXT -1 92 " n\343o conseguir apresentar exatamente as ra\355zes de sejadas, podemos ent\343o executar o comando " }{TEXT 415 6 "fsolve" } {TEXT -1 65 " (resolver com ponto flutuante) para se obter ra\355zes a proximadas." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 27 "equa3 := x^6 - 2*x^2 + 2*x;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%&equa3G,(*$%\"xG\"\"'\"\"\"*$F'\"\"#!\"#F'F+" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 15 "solve(equa3,x);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6$\"\"!-%'RootOfG6#,(*$%#_ZG\"\"&\"\"\"F)!\"#\"\" #F+" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 16 "fsolve(equa3,x);" }} {PARA 11 "" 1 "" {XPPMATH 20 "6$\"\"!$!+7,Vk8!\"*" }}}{EXCHG {PARA 0 " " 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 32 "Por quest\365es pr \341ticas, a fun\347\343o " }{TEXT 416 6 "fsolve" }{TEXT -1 78 " n \343o mostra automaticamente as ra\355zes complexas. \311 preciso adic ionar a op\347\343o " }{TEXT 417 7 "complex" }{TEXT -1 1 "." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 24 "f solve(equa3,x,complex);" }}{PARA 12 "" 1 "" {XPPMATH 20 "6(\"\"!$!+7,V k8!\"*,&$!+\\ggH>!#5\"\"\"%\"IG$!+uv\"*o7F&,&F(F+F,$\"+uv\"*o7F&,&$\"+ 4mv^()F*F+F,$!+c8A>NF*,&F3F+F,$\"+c8A>NF*" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 13 "Os comandos " }{TEXT 418 6 "solve " }{TEXT -1 2 "e " }{TEXT 419 6 "fsolve" }{TEXT -1 57 " \+ tamb\351m funcionam com sistemas. A sintaxe \351 a seguinte: " }} {PARA 263 "" 0 "" {TEXT 420 9 "solve( \{ " }{TEXT -1 8 "equa\347\365es " }{TEXT 422 5 " \},\{ " }{TEXT -1 10 "inc\363gnitas" }{TEXT 421 4 " \+ \} )" }{TEXT -1 1 "." }}{PARA 0 "" 0 "" {TEXT -1 32 "Observe a utiliza \347\343o das chaves " }{TEXT 423 2 "\{\}" }{TEXT -1 55 " para represe ntar conjunto de equa\347\365es e de inc\363gnitas." }}{PARA 0 "" 0 " " {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 27 "equa4 := \+ x + 2*y + 3*z = 7;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%&equa4G/,(%\"x G\"\"\"%\"yG\"\"#%\"zG\"\"$\"\"(" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 24 "equa5 := 5*x - 2*y = 12;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%&equa5G/,&%\"xG\"\"&%\"yG!\"#\"#7" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 28 "equa6 := 2*x - y + 3*z = -6;" }}{PARA 11 " " 1 "" {XPPMATH 20 "6#>%&equa6G/,(%\"xG\"\"#%\"yG!\"\"%\"zG\"\"$!\"'" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 46 "sol := solve( \{equa4,equ a5,equa6\} , \{x,y,z\} );" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%$solG<% /%\"xG#\"#i\"#8/%\"zG#!$D\"\"#R/%\"yG#\"#xF*" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "evalf(sol,13);" }}{PARA 11 "" 1 "" {XPPMATH 20 " 6#<%/%\"xG$\".J#p2BpZ!#7/%\"zG$!.G^?G^?$F(/%\"yG$\".xI#p2BfF(" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT 285 24 "Opera\347\365es com Polin\364m ios" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 112 "Em computa\347\343o alg\351bri ca tamb\351m podemos operar polin\364mios simbolicamente. Consideremos os dois polin\364mios abaixo." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 35 "p := x^4 - x^3 - 10*x^2 + 10 *x + 6;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"pG,,*$%\"xG\"\"%\"\"\"* $F'\"\"$!\"\"*$F'\"\"#!#5F'\"#5\"\"'F)" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 25 "q := x^3 - 4*x^2 + x + 6;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"qG,**$%\"xG\"\"$\"\"\"*$F'\"\"#!\"%F'F)\"\"'F)" }}} {EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 11 "Es crevendo " }{TEXT 286 1 "p" }{TEXT -1 1 "(" }{TEXT 287 1 "x" }{TEXT -1 20 ") em fatores primos:" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 10 "factor(p);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#*&,&%\"xG\"\"\"!\"$F&F&,**$F%\"\"$F&*$F%\"\"#F,F%!\" %!\"#F&F&" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 10 "Dividindo " }{TEXT 288 1 "p" }{TEXT -1 1 "(" }{TEXT 289 1 "x" }{TEXT -1 7 ") por " }{TEXT 290 1 "q" }{TEXT -1 1 "(" }{TEXT 291 1 "x" }{TEXT -1 2 "):" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 4 "p/q;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#*&,,*$%\"xG\"\"%\"\"\"*$F&\"\"$!\"\"*$F&\"\"#!#5F&\"#5\"\"'F(F(, *F)F(F,!\"%F&F(F0F(F+" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }} {PARA 0 "" 0 "" {TEXT -1 56 "Normalizando (simplificando) a express \343o racional acima:" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 10 "normal(\");" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#*&,**$%\"xG\"\"$\"\"\"*$F&\"\"#F*F&!\"%!\"#F(F(,(F)F(F& !\"\"F,F(F." }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 " " {TEXT -1 71 "Ainda podemos converter a express\343o racional acima e m fra\347\365es parciais:" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 25 "convert(p/q, parfrac, x);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,*%\"xG\"\"\"\"\"$F%*$,&F$F%F%F%!\"\"F)*$,&F $F%!\"#F%F)\"\"#" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}} {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT 326 17 "Comandos Diversos" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 82 "Agora veremos mais alguns comandos que poder\343o ser \372teis. Observe que o s\355mbolo ( " } {TEXT 424 1 "#" }{TEXT 292 1 " " }{TEXT -1 86 ") \351 um sinal de come nt\341rio e o que vem depois n\343o \351 levado em considera\347\343o \+ pelo Maple." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 22 "33!; # fatorial de 33" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"F+++!G,W>=b\\')=\")=wJ$o)" }}}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 53 "ifactor(\"); # fatora\347\343o em primos do inteir o acima " }}{PARA 11 "" 1 "" {XPPMATH 20 "6#*8-%!G6#\"\"#\"#J-F%6#\" \"$\"#:-F%6#\"\"&\"\"(-F%6#F0\"\"%-F%6#\"#6F+-F%6#\"#8F'-F%6#\"#<\"\" \"-F%6#\"#>F=-F%6#\"#BF=-F%6#\"#HF=-F%6#F(F=" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 50 "gcd(34,51); # m\341ximo divisor comum entre 34 \+ e 51." }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"#<" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 51 "lcm(2,4,5); # m\355nimo m\372ltiplo comum entre 2,4 e 5." }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"#?" }}}{EXCHG {PARA 0 " > " 0 "" {MPLTEXT 1 0 47 "(3-5*I)*(1+I); # multiplicando dois complex os." }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,&\"\")\"\"\"%\"IG!\"#" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 63 "convert(90*degrees, radians) ; # convertendo graus em radianos." }}{PARA 11 "" 1 "" {XPPMATH 20 "6 #,$%#PiG#\"\"\"\"\"#" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 44 "max (1,-20,13); # m\341ximo entre 1, -20 e 13." }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"#8" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 61 "Sum( k^2, k=1..5); # com S (mai\372scula) indica uma somat\363ria. " }} {PARA 11 "" 1 "" {XPPMATH 20 "6#-%$SumG6$*$%\"kG\"\"#/F';\"\"\"\"\"&" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 59 "sum(k^2, k=1..5); # com \+ s (min\372scula) calcula a somat\363ria." }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"#b" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 55 "S10 := Sum(1/ k^2, k=1..infinity); # somat\363ria infinita." }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%$S10G-%$SumG6$*$%\"kG!\"#/F);\"\"\"%)infinityG" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 32 "value(S10); # value (valor \+ de)." }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,$*$%#PiG\"\"##\"\"\"\"\"'" }} }{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT 293 18 "Coment\341rios Finais" }} {PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" } }{PARA 0 "" 0 "" {TEXT -1 79 "Via de regra, Maple imprime (na tela) to dos resultados quando executados com ( " }{TEXT 425 1 ";" }{TEXT -1 93 " ). Se quisermos que o resultado seja calculado mas n\343o impress o, devemos ent\343o substituir ( " }{TEXT 426 1 ";" }{TEXT -1 9 " ) po r ( " }{TEXT 427 1 ":" }{TEXT -1 2 ")." }}{PARA 0 "" 0 "" {TEXT -1 0 " " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 35 "ano := 1998: # usamos \+ dois pontos." }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 " " {TEXT -1 98 "Observe que o Maple n\343o escreveu nada na tela. Mas o valor 1998 foi de fato atribu\355do \340 constante " }{TEXT 496 3 "an o" }{TEXT -1 2 ". " }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 4 "ano;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"%) *>" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 91 "Para se saber sobre outros comandos e fun\347\365es n\343o abor dados aqui, o leitor poder\341 executar " }{TEXT 428 9 "?contents" } {TEXT -1 17 " (no MapleVR4) e " }{TEXT 508 13 "?introduction" }{TEXT -1 196 " (no MapleVR5) . Em alguns casos podemos obter mais informa \347\365es sobre um assunto executando o s\355mbolo de interroga\347 \343o seguido do assunto. Por exemplo, para se saber sobre trigonometr ia executa-se " }{TEXT 429 5 "?trig" }{TEXT -1 3 ". " }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 5 "?trig" }} }{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{SECT 1 {PARA 3 "" 0 "" {TEXT -1 32 "2 C\341lculo Diferenci al e Integral" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 113 "Neste Cap\355tulo discutiremos alguns dos aspectos pr \341ticos do C\341lculo Diferencial e Integral de uma vari\341vel real . " }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 50 "Apr oveitamos para sugerir a utiliza\347\343o de comando " }{TEXT 430 7 "r estart" }{TEXT -1 184 " (reiniciar) que faz com que o sistema \"limpe \" a mem\363ria do Maple. Os s\355mbolos e letras j\341 atribu\355dos \+ anteriormente ficam tamb\351m liberados. \311 como (quase) se o Maple \+ fosse recarregado." }}{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 296 18 "Calculando Limites" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 " " {TEXT -1 46 "Os limites podem ser calculados com o comando " }{TEXT 431 5 "limit" }{TEXT -1 48 ", que pode ser aplicado \340s fun\347\365e s e express\365es." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 49 "f1 := x-> (x^2+5)/(x^3); # definindo uma f un\347\343o." }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#f1G:6#%\"xG6\"6$%)o peratorG%&arrowGF(*&,&*$9$\"\"#\"\"\"\"\"&F1F1F/!\"$F(F(" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 50 "limit(f1(x), x=1); # limite para \+ x tendendo a 1." }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"\"'" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 64 "limit(f1(x), x=infinity); # limit e para x tendendo a infinito." }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"\"! " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 55 "f2 := sin(x)/x; # def inindo uma express\343o contendo x." }}{PARA 11 "" 1 "" {XPPMATH 20 "6 #>%#f2G*&-%$sinG6#%\"xG\"\"\"F)!\"\"" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 12 "Observe que " }{XPPEDIT 18 0 "f 2" "I#f2G6\"" }{TEXT -1 82 " n\343o \351 uma fun\347\343o para o Maple , mas t\343o somente uma express\343o contendo a vari\341vel " }{TEXT 299 1 "x" }{TEXT -1 22 ". Portanto no comando " }{TEXT 432 5 "limit" } {TEXT -1 12 " escrevemos " }{TEXT 433 2 "f2" }{TEXT -1 7 " e n\343o " }{TEXT 434 5 "f2(x)" }{TEXT -1 2 ". " }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 15 "limit(f2, x=0);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"\"\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 37 "limit(f2(x),x=0); # n\343o faz sentido." }}{PARA 11 "" 1 "" {XPPMATH 20 "6#-%&limitG6$*&--%$sinG6#%\"xGF*\"\"\"-F+F*!\"\"/ F+\"\"!" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 62 "Para se calcular limites laterais basta acrescentar as op \347\365es " }{TEXT 435 4 "left" }{TEXT -1 16 " (esquerda) ou " } {TEXT 436 5 "right" }{TEXT -1 54 " (direita). Vejamos um exemplo com a fun\347\343o tangente " }{TEXT 437 3 "tan" }{TEXT -1 1 "." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 28 "l imit(tan(x), x=Pi/2, left);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#%)infin ityG" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 29 "limit(tan(x), x=Pi/ 2, right);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,$%)infinityG!\"\"" }}} {EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 72 "Se desejamos apenas indicar um limite, ent\343o podemos utilizar o coman do " }{TEXT 438 5 "Limit" }{TEXT -1 13 " com a letra " }{TEXT 300 1 "L " }{TEXT -1 32 " mai\372scula. A sintaxe \351 a mesma." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 32 "Limit( x^2*sin(1/x), x=0, right);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#-%&Limit G6%*&%\"xG\"\"#-%$sinG6#*$F'!\"\"\"\"\"/F'\"\"!%&rightG" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 9 "value(\");" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"\"!" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }} }{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT 297 20 "C\341lc ulo de Integrais" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 69 "As integrais indefin idas ou definidas s\343o obtidas atrav\351s do comando " }{TEXT 439 3 "int" }{TEXT -1 56 " (com letras min\372sculas). Tamb\351m podemos usa r o comando " }{TEXT 440 3 "Int" }{TEXT -1 12 " (com letra " }{TEXT 298 1 "i" }{TEXT -1 61 " mai\372scula) no caso de querermos a integra l apenas indicada." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 42 "f3 := x -> a*x^2; # definindo uma fun\347 \343o." }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#f3G:6#%\"xG6\"6$%)operato rG%&arrowGF(*&%\"aG\"\"\"9$\"\"#F(F(" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "Int(f3(x), x);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#-%$ IntG6$*&%\"aG\"\"\"%\"xG\"\"#F)" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "int(f3(x), x);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,$*&%\"aG\" \"\"%\"xG\"\"$#F&F(" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 13 "int( ln(x),x);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,&*&%\"xG\"\"\"-%#lnG6#F% F&F&F%!\"\"" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 " " {TEXT -1 93 "Para se calcular integrais definidas precisamos fornece r os limites de integra\347\343o. A nota\347\343o " }{TEXT 441 6 "x=a. .b" }{TEXT -1 17 " significa que o " }{TEXT 301 1 "x" }{TEXT -1 10 " v aria de " }{TEXT 302 1 "a" }{TEXT -1 5 " at\351 " }{TEXT 303 1 "b" } {TEXT -1 2 ". " }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> \+ " 0 "" {MPLTEXT 1 0 27 "\301rea := Int(f3(x), x=0..1);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%%|\\wreaG-%$IntG6$*&%\"aG\"\"\"%\"xG\"\"#/F+;\" \"!F*" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "value(\301rea);" } }{PARA 11 "" 1 "" {XPPMATH 20 "6#,$%\"aG#\"\"\"\"\"$" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 41 "f4 := 1/x^2; # definindo uma express \343o." }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#f4G*$%\"xG!\"#" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 23 "Int(f4, x=1..infinity);" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#-%$IntG6$*$%\"xG!\"#/F';\"\"\"%)infini tyG" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 9 "value(\");" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"\"\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 34 "Int(Int(x^2+y^2, x=1..2), y=0..3);" }}{PARA 11 "" 1 " " {XPPMATH 20 "6#-%$IntG6$-F$6$,&*$%\"xG\"\"#\"\"\"*$%\"yGF+F,/F*;F,F+ /F.;\"\"!\"\"$" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 9 "value(\"); " }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"#;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT 304 9 "Derivadas" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 105 "Existem \+ duas maneiras de se derivar fun\347\365es no Maple. Uma delas se faz c om o uso do operador diferencial " }{TEXT 442 1 "D" }{TEXT -1 42 ". Aq ui daremos exemplos atrav\351s da fun\347\343o " }{TEXT 443 4 "diff" } {TEXT -1 15 " (diferenciar)." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "f5 := x^2+sin(x);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#f5G,&*$%\"xG\"\"#\"\"\"-%$sinG6#F'F)" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "diff(f5, x);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,&%\"xG\"\"#-%$cosG6#F$\"\"\"" }}}{EXCHG {PARA 0 " > " 0 "" {MPLTEXT 1 0 42 "diff(f5, x,x); # derivando f5 duas vezes." }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,&\"\"#\"\"\"-%$sinG6#%\"xG!\"\"" }} }{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "f6 := x^3+y^2;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#f6G,&*$%\"xG\"\"$\"\"\"*$%\"yG\"\"#F)" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "diff(f6, x);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,$*$%\"xG\"\"#\"\"$" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "diff(f6, y);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,$%\" yG\"\"#" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 18 "diff(u(x)*v(x),x );" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,&*&-%%diffG6$-%\"uG6#%\"xGF+\" \"\"-%\"vGF*F,F,*&F(F,-F&6$F-F+F,F," }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT 305 16 "S\351ries de Taylor" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }} {EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 9 "A f un\347\343o " }{TEXT 444 6 "series" }{TEXT -1 115 " produz a s\351rie \+ de Taylor para fun\347\365es anal\355ticas. Em geral a resposta \351 d ada em termos de uma expans\343o de ordem 5." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 54 "T1 := series(exp( x), x=0); #expans\343o em torno de x=0." }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#T1G+1%\"xG\"\"\"\"\"!F'\"\"\"#F'\"\"#\"\"##F'\"\"'\"\"$#F'\"# C\"\"%#F'\"$?\"\"\"&-%\"OG6#F'\"\"'" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 54 "Em seguida vamos converter a pa rte principal da s\351rie " }{TEXT 313 2 "T1" }{TEXT -1 15 " num polin \364mio." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 29 "Poli := convert(T1, polynom);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%%PoliG,.\"\"\"F&%\"xGF&*$F'\"\"##F&F)*$F'\"\"$#F&\"\" '*$F'\"\"%#F&\"#C*$F'\"\"&#F&\"$?\"" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 33 "Podemos observar que o resultad o " }{TEXT 306 4 "Poli" }{TEXT -1 33 " acima \351 uma express\343o co ntendo " }{TEXT 307 1 "x" }{TEXT -1 52 ". Por\351m n\343o se trata de \+ uma fun\347\343o cujo argumento \351 " }{TEXT 308 1 "x" }{TEXT -1 23 " . Para transformar uma " }{TEXT 311 9 "express\343o" }{TEXT -1 10 " co ntendo " }{TEXT 309 1 "x" }{TEXT -1 10 " para uma " }{TEXT 312 6 "fun \347\343o" }{TEXT -1 4 " de " }{TEXT 310 1 "x" }{TEXT -1 18 " devemos \+ executar " }{TEXT 445 7 "unapply" }{TEXT -1 2 ". " }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 70 "f7 := unapp ly(Poli, x); #transforma o polin\364mio Poli numa fun\347\343o f7." }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#f7G:6#%\"xG6\"6$%)operatorG%&arro wGF(,.\"\"\"F-9$F-*$F.\"\"##F-F0*$F.\"\"$#F-\"\"'*$F.\"\"%#F-\"#C*$F. \"\"&#F-\"$?\"F(F(" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 10 "f7(1. 0); " }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"+nmm;F!\"*" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" } }{PARA 0 "" 0 "" {TEXT 497 21 "Equa\347\365es Diferenciais" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 158 "Resolver equa\347\365es diferenciais \351 uma \+ das principais tarefas da computa\347\343o cient\355fica. O assunto \+ \351 complexo e extenso. Aqui faremos alguns exemplos do comando " } {TEXT 498 6 "dsolve" }{TEXT -1 1 "." }}{PARA 0 "" 0 "" {TEXT -1 0 "" } }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 38 "ed1 := diff(y(t),t,t) + y( t) = sin(t);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%$ed1G/,&-%%diffG6$-F (6$-%\"yG6#%\"tGF/F/\"\"\"F,F0-%$sinGF." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 18 "dsolve(ed1, y(t));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6 #/-%\"yG6#%\"tG,**&-%$cosGF&\"\"\"F'F,#!\"\"\"\"#-%$sinGF&#F,F/*&%$_C1 GF,F0F,F,*&%$_C2GF,F*F,F," }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 29 "ed2 := diff(y(t),t) = y(t)^2;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#> %$ed2G/-%%diffG6$-%\"yG6#%\"tGF,*$F)\"\"#" }}}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 19 "dsolve(ed2, y(t)); " }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/*$-%\"yG6#%\"tG!\"\",&F(F)%$_C1G\"\"\"" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 117 "A maioria dos problem as de equa\347\365es diferenciais n\343o podem ser resolvidas analitic amente (de forma exata). O comando " }{TEXT 499 6 "dsolve" }{TEXT -1 107 " possui uma op\347\343o de solu\347\343o num\351rica. Como exempl o, resolveremos um problema de valor inicial n\343o linear. " }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 37 "e d3 := diff(y(t),t)+sin(y(t))=cos(t);" }}{PARA 11 "" 1 "" {XPPMATH 20 " 6#>%$ed3G/,&-%%diffG6$-%\"yG6#%\"tGF-\"\"\"-%$sinG6#F*F.-%$cosGF," }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 50 "yy := dsolve( \{ed3, y(0)=0 \}, y(t), type=numeric );" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#yyG:6# %(rkf45_xG6'%\"iG%(rkf45_sG%)outpointG%#r1G%#r2G6#%aoCopyright~(c)~199 3~by~the~University~of~Waterloo.~All~rights~reserved.G6\"C&>8&-%&evalf G6#9$@$52-%$absG6#,$F3!\"\"-F<6#,&&%,loc_controlG6#\"\"#\"\"\"F3F?4-%' memberG6$&FD6#\"\"'<*$FG\"\"!$F?FQ$!\"#FQF?FGFTFF$FFFQC%>FD-%%copyG6#= F06#;FG\"#EE\\[l;FGFG\"\"($FG!\"*\"#5FQ\"#?FQ\"#BFQ\"#=FQ\"\")\"&++$\" #;FQ\"#9FQ\"#8FQ\"\"*\"%+5\"#AFQ\"#@FQ\"#DFQ\"#>FQ\"\"&$FG!\")\"\"%F]p FhnFQ\"\"$FQ\"#7FQFFFQFNFG\"#%'loc_y0G-FY6#=F06# ;FGFGE\\[l\"FGFQ>%'loc_y1G-FY6#=F0F[qE\\[l!@$0F;FQC$>&FD6#F`pF3@%1%'Di gitsG-%'evalhfG6#F\\rC$>8%-%*traperrorG6#-F^r6#-%=dsolve/numeric_solna ll_rkf45G6,%&loc_FG-%$varG6#FD-F]s6#Fgp-F]s6#F_q-F]s6#%'loc_F1G-F]s6#% 'loc_F2G-F]s6#%'loc_F3G-F]s6#%'loc_F4G-F]s6#%'loc_F5G-F]s6#%)loc_workG @$/Fbr%*lasterrorGC%>8'-%+searchtextG6$.F^r-%(convertG6$-%#opG6$FG7#Fb r%%nameG>8(-F\\u6$.%)hardwareGF_u@%50FjtFQ0FhuFQ-Fir6,F[sFDFgpF_qFesFh sF[tF^tFatFdt-%&ERRORG6#FbrFav7$/%\"tGF7-%$seqG6$/&%$ordG6#,&8$FGFGFG& Fgp6#Faw/FawF\\qF06%FDFgpF_q" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 45 "Vejamos agora como se trabalha com a so lu\347\343o " }{TEXT 500 2 "yy" }{TEXT -1 33 " acima, que \351 de fato uma fun\347\343o." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 6 "yy(0);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#7$ /%\"tG\"\"!/-%\"yG6#F%F&" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 " yy(2.1);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#7$/%\"tG$\"#@!\"\"/-%\"yG6 #F%$\"1QB=n[!zE\"!#;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }} }{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT 314 12 "Notas F inais" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 54 "Neste cap\355tulo exploramos os seguintes comandos Maple:" }}{PARA 0 "" 0 "" {TEXT 446 63 " diff \+ int Int limit Limit series unapply dsolve" }}{PARA 0 "" 0 "" {TEXT -1 105 "Existem muitos outros comandos para o c\341lculo de d erivadas e integrais. Explore os tutoriais contidos em " }{TEXT 447 9 "?contents" }{TEXT -1 5 " ou " }{TEXT 509 13 "?introduction" }{TEXT -1 178 ", conforme o caso. Para se fazer trabalhos mais espec\355fico s com equa\347\365es diferenciais \351 fundamental consultar os textos especializados. O leitor poder\341 come\347ar por experimentar " } {TEXT 501 7 "?dsolve" }{TEXT -1 1 "." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{SECT 1 {PARA 3 "" 0 "" {TEXT -1 29 "3 Gr\341ficos em 2 e 3 Dimens\365es" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 " " {TEXT -1 83 "Os gr\341ficos de fun\347\365es de uma ou duas vari\341 veis s\343o produzidos atrav\351s das fun\347\365es " }{TEXT 448 4 "pl ot" }{TEXT -1 3 " e " }{TEXT 449 6 "plot3d" }{TEXT -1 80 ". Algumas ex press\365es de tr\352s vari\341veis podem ser plotadas utilizando-se a op\347\343o " }{TEXT 450 8 "implicit" }{TEXT -1 2 ". " }}{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 315 23 "Fun \347\365es de uma Vari\341vel" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }} {EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 20 "A \+ sintaxe b\341sica de " }{TEXT 451 4 "plot" }{TEXT -1 16 " \351 a segui nte: " }}{PARA 261 "" 0 "" {TEXT -1 1 " " }{TEXT 452 5 "plot(" } {TEXT -1 7 " fun\347\343o" }{TEXT 453 1 "," }{TEXT -1 7 "dom\355nio" } {TEXT 454 1 "," }{TEXT -1 15 " contra-dom\355nio" }{TEXT 455 1 "," } {TEXT -1 8 " op\347\365es " }{TEXT 456 1 ")" }{TEXT -1 1 "." }}{PARA 0 "" 0 "" {TEXT -1 24 "O dom\355nio de uma fun\347\343o " }{XPPEDIT 18 0 "f(x)" "-%\"fG6#%\"xG" }{TEXT -1 16 " \351 indicada por " } {XPPEDIT 18 0 "x=a..b" "/%\"xG;%\"aG%\"bG" }{TEXT -1 123 ". O uso do c ontra-dom\355nio n\343o \351 obrigat\363rio e serve para fazer um cont role vertical do gr\341fico. Entre as op\347\365es do comando " } {TEXT 458 4 "plot" }{TEXT -1 12 " usaremos o " }{TEXT 459 5 "title" } {TEXT -1 14 " (t\355tulo) , o " }{TEXT 460 5 "color" }{TEXT -1 11 " (c or) e o " }{TEXT 457 12 "discont=true" }{TEXT -1 33 " (fun\347\365es \+ com descontinuidades)." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 23 "plot(sin(2*x), x=0..4);" }}{PARA 13 "" 1 "" {INLPLOT "6%-%'CURVESG6$7^o7$\"\"!F(7$$\"1mmmm;')=()!#<$\"1 <71!\\[\\t\"!#;7$$\"1LLLe'40j\"F/$\"1x'F/7$$\"1LLLeF>(>%F/$\"1DkMnDoU uF/7$$\"1mmm\">K'*)\\F/$\"1(=GWE)[.%)F/7$$\"1*****\\Kd,\"eF/$\"1k1P2Y7 w\"*F/7$$\"1KLLe9XMiF/$\"1!R`)=Z**z%*F/7$$\"1mmm\"fX(emF/$\"1J#H(\\,k: (*F/7$$\"1LLL3!z;3(F/$\"1[U#=rY4))*F/7$$\"1*****\\U7Y](F/$\"1)y)yh\")f v**F/7$$\"1LL3F>8AxF/$\"1Y3VKL_'***F/7$$\"1mm;H9lRzF/$\"1Y$[JY@e%**F/7 $$\"1+++DI(yv)F/$\"1)G<-gSq$)*F/7$$\"1nmm;c0T\"*F/$\"1pu-ON^q'*F/7$$\" 1+++I,Q+5!#:$\"1STxUy!)*3*F/7$$\"1+++]*3q3\"F]q$\"1@G5\")H7N#)F/7$$\"1 +++q=\\q6F]q$\"1xgn?>!y<(F/7$$\"1nm;fBIY7F]q$\"1c_*e2/Q/'F/7$$\"1LLLj$ [kL\"F]q$\"1M8F/7$$\"1++]*o; G*RJ]F/7$$\"1LL$eDBJ\">F]q$!1\"e=s9\\SK'F/7$$\"1nmmTc-)*>F]q$!1ra$R[b@ a(F/7$$\"1mm;f`@'3#F]q$!1XM)fR,td)F/7$$\"1++]nZ)H;#F]q$!11g+NTki#*F/7$ $\"1LLe*HTW?#F]q$!1Zcg>T%Ha*F/7$$\"1mmmJy*eC#F]q$!1?^6#)znd(*F/7$$\"1L L$e[E()G#F]q$!1?F#yT*44**F/7$$\"1+++S^bJBF]q$!1b&f`]gy)**F/7$$\"1++D\" )[]_BF]q$!18D&ptF(****F/7$$\"1++]AYXtBF]q$!1t'3$[B/%***F/7$$\"1++vjVS% R#F]q$!1V\"3(**F/7$$\"1+++0TN:CF]q$!1yPb@W3I**F/7$$\"1++v3S*eX#F]q $!1:a\\Pz&=!)*F/7$$\"1++]7RV'\\#F]q$!1NO?n*H#4'*F/7$$\"1+++:#fke#F]q$! 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0 0 0 0 0 0 }}} {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT 319 15 "Plotando Pontos" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 204 "Em experimentos cient \355ficos \351 comum querermos plotar gr\341ficos a partir dos dados o btidos. Esses dados em geral vem em forma de um conjunto finito de pon tos. No Maple os dados s\343o inseridos com o comando " }{TEXT 507 3 "seq" }{TEXT -1 54 " (sequ\352ncias) ou simplesmente colocados em colc hetes " }{TEXT 467 2 "[]" }{TEXT -1 1 "." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 61 "Dados := [ [0,1], [1 ,1], [2,2], [3,2], [4,3], [5,3], [6,2] ];" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%&DadosG7)7$\"\"!\"\"\"7$F(F(7$\"\"#F+7$\"\"$F+7$\"\"% F-7$\"\"&F-7$\"\"'F+" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 38 "plo t(Dados); # sem par\342metros extras." }}{PARA 13 "" 1 "" {INLPLOT "6 #-%'CURVESG6$7)7$\"\"!$\"\"\"F(7$F)F)7$$\"\"#F(F-7$$\"\"$F(F-7$$\"\"%F (F07$$\"\"&F(F07$$\"\"'F(F--%'COLOURG6&%$RGBG$\"#5!\"\"F(F(" 2 374 374 374 2 0 1 0 2 9 0 4 2 1.000000 45.000000 45.000000 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 52 "plot(Dados, style=point, symbol=circle, color=bl ue);" }}{PARA 13 "" 1 "" {INLPLOT "6&-%'CURVESG6#7)7$\"\"!$\"\"\"F(7$F )F)7$$\"\"#F(F-7$$\"\"$F(F-7$$\"\"%F(F07$$\"\"&F(F07$$\"\"'F(F--%'COLO URG6&%$RGBGF(F($\"*++++\"!\")-%&STYLEG6#%&POINTG-%'SYMBOLG6#%'CIRCLEG " 2 374 374 374 5 4 1 0 2 6 0 4 2 1.000000 45.000000 45.000000 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT 318 13 "Notas Finais " }} {PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" } }{PARA 0 "" 0 "" {TEXT -1 135 "A produ\347\343o de gr\341ficos em 2D e 3D \351 um dos pontos fortes do Maple V. O leitor interessado n\343o deve deixar de consultar o tutorial em " }{TEXT 325 6 "?plots" } {TEXT -1 1 "." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 6 "?plots" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}} {SECT 1 {PARA 3 "" 0 "" {TEXT -1 20 "4 Programa\347\343o B\341sica" }} {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 164 "Atualmen te todos os sistemas de computa\347\343o alg\351brica possuem recursos para programa\347\343o. A estrutura b\341sica de programa\347\343o no Maple \351 derivado do Algol e do Pascal. " }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 356 "O nosso objetivo \351 apresent ar os elementos essenciais em programa\347\343o Maple de forma que o l eitor possa prosseguir por si mesmo para programas mais avan\347ados. \+ A nossa abordagem n\343o far\341 uso de nenhum conhecimento pr\351vio \+ em linguagens de programa\347\343o. Entretanto algum conhecimento em a lgoritmos matem\341ticos facilitar\341 a compreen\347\343o dos exemplo s apresentados." }}{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 327 29 "Comandos de Entradas e Sa\355das" }} {PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" } }{PARA 0 "" 0 "" {TEXT -1 184 "Um programa deve come\347ar por ler os \+ dados e terminar por escrever os resultados. Durante as sess\365es int erativas do Maple, a leitura de dados \351 feita atrav\351s do comando de atribui\347\343o ( " }{TEXT 357 2 ":=" }{TEXT -1 90 " ). Tabelas d e dados armazenados em arquivos tamb\351m podem ser lidas, com o uso d o comando " }{TEXT 358 4 "read" }{TEXT -1 10 ". Execute " }{TEXT 359 5 "?read" }{TEXT -1 29 " para se saber como funciona." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 52 "Os comandos espec\355f icos para escrever na tela s\343o o " }{TEXT 353 5 "print" }{TEXT -1 16 " (imprimir) e o " }{TEXT 354 6 "lprint" }{TEXT -1 48 ". Esses coma ndos possuem a seguinte estrutura: " }{TEXT 355 6 "print(" }{TEXT -1 1 " " }{TEXT 515 10 "express\343o1" }{TEXT 360 1 "," }{TEXT -1 1 " " } {TEXT 516 10 "express\343o2" }{TEXT 361 1 "," }{TEXT -1 2 " " }{TEXT 517 6 "etc..." }{TEXT -1 1 " " }{TEXT 362 1 ")" }{TEXT -1 123 ". As e xpress\365es podem ser valores num\351ricos ou coment\341rios. Em caso de coment\341rios, esses devem estar entre aspa simples (" }{TEXT 376 1 "`" }{TEXT -1 3 "). " }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 45 "print(`O valor do pi \351 quase`, e valf(Pi,17));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6$%6O~valor~do~pi~|dy~q uaseG$\"2Kz*e`EfTJ!#;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 9 "m : = 2*x;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"mG,$%\"xG\"\"#" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 25 "print(`O cubo m \351`, m^3); " }}{PARA 11 "" 1 "" {XPPMATH 20 "6$%+O~cubo~m~|dyG,$*$%\"xG\"\"$\"\") " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 44 "lprint(`O cubo m \351`, m^3); # usando lprint." }}{PARA 6 "" 1 "" {TEXT -1 18 "O cubo m \351 8*x^3" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 10 "O comando " }{TEXT 363 6 "lprint" }{TEXT -1 30 " possui a mesma sintaxe que o " }{TEXT 364 5 "print" }{TEXT -1 74 " mas escreve os resultados alinhados \340 esquerda e s\363 usa caracteres ASCII." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT 328 32 "Comandos de Repeti\347\343o e Itera\347\343o" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 " " {TEXT -1 152 "Durante a concep\347\343o de um algoritmo deparamo-nos muitas vezes com situa\347\365es onde uma certa instru\347\343o \351 \+ repetida v\341rias vezes. Para isso temos o comando " }{TEXT 329 3 "fo r" }{TEXT -1 35 ". A sua utiliza\347\343o segue um equema " }{TEXT 330 9 "for-do-od" }{TEXT -1 19 " da seguinte forma:" }}{PARA 0 "" 0 " " {TEXT -1 5 " " }{TEXT 334 3 "for" }{TEXT -1 2 " " }{TEXT 339 1 "j" }{TEXT -1 2 " " }{TEXT 335 4 "from" }{TEXT -1 2 " " }{TEXT 340 6 "in\355cio" }{TEXT -1 2 " " }{TEXT 336 2 "to" }{TEXT -1 2 " " } {TEXT 341 5 "fim " }{TEXT 337 2 "do" }}{PARA 0 "" 0 "" {TEXT -1 13 " \+ " }{TEXT 342 28 "express\365es a serem repetidas" }}{PARA 0 "" 0 "" {TEXT -1 5 " " }{TEXT 338 2 "od" }}{PARA 0 "" 0 "" {TEXT -1 67 "O esquema \351 bastante leg\355vel se adotarmos as seguin tes tradu\347\365es: " }{TEXT 331 3 "for" }{TEXT -1 9 " (para), " } {TEXT 332 4 "from" }{TEXT -1 16 " (a partir de), " }{TEXT 333 2 "to" } {TEXT -1 20 " (preposi\347\343o a) e " }{TEXT 343 2 "do" }{TEXT -1 68 " (fa\347a). Como exemplo vamos calcular os quadrados de 1, 2, 3 ,4 e 5." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 21 "for j from 1 to 5 do " }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 3 "j^2" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 3 "od;" }}{PARA 11 "" 1 " " {XPPMATH 20 "6#\"\"\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"\"%" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#\"\"*" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"#;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"#D" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 70 "A representa\347\343 o de sequ\352ncias indexadas no Maple se faz com colchetes " }{TEXT 344 2 "[]" }{TEXT -1 54 ". Vamos escrever os 5 primeiros termos da se qu\352ncia " }{XPPEDIT 18 0 "y[k]=1/(1+k)" "/&%\"yG6#%\"kG*&\"\"\"\" \"\",&\"\"\"F)F&F)!\"\"" }{TEXT -1 2 " ." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "for k from 1 to 5 do " }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 15 "y[k] := 1/(1+k)" }}{PARA 0 "> \+ " 0 "" {MPLTEXT 1 0 3 "od;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>&%\"yG6 #\"\"\"#F'\"\"#" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>&%\"yG6#\"\"##\"\" \"\"\"$" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>&%\"yG6#\"\"$#\"\"\"\"\"% " }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>&%\"yG6#\"\"%#\"\"\"\"\"&" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#>&%\"yG6#\"\"&#\"\"\"\"\"'" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 13 "Em proces sos " }{TEXT 510 10 "iterativos" }{TEXT -1 177 " (recursivos) devemos \+ utilizar o conceito da reatribui\347\343o din\342mica de vari\341veis. Digamos que estamos interessados em somar os n\372meros de 1 a 100. P ara isso come\347amos com a soma " }{XPPEDIT 18 0 "S=0" "/%\"SG\"\"!" }{TEXT -1 28 ". Na primeira etapa fazemos " }{XPPEDIT 18 0 "S=S+1" "/% \"SG,&F#\"\"\"\"\"\"F%" }{TEXT -1 8 " (agora " }{TEXT 513 1 "S" } {TEXT -1 35 " vale 1). Na segunda etapa fazemos " }{XPPEDIT 18 0 "S=S+ 2" "/%\"SG,&F#\"\"\"\"\"#F%" }{TEXT -1 8 " (agora " }{TEXT 511 1 "S" } {TEXT -1 36 " vale 3). Na terceira etapa fazemos " }{XPPEDIT 18 0 "S=S +3" "/%\"SG,&F#\"\"\"\"\"$F%" }{TEXT -1 8 " (agora " }{TEXT 512 1 "S" }{TEXT -1 34 " vale 6). Na quarta etapa fazemos " }{XPPEDIT 18 0 "S=S+ 4" "/%\"SG,&F#\"\"\"\"\"%F%" }{TEXT -1 8 " (agora " }{TEXT 514 1 "S" } {TEXT -1 77 " vale 10), e assim sucessivamente. Ao chegarmos na cent \351sima etapa teremos " }{XPPEDIT 18 0 "S=Sum(j,j=1..100)" "/%\"SG-% $SumG6$%\"jG/F';\"\"\"\"$+\"" }{TEXT -1 45 " . Vejamos como essa soma \351 obtida no Maple." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 5 "S:=0;" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 22 "for j from 1 to 100 do" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 6 "S: =S+j" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 3 "od:" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "Soma_Final:=S;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>% \"SG\"\"!" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%+Soma_FinalG\"%]]" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 235 "Agora podemos estudar um exemplo t\355picamente acad\352mico. O problema \351 o c\341lculo da \+ raiz quadrada via aproxima\347\365es sucessivas. O algor\355tmo, basea do no M\351todo de Newton, \351 muito simples. Suponhamos que se quer \+ calcular a raiz quadrada de " }{TEXT 345 1 "a" }{TEXT -1 39 ". Ent\343 o, a partir de um valor inicial " }{XPPEDIT 18 0 "r[0]" "&%\"rG6#\"\" !" }{TEXT -1 33 " (arbitr\341rio) a raiz quadrada de " }{TEXT 346 1 "a " }{TEXT -1 26 " \351 o limite da sequ\352ncia " }{XPPEDIT 18 0 "r[k] " "&%\"rG6#%\"kG" }{TEXT -1 7 " onde " }{XPPEDIT 18 0 "r[k]=0.5 *(r[k -1]+a/r[k-1])" "/&%\"rG6#%\"kG*&$\"\"&!\"\"\"\"\",&&F$6#,&F&F+\"\"\"! \"\"F+*&%\"aGF+&F$6#,&F&F+\"\"\"F1F1F+F+" }{TEXT -1 3 ", " }{XPPEDIT 18 0 "k=1,2,3" "6%/%\"kG\"\"\"\"\"#\"\"$" }{TEXT -1 42 ", .... Vamos \+ obter o valor aproximado de " }{XPPEDIT 18 0 "sqrt(11.3)" "-%%sqrtG6#$ \"$8\"!\"\"" }{TEXT -1 7 " com " }{XPPEDIT 18 0 "r[0]=1" "/&%\"rG6# \"\"!\"\"\"" }{TEXT -1 33 ", fazendo-se somente 5 itera\347\365es." }} {PARA 0 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "rr:=1; " }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#rrG\"\"\"" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 21 "for k from 1 to 5 do " }} {PARA 0 "> " 0 "" {MPLTEXT 1 0 25 "rr:= 0.5 * (rr + 11.3/rr)" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 3 "od;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%# rrG$\"$:'!\"#" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#rrG$\"+(=*p$*R!\"* " }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#rrG$\"+z!y:T$!\"*" }}{PARA 11 " " 1 "" {XPPMATH 20 "6#>%#rrG$\"+9T\">O$!\"*" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#rrG$\"+$GZ:O$!\"*" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 11 "sqrt(11.3);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"+js ahL!\"*" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT 347 19 "Comandos de Sele \347\343o" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 172 "Os comandos de sele\347 \343o (ou de desvio) s\343o utilizados para se decidir se um certo val or satisfaz ou n\343o uma certa condi\347\343o. Essas condi\347\365es \+ s\343o determinadas pelas rela\347\365es " }{TEXT 378 1 "=" }{TEXT -1 15 " (igualdade), " }{TEXT 379 1 "<" }{TEXT -1 15 " (menor que), \+ " }{TEXT 380 1 ">" }{TEXT -1 15 " (maior que), " }{TEXT 381 2 "<=" } {TEXT -1 20 " (menor ou igual), " }{TEXT 382 2 ">=" }{TEXT -1 20 " (m aior ou igual) e " }{TEXT 377 2 "<>" }{TEXT -1 42 " (diferente). Os op eradores l\363gicos s\343o: " }{TEXT 348 2 "if" }{TEXT -1 9 " (se), \+ " }{TEXT 349 4 "elif" }{TEXT -1 12 " (ou se), " }{TEXT 350 4 "else " }{TEXT -1 15 " (ou ent\343o) e " }{TEXT 351 4 "then" }{TEXT -1 47 " (ent\343o). Trabalha-se com o seguinte esquema: " }{TEXT 352 25 "if- then-elif-then-else-fi" }{TEXT -1 1 "." }}{PARA 0 "" 0 "" {TEXT -1 0 " " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 18 "if 1 = 2 then AZUL" }} {PARA 0 "> " 0 "" {MPLTEXT 1 0 13 "else VERMELHO" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 3 "fi;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#%)VERMELHOG" }} }{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 28 "if 1 > 10 then print(GRANDE )" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 32 "elif 1 < -10 then print(PEQUEN O)" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "else print(MEDIO)" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 3 "fi;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#%&MED IOG" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT 356 19 "Procedimentos Maple" }} {PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" } }{PARA 0 "" 0 "" {TEXT -1 111 "Veremos agora uma forma muito pr\341tic a de se construir pequenos programas \"execut\341veis\". No Maple s \343o chamados " }{TEXT 365 9 "procedure" }{TEXT 375 2 " " }{TEXT -1 70 "(procedimento). A sintaxe para se contruir procedimentos \351 a seguinte:" }}{PARA 0 "" 0 "" {TEXT 367 17 " Nome := proc(" }{TEXT 370 10 "argumentos" }{TEXT 369 1 ")" }}{PARA 0 "" 0 "" {TEXT -1 15 " \+ " }{TEXT 371 33 "instru\347\365es contendo os argumentos " }{TEXT -1 1 " " }}{PARA 0 "" 0 "" {TEXT 368 7 " end" }{TEXT -1 1 "." }}{PARA 0 "" 0 "" {TEXT -1 104 "\311 claro que existem muitas outr as op\347\365es a serem consideradas. O leitor poder\341 consultar o t utorial em " }{TEXT 366 5 "?proc" }{TEXT -1 76 ". O primeiro procedim ento que escreveremos mostra a soma de 2 n\372meros dados." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "Som a := proc(x,y)" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 32 "print(`A soma pro curada \351`, x+y)" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 4 "end;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%%SomaG:6$%\"xG%\"yG6\"F)F)-%&printG6$%3A~s oma~procurada~|dyG,&9$\"\"\"9%F0F)F)" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 10 "Soma(2,2);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6$%3A~som a~procurada~|dyG\"\"%" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 18 "So ma(alpha, beta);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6$%3A~soma~procurada ~|dyG,&%&alphaG\"\"\"%%betaGF&" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT 372 35 "Definindo Fun\347\365es com Procedimentos" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 " " {TEXT -1 112 "Os procedimentos Maple s\343o na verdade fun\347\365es dos argumentos de entrada. Logo tamb\351m podemos utilizar o comando \+ " }{TEXT 373 4 "proc" }{TEXT -1 66 " para definir fun\347\365es matem \341ticas. Vejamos como definir a fun\347\343o " }{XPPEDIT 18 0 "f(x)= x^3*sqrt(x)" "/-%\"fG6#%\"xG*&F&\"\"$-%%sqrtG6#F&\"\"\"" }{TEXT -1 30 " de duas maneiras diferentes." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 42 "f1 := x -> x^3*sqrt(x); # \+ maneira usual." }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#f1G:6#%\"xG6\"6$% )operatorG%&arrowGF(*&9$\"\"$-%%sqrtG6#F-\"\"\"F(F(" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 6 "f1(7);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6# ,$*$\"\"(#\"\"\"\"\"#\"$V$" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 30 "f2 := proc(x) x^3*sqrt(x) end;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6# >%#f2G:6#%\"xG6\"F(F(*&9$\"\"$-%%sqrtG6#F*\"\"\"F(F(" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 6 "f2(7);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6# ,$*$\"\"(#\"\"\"\"\"#\"$V$" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }} {PARA 0 "" 0 "" {TEXT -1 128 "Certas fun\347\365es podem exigir algum \+ conhecimento em programa\347\343o para serem definidas. Vamos construi r uma fun\347\343o que vale 1 para " }{XPPEDIT 18 0 "x<0" "2%\"xG\"\" !" }{TEXT -1 6 " e " }{XPPEDIT 18 0 "cos(10*x)" "-%$cosG6#*&\"#5\" \"\"%\"xGF'" }{TEXT -1 8 " para " }{XPPEDIT 18 0 "x>=0" "1\"\"!%\"xG " }{TEXT -1 3 ". " }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 13 "f3 := proc(x)" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 24 " if evalf(x) < 0 then 1" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 18 " else cos(10.0*x)" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 4 " fi" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 4 "end;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#f3G:6#%\"xG6\"F(F(@%2-%&evalfG6#9$\"\"!\"\"\"-%$cosG 6#,$F.$\"$+\"!\"\"F(F(" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 7 "f3 (-1);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"\"\"" }}}{EXCHG {PARA 0 "> \+ " 0 "" {MPLTEXT 1 0 6 "f3(1);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$!+\" H:2R)!#5" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 16 "plot(f3, -1..1) ;" }}{PARA 13 "" 1 "" {INLPLOT "6$-%'CURVESG6$7fq7$$!\"\"\"\"!$\"\"\"F *7$$!1nmm;p0k&*!#;F+7$$!1LL$3s%HaF0F+7$$!1 +++]$*4)*\\F0F+7$$!1+++]_&\\c%F0F+7$$!1+++]1aZTF0F+7$$!1nm;/#)[oPF0F+7 $$!1MLL$=exJ$F0F+7$$!1MLLL2$f$HF0F+7$$!1++]PYx\"\\#F0F+7$$!1MLLL7i)4#F 0F+7$$!1++]P'psm\"F0F+7$$!1++]74_c7F0F+7$$!1JLL$3x%z#)!#F+7$$\"1(H$3x\"yY_%!#=$\"18 4'**Ql(*)**F07$$\"1GL3_Nl.5Fjo$\"1$>8@Cw'\\**F07$$\"1E$ekGR[b\"Fjo$\"1 *o]81n$z)*F07$$\"1CL$3-Dg5#Fjo$\"1*34pR^!z(*F07$$\"1@Le*['R3KFjo$\"1,9 =!e4(*[*F07$$\"1ZLF07$$\"1***\\PzglL\"F0$\"1#p' pCY*4K#F07$$\"1mm;HCjV9F0$\"11'o*RX@o7F07$$\"1LLekSq]:F0$\"1d@yO544?Fj o7$$\"1*******pvxl\"F0$!14#4FAupo)Fjo7$$\"1***\\iSCDw\"F0$!1ku%[$fb0>F 07$$\"1****\\7JFn=F0$!1B!)*HCD:#HF07$$\"1)**\\(==-s>F0$!1\\GWC!oa!RF07 $$\"1)****\\_qn2#F0$!16f4S!)fY[F07$$\"1)**\\P/q%zAF0$!13'>_&RF3lF07$$ \"1)***\\i&p@[#F0$!1W])e7eM!zF07$$\"1)**\\(=GB2FF0$!1X;:(G'Rr!*F07$$\" 1)****\\2'HKHF0$!1m6.zIx\"y*F07$$\"1K$e9T`G)HF0$!124,/OFu)*F07$$\"1lm \"zu5M.$F0$!1)G'3C/aT**F07$$\"1)*\\P%3oR3$F0$!1*R2*Q;S$)**F07$$\"1KL$3 UDX8$F0$!1P_9s-v****F07$$\"1l;HdF3&=$F0$!1)pp[aW0***F07$$\"1***\\P4ScB $F0$!1McJ#)z!e&**F07$$\"1K$3-V(>'G$F0$!14Tw`$Hc*)*F07$$\"1lmmmZvOLF0$! 1ADpXC;5)*F07$$\"1KLLexn_NF0$!18\"f4]xo;*F07$$\"1+++]2goPF0$!1rRxMb'y4 )F07$$\"1mm\"H2fU'RF0$!1Df-ICp-oF07$$\"1KL$eR<*fTF0$!1*[pu;FzC&F07$$\" 1**\\P40(oE%F0$!1s#o))*zD4VF07$$\"1mm\"HiBQP%F0$!1M,tMBM@LF07$$\"1L$ek tw2[%F0$!1!pBH9qaH#F07$$\"1+++])Hxe%F0$!1%G:6;lLC\"F07$$\"1m;z%Rk$)o%F 0$!1-7=duA-CFjo7$$\"1KLeR*)**)y%F0$\"1v-?yU]`wFjo7$$\"1)*\\P%[L'*)[F0$ \"1>6B)>zJw\"F07$$\"1lm;H!o-*\\F0$\"1/F1on;VFF07$$\"1KL$3A_1?&F0$\"1tm R\"zF4p%F07$$\"1****\\7k.6aF0$\"1T1&H(f#=V'F07$$\"1KLe9as;cF0$\"1)Hn\" o5:gyF07$$\"1mmm;WTAeF0$\"1'4g#f**4d*)F07$$\"1**\\7yI3IfF0$\"18$o$oW/$ Q*F07$$\"1KLeR'F0$\"1zz%Q'*)zk**F07$ $\"1****\\i!*3`iF0$\"13D7A9Z&***F07$$\"1mTN@z$\\I'F0$\"1z7<7Uj(***F07$ $\"1K$3-y'ycjF0$\"1^40Tj#H(**F07$$\"1*\\i!Rcj3kF0$\"15a:;UT@**F07$$\"1 mm\"z\\%[gkF0$\"1EUs'GOK%)*F07$$\"1,]i:A=klF0$\"1eH:&f%z2'*F07$$\"1MLL L*zym'F0$\"1L.'RvI\"p#*F07$$\"1LL$3sr*zoF0$\"16:cu(e9F)F07$$\"1LLL3N1# 4(F0$\"1MFaM]5.pF07$$\"1++vo!*R-tF0$\"1k&3\\\\d.C&F07$$\"1mm;HYt7vF0$ \"1Q&p9_CmM$F07$$\"1LLek6,1xF0$\"1;4;\\3Ju9F07$$\"1*******p(G**yF0$!1$ [$=6o0HXFjo7$$\"1nmTgg/5!)F0$!1:\\MsnJa:F07$$\"1LL$3U/37)F0$!1S5++*zmj #F07$$\"1***\\7yi:B)F0$!12M?N3t'o$F07$$\"1mmmT6KU$)F0$!1)3p5L,;p%F07$$ \"1++]P$[/a)F0$!1()oYP<3QjF07$$\"1LLLLbdQ()F0$!16T[SudOxF07$$\"1nm\"zW ?)\\*)F0$!12ZE=:7$*))F07$$\"1++]i`1h\"*F0$!1NnfM))Ga'*F07$$\"1++DJ&f@E *F0$!1D[egt1o)*F07$$\"1++++PDj$*F0$!1/8$fzz5)**F07$$\"1+]P%y+QT*F0$!1` >/9vR****F07$$\"1++voyMk%*F0$!1BNQL@<#***F07$$\"1+]7`\\*[^*F0$!1+#H46A %f**F07$$\"1++]P?Wl&*F0$!1J^U06B,**F07$$\"1++v=5s#y*F0$!12!e%4X>m$*F07 $F+$!1CXw!H:2R)F0-%'COLOURG6&%$RGBG$\"#5F)F*F*-%%VIEWG6$;F(F+%(DEFAULT G" 2 374 374 374 2 0 1 0 2 9 0 4 2 1.000000 45.000000 45.000000 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 74 32187 0 0 0 0 0 0 }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" } }{PARA 0 "" 0 "" {TEXT 374 18 "Coment\341rios Finais" }}{PARA 0 "" 0 " " {TEXT -1 0 "" }}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 214 "As t\351cnicas de programa\347\343o s\343o geralmente objetos de muitos livros e manuais. Entretanto, esperamos que o leito r acredite que a programa\347\343o Maple \351 acess\355vel e bastante \+ intuitiva. Veja as refer\352ncias do Cap\355tulo 5." }}{PARA 0 "" 0 " " {TEXT -1 0 "" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{SECT 1 {PARA 3 " " 0 "" {TEXT -1 21 "5 Dicas e Refer\352ncias" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT 502 27 "Fun\347\365es Especiais (Pacot es)" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 143 "Os comandos espec\355ficos par a Equa\347\365es Diferenciais, \301lgebra Linear, Estat\355stica, Gr \341ficos, etc... est\343o colecionados separadamente em pacotes (" } {TEXT 506 22 "bibliotecas de fun\347\365es" }{TEXT -1 51 "). Uma lista completa pode ser vista executando-se " }{TEXT 503 15 "?index[package ]" }{TEXT -1 55 ". Esses pacotes s\343o carregados com aux\355lio do \+ comando " }{TEXT 504 4 "with" }{TEXT -1 45 ". Veremos a seguir alguns \+ exemplos do pacote " }{TEXT 505 6 "linalg" }{TEXT -1 71 ", que s\343o \+ espec\355ficos para matrizes, vetores e transforma\347\365es lineares. " }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "restart:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 13 "with(linalg);" }}{PARA 7 "" 1 "" {TEXT -1 32 "Warning, new definition for norm" }}{PARA 7 "" 1 "" {TEXT -1 33 "Warning, new definition for \+ trace" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#7^r%.BlockDiagonalG%,GramSchm idtG%,JordanBlockG%)LUdecompG%)QRdecompG%*WronskianG%'addcolG%'addrowG %$adjG%(adjointG%&angleG%(augmentG%(backsubG%%bandG%&basisG%'bezoutG%, blockmatrixG%(charmatG%)charpolyG%)choleskyG%$colG%'coldimG%)colspaceG %(colspanG%*companionG%'concatG%%condG%)copyintoG%*crossprodG%%curlG%) definiteG%(delcolsG%(delrowsG%$detG%%diagG%(divergeG%(dotprodG%*eigenv alsG%,eigenvaluesG%-eigenvectorsG%+eigenvectsG%,entermatrixG%&equalG%, exponentialG%'extendG%,ffgausselimG%*fibonacciG%+forwardsubG%*frobeniu sG%*gausselimG%*gaussjordG%(geneqnsG%*genmatrixG%%gradG%)hadamardG%(he rmiteG%(hessianG%(hilbertG%+htransposeG%)ihermiteG%*indexfuncG%*innerp rodG%)intbasisG%(inverseG%'ismithG%*issimilarG%'iszeroG%)jacobianG%'jo rdanG%'kernelG%*laplacianG%*leastsqrsG%)linsolveG%'mataddG%'matrixG%&m inorG%(minpolyG%'mulcolG%'mulrowG%)multiplyG%%normG%*normalizeG%*nulls paceG%'orthogG%*permanentG%&pivotG%*potentialG%+randmatrixG%+randvecto rG%%rankG%(ratformG%$rowG%'rowdimG%)rowspaceG%(rowspanG%%rrefG%*scalar mulG%-singularvalsG%&smithG%&stackG%*submatrixG%*subvectorG%)sumbasisG %(swapcolG%(swaprowG%*sylvesterG%)toeplitzG%&traceG%*transposeG%,vande rmondeG%*vecpotentG%(vectdimG%'vectorG%*wronskianG" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 43 "A := matrix( [ [1,2,3],[2,0,1],[0,3,0] ] );" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"AG-%'MATRIXG6#7%7%\"\"\"\"\"#\"\"$7%F+\"\"!F*7%F.F, F." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 13 "b := [5,5,0];" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"bG7%\"\"&F&\"\"!" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 47 "X := linsolve(A,b); # Resolvendo o sistem AX=b." }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"XG-%'VECTORG6#7%\"\"#\" \"!\"\"\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 50 "multiply(A,X); # Multiplicando as matrizes A e X." }}{PARA 11 "" 1 "" {XPPMATH 20 " 6#-%'VECTORG6#7%\"\"&F'\"\"!" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 30 "det(A); # Determinante de A." }}{PARA 11 "" 1 "" {XPPMATH 20 " 6#\"#:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 42 "inverse(A); # C alculando a inversa de A." }}{PARA 11 "" 1 "" {XPPMATH 20 "6#-%'MATRIX G6#7%7%#!\"\"\"\"&#\"\"$F*#\"\"#\"#:7%\"\"!F1#\"\"\"F,7%#F.F*F(#!\"%F/ " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT 476 12 "Maple no WEB" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 168 "Relacionamos abaixo alguns sites especializado s em Maple V na internet. Todos esses sites possuem artigos t\351cnico s, notas de cursos e programas em computa\347\343o alg\351brica." }} {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 55 "Stat/Math Center em Indiana University (o meu favorito)" }}{PARA 0 "" 0 "" {TEXT 485 42 "http://www.indiana.edu/statmath/math/maple" }}{PARA 0 " " 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 24 "CyberMath (Site Of icial)" }}{PARA 0 "" 0 "" {TEXT 486 24 "http://www.cybermath.com" }} {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 39 "Maple em \+ Los Alamos National Laboratory" }}{PARA 0 "" 0 "" {TEXT 487 42 "http:/ /saaz.lanl.gov/Maple/Maple_Home.html" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 26 "Maple e LaTeX em Portugu\352s" }}{PARA 0 "" 0 "" {TEXT 518 31 "http://www.geocities.com/cnumat" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT 469 22 "Livros Especializados " }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 77 " Os tr\352s livros listados abaixo formam o n\372cleo de toda bibliogra fia em Maple." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT 471 83 "B. W. Char, K. O. Geddes, G. H. Gonnet, B. L. Leong, \+ M. B. Monagan, S. M. Watt" }{TEXT -1 3 ", " }{TEXT 470 14 "First Le aves: " }}{PARA 0 "" 0 "" {TEXT 519 34 "A Tutorial Introduction to Map le V" }{TEXT -1 46 ", Springer-Verlag, 1992. (ISBN 0-387-97621-3)." }} {PARA 0 "" 0 "" {TEXT -1 1 "\n" }{TEXT 474 83 "B. W. Char, K. O. Gedd es, G. H. Gonnet, B. L. Leong, M. B. Monagan, S. M. Watt" }{TEXT -1 2 ", " }{TEXT 472 32 "Maple V Library Reference Manual" }{TEXT -1 46 ", Springer-Verlag, 1991. (ISBN 0-387-97592-6)." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT 475 83 "B. W. Char, K. O. Gedde s, G. H. Gonnet, B. L. Leong, M. B. Monagan, S. M. Watt" }{TEXT -1 2 ", " }{TEXT 473 33 "Maple V Language Reference Manual" }{TEXT -1 46 ", Springer Verlag, 1991. (ISBN 0-387-97622-1)." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 77 "A seguir indicamos alguns livros que s\343o destinados ao ensino universit\341rio. " }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT 477 25 "M. Abell & J. \+ Braselton" }{TEXT -1 2 ", " }{TEXT 478 35 "Differential Equations with Maple V" }{TEXT -1 59 ", Academic Press Professional, 1994. (ISBN 0-1 2-041548-8).\n" }}{PARA 0 "" 0 "" {TEXT 489 9 "D. Barrow" }{TEXT -1 2 ", " }{TEXT 490 52 "Solving Ordinary Differential Equations with Maple V" }{TEXT -1 58 ", Brooks/Cole Publishing Co., 1997. (ISBN 0-5343-440 2-X). " }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT 479 38 "W. C. Bauldry, B. Evans & J. Johnson" }{TEXT -1 2 ", " }{TEXT 480 25 "Linear Algebra with Maple" }{TEXT -1 50 ", John Wiley & Sons, \+ 1995. (ISBN 0-471-06368-1). \n" }}{PARA 0 "" 0 "" {TEXT 481 12 "J. S. \+ Devitt" }{TEXT -1 2 ", " }{TEXT 483 21 "Calculus with Maple V" }{TEXT -1 59 ", Brooks/Cole Publishing Co. ,1993. (ISBN 0-534-16362-9).\n\n" }{TEXT 482 11 "R. J. Lopez" }{TEXT -1 2 ", " }{TEXT 484 40 "Maple V: M athematics and Its Application" }{TEXT -1 42 ", Birkh\344user, 1994. ( ISBN 0-8176-3791-5).\n" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT 468 29 "Lista de Comandos (em ingl\352s)" }}{PARA 0 "" 0 " " {TEXT -1 0 "" }}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 82 "Aqui inclu\355mos uma lista de fun\347\365es e comando s Maple que foi obtida executando-se " }{TEXT 488 17 "?index[functions ]" }{TEXT -1 102 ". Cada \355tem listado est\341 ligado automaticament e ao seu correspondente tutorial atrav\351s de hyperlinks. " }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 17 "" 0 "" {HYPERLNK 17 "AFactor" 2 "AFactor" "" }{TEXT 23 6 " " } {HYPERLNK 17 "AFactors" 2 "AFactors" "" }{TEXT 23 10 " " } {HYPERLNK 17 "AiryAi" 2 "Airy" "" }{TEXT 23 11 " " } {HYPERLNK 17 "AiryBi" 2 "Airy" "" }{TEXT 23 11 " \n" } {HYPERLNK 17 "AngerJ" 2 "AngerJ" "" }{TEXT 23 7 " " }{HYPERLNK 17 "Berlekamp" 2 "Berlekamp" "" }{TEXT 23 9 " " }{HYPERLNK 17 "BesselI" 2 "Bessel" "" }{TEXT 23 10 " " }{HYPERLNK 17 "Besse lJ" 2 "Bessel" "" }{TEXT 23 10 " \n" }{HYPERLNK 17 "BesselK" 2 "Bessel" "" }{TEXT 23 6 " " }{HYPERLNK 17 "BesselY" 2 "Bessel" "" }{TEXT 23 11 " " }{HYPERLNK 17 "Beta" 2 "Beta" "" }{TEXT 23 13 " " }{HYPERLNK 17 "C" 2 "C" "" }{TEXT 23 16 " \+ \n" }{HYPERLNK 17 "Chi" 2 "Si" "" }{TEXT 23 10 " " } {HYPERLNK 17 "Ci" 2 "Si" "" }{TEXT 23 16 " " } {HYPERLNK 17 "CompSeq" 2 "CompSeq" "" }{TEXT 23 10 " " } {HYPERLNK 17 "Content" 2 "Content" "" }{TEXT 23 10 " \n" } {HYPERLNK 17 "D" 2 "D" "" }{TEXT 23 12 " " }{HYPERLNK 17 "D ESol" 2 "DESol" "" }{TEXT 23 13 " " }{HYPERLNK 17 "Det" 2 "Det" "" }{TEXT 23 14 " " }{HYPERLNK 17 "Diff" 2 "diff" " " }{TEXT 23 13 " \n" }{HYPERLNK 17 "Dirac" 2 "Dirac" "" } {TEXT 23 8 " " }{HYPERLNK 17 "DistDeg" 2 "DistDeg" "" }{TEXT 23 11 " " }{HYPERLNK 17 "Divide" 2 "Divide" "" }{TEXT 23 11 " " }{HYPERLNK 17 "Ei" 2 "Ei" "" }{TEXT 23 15 " \+ \n" }{HYPERLNK 17 "Eigenvals" 2 "Eigenvals" "" }{TEXT 23 4 " " } {HYPERLNK 17 "EllipticCE" 2 "EllipticE" "" }{TEXT 23 8 " " } {HYPERLNK 17 "EllipticCK" 2 "EllipticF" "" }{TEXT 23 7 " " } {HYPERLNK 17 "EllipticCPi" 2 "EllipticPi" "" }{TEXT 23 6 " \n" } {HYPERLNK 17 "EllipticE" 2 "EllipticE" "" }{TEXT 23 4 " " } {HYPERLNK 17 "EllipticF" 2 "EllipticF" "" }{TEXT 23 9 " " } {HYPERLNK 17 "EllipticK" 2 "EllipticF" "" }{TEXT 23 8 " " } {HYPERLNK 17 "EllipticModulus" 2 "EllipticModulus" "" }{TEXT 23 2 " \n " }{HYPERLNK 17 "EllipticNome" 2 "EllipticNome" "" }{TEXT 23 1 " " } {HYPERLNK 17 "EllipticPi" 2 "EllipticPi" "" }{TEXT 23 8 " " } {HYPERLNK 17 "Eval" 2 "Eval" "" }{TEXT 23 13 " " } {HYPERLNK 17 "Expand" 2 "Expand" "" }{TEXT 23 11 " \n" } {HYPERLNK 17 "FFT" 2 "FFT" "" }{TEXT 23 10 " " }{HYPERLNK 17 "Factor" 2 "Factor" "" }{TEXT 23 12 " " }{HYPERLNK 17 "Fact ors" 2 "Factors" "" }{TEXT 23 10 " " }{HYPERLNK 17 "FresnelC " 2 "Fresnel" "" }{TEXT 23 9 " \n" }{HYPERLNK 17 "FresnelS" 2 " Fresnel" "" }{TEXT 23 5 " " }{HYPERLNK 17 "Fresnelf" 2 "Fresnel" " " }{TEXT 23 10 " " }{HYPERLNK 17 "Fresnelg" 2 "Fresnel" "" } {TEXT 23 9 " " }{HYPERLNK 17 "Frobenius" 2 "Frobenius" "" } {TEXT 23 8 " \n" }{HYPERLNK 17 "GAMMA" 2 "GAMMA" "" }{TEXT 23 8 " " }{HYPERLNK 17 "GaussAGM" 2 "GaussAGM" "" }{TEXT 23 10 " \+ " }{HYPERLNK 17 "Gaussejord" 2 "Gausselim" "" }{TEXT 23 7 " \+ " }{HYPERLNK 17 "Gausselim" 2 "Gausselim" "" }{TEXT 23 8 " \n " }{HYPERLNK 17 "Gcd" 2 "Gcd" "" }{TEXT 23 10 " " }{HYPERLNK 17 "Gcdex" 2 "Gcdex" "" }{TEXT 23 13 " " }{HYPERLNK 17 "Ha nkelH1" 2 "Bessel" "" }{TEXT 23 9 " " }{HYPERLNK 17 "HankelH2 " 2 "Bessel" "" }{TEXT 23 9 " \n" }{HYPERLNK 17 "Heaviside" 2 " Dirac" "" }{TEXT 23 4 " " }{HYPERLNK 17 "Hermite" 2 "Hermite" "" } {TEXT 23 11 " " }{HYPERLNK 17 "Im" 2 "Re" "" }{TEXT 23 15 " \+ " }{HYPERLNK 17 "Indep" 2 "Indep" "" }{TEXT 23 12 " \+ \n" }{HYPERLNK 17 "Interp" 2 "Interp" "" }{TEXT 23 7 " " } {HYPERLNK 17 "Inverse" 2 "Inverse" "" }{TEXT 23 11 " " } {HYPERLNK 17 "Irreduc" 2 "Irreduc" "" }{TEXT 23 10 " " } {HYPERLNK 17 "Issimilar" 2 "Issimilar" "" }{TEXT 23 8 " \n" } {HYPERLNK 17 "JacobiAM" 2 "JacobiSN" "" }{TEXT 23 5 " " } {HYPERLNK 17 "JacobiCD" 2 "JacobiSN" "" }{TEXT 23 10 " " } {HYPERLNK 17 "JacobiCN" 2 "JacobiSN" "" }{TEXT 23 9 " " } {HYPERLNK 17 "JacobiCS" 2 "JacobiSN" "" }{TEXT 23 9 " \n" } {HYPERLNK 17 "JacobiDC" 2 "JacobiSN" "" }{TEXT 23 5 " " } {HYPERLNK 17 "JacobiDN" 2 "JacobiSN" "" }{TEXT 23 10 " " } {HYPERLNK 17 "JacobiDS" 2 "JacobiSN" "" }{TEXT 23 9 " " } {HYPERLNK 17 "JacobiNC" 2 "JacobiSN" "" }{TEXT 23 9 " \n" } {HYPERLNK 17 "JacobiND" 2 "JacobiSN" "" }{TEXT 23 5 " " } {HYPERLNK 17 "JacobiNS" 2 "JacobiSN" "" }{TEXT 23 10 " " } {HYPERLNK 17 "JacobiSC" 2 "JacobiSN" "" }{TEXT 23 9 " " } {HYPERLNK 17 "JacobiSD" 2 "JacobiSN" "" }{TEXT 23 9 " \n" } {HYPERLNK 17 "JacobiSN" 2 "JacobiSN" "" }{TEXT 23 5 " " } {HYPERLNK 17 "JacobiTheta1" 2 "JacobiTheta1" "" }{TEXT 23 6 " " } {HYPERLNK 17 "JacobiTheta2" 2 "JacobiTheta1" "" }{TEXT 23 5 " " } {HYPERLNK 17 "JacobiTheta3" 2 "JacobiTheta1" "" }{TEXT 23 5 " \n" } {HYPERLNK 17 "JacobiTheta4" 2 "JacobiTheta1" "" }{TEXT 23 1 " " } {HYPERLNK 17 "JacobiZeta" 2 "JacobiZeta" "" }{TEXT 23 8 " " } {HYPERLNK 17 "KelvinBei" 2 "Kelvin" "" }{TEXT 23 8 " " } {HYPERLNK 17 "KelvinBer" 2 "Kelvin" "" }{TEXT 23 8 " \n" } {HYPERLNK 17 "KelvinHei" 2 "Kelvin" "" }{TEXT 23 4 " " }{HYPERLNK 17 "KelvinHer" 2 "Kelvin" "" }{TEXT 23 9 " " }{HYPERLNK 17 "Ke lvinKei" 2 "Kelvin" "" }{TEXT 23 8 " " }{HYPERLNK 17 "KelvinKer " 2 "Kelvin" "" }{TEXT 23 8 " \n" }{HYPERLNK 17 "LambertW" 2 "La mbertW" "" }{TEXT 23 5 " " }{HYPERLNK 17 "Lcm" 2 "Lcm" "" }{TEXT 23 15 " " }{HYPERLNK 17 "LegendreE" 2 "Legendre" "" } {TEXT 23 8 " " }{HYPERLNK 17 "LegendreEc" 2 "Legendre" "" } {TEXT 23 7 " \n" }{HYPERLNK 17 "LegendreEc1" 2 "Legendre" "" } {TEXT 23 2 " " }{HYPERLNK 17 "LegendreF" 2 "Legendre" "" }{TEXT 23 9 " " }{HYPERLNK 17 "LegendreKc" 2 "Legendre" "" }{TEXT 23 7 " \+ " }{HYPERLNK 17 "LegendreKc1" 2 "Legendre" "" }{TEXT 23 6 " \+ \n" }{HYPERLNK 17 "LegendrePi" 2 "Legendre" "" }{TEXT 23 3 " " } {HYPERLNK 17 "LegendrePic" 2 "Legendre" "" }{TEXT 23 7 " " } {HYPERLNK 17 "LegendrePic1" 2 "Legendre" "" }{TEXT 23 5 " " } {HYPERLNK 17 "Li" 2 "Li" "" }{TEXT 23 15 " \n" } {HYPERLNK 17 "Linsolve" 2 "Linsolve" "" }{TEXT 23 5 " " } {HYPERLNK 17 "MOLS" 2 "MOLS" "" }{TEXT 23 14 " " } {HYPERLNK 17 "Maple_floats" 2 "Maple_floats" "" }{TEXT 23 5 " " } {HYPERLNK 17 "MeijerG" 2 "MeijerG" "" }{TEXT 23 10 " \n" } {HYPERLNK 17 "Norm" 2 "Norm" "" }{TEXT 23 9 " " }{HYPERLNK 17 "Normal" 2 "Normal" "" }{TEXT 23 12 " " }{HYPERLNK 17 "Null space" 2 "Nullspace" "" }{TEXT 23 8 " " }{HYPERLNK 17 "Power" 2 "Power" "" }{TEXT 23 12 " \n" }{HYPERLNK 17 "Powmod" 2 "Po wmod" "" }{TEXT 23 7 " " }{HYPERLNK 17 "Prem" 2 "Prem" "" } {TEXT 23 14 " " }{HYPERLNK 17 "Primfield" 2 "Primfield" " " }{TEXT 23 8 " " }{HYPERLNK 17 "Primitive" 2 "Primitive" "" } {TEXT 23 8 " \n" }{HYPERLNK 17 "Primpart" 2 "Content" "" }{TEXT 23 5 " " }{HYPERLNK 17 "ProbSplit" 2 "ProbSplit" "" }{TEXT 23 9 " \+ " }{HYPERLNK 17 "Product" 2 "product" "" }{TEXT 23 10 " \+ " }{HYPERLNK 17 "Psi" 2 "Psi" "" }{TEXT 23 14 " \n" } {HYPERLNK 17 "Quo" 2 "Rem" "" }{TEXT 23 10 " " }{HYPERLNK 17 "RESol" 2 "RESol" "" }{TEXT 23 13 " " }{HYPERLNK 17 "Randp oly" 2 "Randpoly" "" }{TEXT 23 9 " " }{HYPERLNK 17 "Randprime " 2 "Randpoly" "" }{TEXT 23 8 " \n" }{HYPERLNK 17 "Ratrecon" 2 " Ratrecon" "" }{TEXT 23 5 " " }{HYPERLNK 17 "Re" 2 "Re" "" }{TEXT 23 16 " " }{HYPERLNK 17 "Rem" 2 "Rem" "" }{TEXT 23 14 " " }{HYPERLNK 17 "Resultant" 2 "Resultant" "" }{TEXT 23 8 " \n" }{HYPERLNK 17 "RootOf" 2 "RootOf" "" }{TEXT 23 7 " \+ " }{HYPERLNK 17 "Roots" 2 "Roots" "" }{TEXT 23 13 " " } {HYPERLNK 17 "SPrem" 2 "Prem" "" }{TEXT 23 12 " " } {HYPERLNK 17 "Searchtext" 2 "searchtext" "" }{TEXT 23 7 " \n" } {HYPERLNK 17 "Shi" 2 "Si" "" }{TEXT 23 10 " " }{HYPERLNK 17 " Si" 2 "Si" "" }{TEXT 23 16 " " }{HYPERLNK 17 "Smith" 2 "Hermite" "" }{TEXT 23 12 " " }{HYPERLNK 17 "Sqrfree" 2 "Sq rfree" "" }{TEXT 23 10 " \n" }{HYPERLNK 17 "Ssi" 2 "Si" "" } {TEXT 23 10 " " }{HYPERLNK 17 "StruveH" 2 "StruveH" "" } {TEXT 23 11 " " }{HYPERLNK 17 "StruveL" 2 "StruveH" "" } {TEXT 23 10 " " }{HYPERLNK 17 "Sum" 2 "sum" "" }{TEXT 23 14 " \n" }{HYPERLNK 17 "Svd" 2 "Svd" "" }{TEXT 23 10 " \+ " }{HYPERLNK 17 "TEXT" 2 "TEXT" "" }{TEXT 23 14 " " } {HYPERLNK 17 "Trace" 2 "Trace" "" }{TEXT 23 12 " " } {HYPERLNK 17 "WeberE" 2 "AngerJ" "" }{TEXT 23 11 " \n" } {HYPERLNK 17 "WeierstrassP" 2 "WeierstrassP" "" }{TEXT 23 1 " " } {HYPERLNK 17 "WeierstrassPPrime" 2 "WeierstrassP" "" }{TEXT 23 1 " " } {HYPERLNK 17 "WeierstrassSigma" 2 "WeierstrassP" "" }{TEXT 23 1 " " } {HYPERLNK 17 "WeierstrassZeta" 2 "WeierstrassP" "" }{TEXT 23 2 " \n" } {HYPERLNK 17 "Zeta" 2 "Zeta" "" }{TEXT 23 9 " " }{HYPERLNK 17 "abs" 2 "abs" "" }{TEXT 23 15 " " }{HYPERLNK 17 "add" 2 "add" "" }{TEXT 23 14 " " }{HYPERLNK 17 "addcoords" 2 "ad dcoords" "" }{TEXT 23 8 " \n" }{HYPERLNK 17 "addressof" 2 "assem ble" "" }{TEXT 23 4 " " }{HYPERLNK 17 "algebraic" 2 "algebraic" "" }{TEXT 23 9 " " }{HYPERLNK 17 "algsubs" 2 "algsubs" "" }{TEXT 23 10 " " }{HYPERLNK 17 "alias" 2 "alias" "" }{TEXT 23 12 " \+ \n" }{HYPERLNK 17 "allvalues" 2 "allvalues" "" }{TEXT 23 4 " \+ " }{HYPERLNK 17 "anames" 2 "anames" "" }{TEXT 23 12 " " }{HYPERLNK 17 "antisymm" 2 "antisymm" "" }{TEXT 23 9 " " } {HYPERLNK 17 "applyop" 2 "applyop" "" }{TEXT 23 10 " \n" } {HYPERLNK 17 "arccos" 2 "invtrig" "" }{TEXT 23 7 " " }{HYPERLNK 17 "arccosh" 2 "invtrig" "" }{TEXT 23 11 " " }{HYPERLNK 17 " arccot" 2 "invtrig" "" }{TEXT 23 11 " " }{HYPERLNK 17 "arcco th" 2 "invtrig" "" }{TEXT 23 10 " \n" }{HYPERLNK 17 "arccsc" 2 "invtrig" "" }{TEXT 23 7 " " }{HYPERLNK 17 "arccsch" 2 "invtri g" "" }{TEXT 23 11 " " }{HYPERLNK 17 "arcsec" 2 "invtrig" " " }{TEXT 23 11 " " }{HYPERLNK 17 "arcsech" 2 "invtrig" "" } {TEXT 23 10 " \n" }{HYPERLNK 17 "arcsin" 2 "invtrig" "" } {TEXT 23 7 " " }{HYPERLNK 17 "arcsinh" 2 "invtrig" "" }{TEXT 23 11 " " }{HYPERLNK 17 "arctan" 2 "invtrig" "" }{TEXT 23 11 " \+ " }{HYPERLNK 17 "arctanh" 2 "invtrig" "" }{TEXT 23 10 " \+ \n" }{HYPERLNK 17 "argument" 2 "argument" "" }{TEXT 23 5 " " } {HYPERLNK 17 "array" 2 "array" "" }{TEXT 23 13 " " } {HYPERLNK 17 "assign" 2 "assign" "" }{TEXT 23 11 " " } {HYPERLNK 17 "assigned" 2 "assigned" "" }{TEXT 23 9 " \n" } {HYPERLNK 17 "asspar" 2 "asspar" "" }{TEXT 23 7 " " }{HYPERLNK 17 "assume" 2 "assume" "" }{TEXT 23 12 " " }{HYPERLNK 17 "a subs" 2 "asubs" "" }{TEXT 23 12 " " }{HYPERLNK 17 "asympt" 2 "asympt" "" }{TEXT 23 11 " \n" }{HYPERLNK 17 "attribute" 2 "attributes" "" }{TEXT 23 4 " " }{HYPERLNK 17 "bernstein" 2 "bernst ein" "" }{TEXT 23 9 " " }{HYPERLNK 17 "branches" 2 "branches" "" }{TEXT 23 9 " " }{HYPERLNK 17 "bspline" 2 "bspline" "" } {TEXT 23 10 " \n" }{HYPERLNK 17 "cat" 2 "cat" "" }{TEXT 23 10 " " }{HYPERLNK 17 "ceil" 2 "trunc" "" }{TEXT 23 14 " \+ " }{HYPERLNK 17 "chrem" 2 "chrem" "" }{TEXT 23 12 " " }{HYPERLNK 17 "close" 2 "fclose" "" }{TEXT 23 12 " \n" } {HYPERLNK 17 "close" 2 "fflush" "" }{TEXT 23 8 " " }{HYPERLNK 17 "coeff" 2 "coeff" "" }{TEXT 23 13 " " }{HYPERLNK 17 "co effs" 2 "coeffs" "" }{TEXT 23 11 " " }{HYPERLNK 17 "coeftayl " 2 "coeftayl" "" }{TEXT 23 9 " \n" }{HYPERLNK 17 "collect" 2 " collect" "" }{TEXT 23 6 " " }{HYPERLNK 17 "combine" 2 "combine" " " }{TEXT 23 11 " " }{HYPERLNK 17 "commutat" 2 "commutat" "" }{TEXT 23 9 " " }{HYPERLNK 17 "comparray" 2 "comparray" "" } {TEXT 23 8 " \n" }{HYPERLNK 17 "compoly" 2 "compoly" "" }{TEXT 23 6 " " }{HYPERLNK 17 "conjugate" 2 "conjugate" "" }{TEXT 23 9 " " }{HYPERLNK 17 "content" 2 "content" "" }{TEXT 23 10 " \+ " }{HYPERLNK 17 "convergs" 2 "convergs" "" }{TEXT 23 9 " \n " }{HYPERLNK 17 "convert" 2 "convert" "" }{TEXT 23 6 " " } {HYPERLNK 17 "coords" 2 "coords" "" }{TEXT 23 12 " " } {HYPERLNK 17 "copy" 2 "copy" "" }{TEXT 23 13 " " } {HYPERLNK 17 "cos" 2 "trig" "" }{TEXT 23 14 " \n" } {HYPERLNK 17 "cosh" 2 "trig" "" }{TEXT 23 9 " " }{HYPERLNK 17 "cost" 2 "cost" "" }{TEXT 23 14 " " }{HYPERLNK 17 "cot" 2 "trig" "" }{TEXT 23 14 " " }{HYPERLNK 17 "coth" 2 "trig " "" }{TEXT 23 13 " \n" }{HYPERLNK 17 "csc" 2 "trig" "" } {TEXT 23 10 " " }{HYPERLNK 17 "csch" 2 "trig" "" }{TEXT 23 14 " " }{HYPERLNK 17 "csgn" 2 "csgn" "" }{TEXT 23 13 " \+ " }{HYPERLNK 17 "dawson" 2 "dawson" "" }{TEXT 23 11 " \+ \n" }{HYPERLNK 17 "define" 2 "define" "" }{TEXT 23 7 " " } {HYPERLNK 17 "degree" 2 "degree" "" }{TEXT 23 12 " " } {HYPERLNK 17 "denom" 2 "numer" "" }{TEXT 23 12 " " } {HYPERLNK 17 "depends" 2 "depends" "" }{TEXT 23 10 " \n" } {HYPERLNK 17 "diagonal" 2 "diagonal" "" }{TEXT 23 5 " " } {HYPERLNK 17 "diff" 2 "diff" "" }{TEXT 23 14 " " } {HYPERLNK 17 "dilog" 2 "dilog" "" }{TEXT 23 12 " " } {HYPERLNK 17 "dinterp" 2 "dinterp" "" }{TEXT 23 10 " \n" } {HYPERLNK 17 "disassemble" 2 "assemble" "" }{TEXT 23 2 " " } {HYPERLNK 17 "discont" 2 "discont" "" }{TEXT 23 11 " " } {HYPERLNK 17 "discrim" 2 "discrim" "" }{TEXT 23 10 " " } {HYPERLNK 17 "dismantle" 2 "dismantle" "" }{TEXT 23 8 " \n" } {HYPERLNK 17 "divide" 2 "divide" "" }{TEXT 23 7 " " }{HYPERLNK 17 "dsolve" 2 "dsolve" "" }{TEXT 23 12 " " }{HYPERLNK 17 "e liminate" 2 "eliminate" "" }{TEXT 23 8 " " }{HYPERLNK 17 "ellip soid" 2 "ellipsoid" "" }{TEXT 23 8 " \n" }{HYPERLNK 17 "entries " 2 "indices" "" }{TEXT 23 6 " " }{HYPERLNK 17 "eqn" 2 "eqn" "" } {TEXT 23 15 " " }{HYPERLNK 17 "erf" 2 "erf" "" }{TEXT 23 14 " " }{HYPERLNK 17 "erfc" 2 "erf" "" }{TEXT 23 13 " \+ \n" }{HYPERLNK 17 "eulermac" 2 "eulermac" "" }{TEXT 23 5 " \+ " }{HYPERLNK 17 "eval" 2 "eval" "" }{TEXT 23 14 " " } {HYPERLNK 17 "evala" 2 "evala" "" }{TEXT 23 12 " " } {HYPERLNK 17 "evalapply" 2 "evalapply" "" }{TEXT 23 8 " \n" } {HYPERLNK 17 "evalb" 2 "evalb" "" }{TEXT 23 8 " " }{HYPERLNK 17 "evalc" 2 "evalc" "" }{TEXT 23 13 " " }{HYPERLNK 17 "ev alf" 2 "evalf" "" }{TEXT 23 12 " " }{HYPERLNK 17 "evalfint " 2 "evalfint" "" }{TEXT 23 9 " \n" }{HYPERLNK 17 "evalgf" 2 "e valgf" "" }{TEXT 23 7 " " }{HYPERLNK 17 "evalhf" 2 "evalhf" "" } {TEXT 23 12 " " }{HYPERLNK 17 "evalm" 2 "evalm" "" }{TEXT 23 12 " " }{HYPERLNK 17 "evaln" 2 "evaln" "" }{TEXT 23 12 " \n" }{HYPERLNK 17 "evalr" 2 "evalr" "" }{TEXT 23 8 " \+ " }{HYPERLNK 17 "exp" 2 "exp" "" }{TEXT 23 15 " " } {HYPERLNK 17 "expand" 2 "expand" "" }{TEXT 23 11 " " } {HYPERLNK 17 "expandoff" 2 "expandoff" "" }{TEXT 23 8 " \n" } {HYPERLNK 17 "expandon" 2 "expandoff" "" }{TEXT 23 5 " " } {HYPERLNK 17 "extract" 2 "priqueue" "" }{TEXT 23 11 " " } {HYPERLNK 17 "factor" 2 "factor" "" }{TEXT 23 11 " " } {HYPERLNK 17 "factors" 2 "factors" "" }{TEXT 23 10 " \n" } {HYPERLNK 17 "fclose" 2 "fclose" "" }{TEXT 23 7 " " }{HYPERLNK 17 "feof" 2 "feof" "" }{TEXT 23 14 " " }{HYPERLNK 17 "ffl ush" 2 "fflush" "" }{TEXT 23 11 " " }{HYPERLNK 17 "filepos" 2 "filepos" "" }{TEXT 23 10 " \n" }{HYPERLNK 17 "fixdiv" 2 "fi xdiv" "" }{TEXT 23 7 " " }{HYPERLNK 17 "float" 2 "float" "" } {TEXT 23 13 " " }{HYPERLNK 17 "floor" 2 "trunc" "" }{TEXT 23 12 " " }{HYPERLNK 17 "fnormal" 2 "fnormal" "" }{TEXT 23 10 " \n" }{HYPERLNK 17 "fopen" 2 "fopen" "" }{TEXT 23 8 " \+ " }{HYPERLNK 17 "forget" 2 "forget" "" }{TEXT 23 12 " " }{HYPERLNK 17 "fortran" 2 "fortran" "" }{TEXT 23 10 " " } {HYPERLNK 17 "fprintf" 2 "printf" "" }{TEXT 23 10 " \n" } {HYPERLNK 17 "frac" 2 "trunc" "" }{TEXT 23 9 " " }{HYPERLNK 17 "freeze" 2 "freeze" "" }{TEXT 23 12 " " }{HYPERLNK 17 "f remove" 2 "fremove" "" }{TEXT 23 10 " " }{HYPERLNK 17 "fronte nd" 2 "frontend" "" }{TEXT 23 9 " \n" }{HYPERLNK 17 "fscanf" 2 "sscanf" "" }{TEXT 23 7 " " }{HYPERLNK 17 "fsolve" 2 "fsolve" " " }{TEXT 23 12 " " }{HYPERLNK 17 "galois" 2 "galois" "" } {TEXT 23 11 " " }{HYPERLNK 17 "gc" 2 "gc" "" }{TEXT 23 15 " \+ \n" }{HYPERLNK 17 "gcd" 2 "gcd" "" }{TEXT 23 10 " \+ " }{HYPERLNK 17 "gcdex" 2 "gcdex" "" }{TEXT 23 13 " " } {HYPERLNK 17 "genpoly" 2 "genpoly" "" }{TEXT 23 10 " " } {HYPERLNK 17 "harmonic" 2 "harmonic" "" }{TEXT 23 9 " \n" } {HYPERLNK 17 "has" 2 "has" "" }{TEXT 23 10 " " }{HYPERLNK 17 "hasfun" 2 "hasfun" "" }{TEXT 23 12 " " }{HYPERLNK 17 "haso ption" 2 "hasoption" "" }{TEXT 23 8 " " }{HYPERLNK 17 "hastype " 2 "hastype" "" }{TEXT 23 10 " \n" }{HYPERLNK 17 "heap" 2 "he ap" "" }{TEXT 23 9 " " }{HYPERLNK 17 "history" 2 "history" "" }{TEXT 23 11 " " }{HYPERLNK 17 "hypergeom" 2 "hypergeom" "" }{TEXT 23 8 " " }{HYPERLNK 17 "iFFT" 2 "FFT" "" }{TEXT 23 13 " \+ \n" }{HYPERLNK 17 "icontent" 2 "icontent" "" }{TEXT 23 5 " \+ " }{HYPERLNK 17 "identity" 2 "identity" "" }{TEXT 23 10 " \+ " }{HYPERLNK 17 "igcd" 2 "igcd" "" }{TEXT 23 13 " " } {HYPERLNK 17 "igcdex" 2 "igcdex" "" }{TEXT 23 11 " \n" } {HYPERLNK 17 "ilcm" 2 "igcd" "" }{TEXT 23 9 " " }{HYPERLNK 17 "ilog" 2 "ilog10" "" }{TEXT 23 14 " " }{HYPERLNK 17 "ilog 10" 2 "ilog10" "" }{TEXT 23 11 " " }{HYPERLNK 17 "implicitdi ff" 2 "implicitdiff" "" }{TEXT 23 5 " \n" }{HYPERLNK 17 "indets" 2 "indets" "" }{TEXT 23 7 " " }{HYPERLNK 17 "index" 2 "index" "" } {TEXT 23 13 " " }{HYPERLNK 17 "indexed" 2 "indexed" "" } {TEXT 23 10 " " }{HYPERLNK 17 "indices" 2 "indices" "" } {TEXT 23 10 " \n" }{HYPERLNK 17 "inifcn" 2 "inifcn" "" }{TEXT 23 7 " " }{HYPERLNK 17 "ininame" 2 "ininame" "" }{TEXT 23 11 " \+ " }{HYPERLNK 17 "initialize" 2 "priqueue" "" }{TEXT 23 7 " \+ " }{HYPERLNK 17 "insert" 2 "priqueue" "" }{TEXT 23 11 " \+ \n" }{HYPERLNK 17 "int" 2 "int" "" }{TEXT 23 10 " " } {HYPERLNK 17 "interface" 2 "interface" "" }{TEXT 23 9 " " } {HYPERLNK 17 "interp" 2 "interp" "" }{TEXT 23 11 " " } {HYPERLNK 17 "invfunc" 2 "invfunc" "" }{TEXT 23 10 " \n" } {HYPERLNK 17 "invztrans" 2 "invztrans" "" }{TEXT 23 4 " " } {HYPERLNK 17 "iostatus" 2 "iostatus" "" }{TEXT 23 10 " " } {HYPERLNK 17 "iperfpow" 2 "iperfpow" "" }{TEXT 23 9 " " } {HYPERLNK 17 "iquo" 2 "irem" "" }{TEXT 23 13 " \n" } {HYPERLNK 17 "iratrecon" 2 "iratrecon" "" }{TEXT 23 4 " " } {HYPERLNK 17 "irem" 2 "irem" "" }{TEXT 23 14 " " } {HYPERLNK 17 "iroot" 2 "isqrt" "" }{TEXT 23 12 " " } {HYPERLNK 17 "irreduc" 2 "irreduc" "" }{TEXT 23 10 " \n" } {HYPERLNK 17 "iscont" 2 "iscont" "" }{TEXT 23 7 " " }{HYPERLNK 17 "isdifferentiable" 2 "isdifferentiable" "" }{TEXT 23 2 " " } {HYPERLNK 17 "isolate" 2 "isolate" "" }{TEXT 23 10 " " } {HYPERLNK 17 "ispoly" 2 "ispoly" "" }{TEXT 23 11 " \n" } {HYPERLNK 17 "isqrfree" 2 "isqrfree" "" }{TEXT 23 5 " " } {HYPERLNK 17 "isqrt" 2 "isqrt" "" }{TEXT 23 13 " " } {HYPERLNK 17 "issqr" 2 "issqr" "" }{TEXT 23 12 " " } {HYPERLNK 17 "latex" 2 "latex" "" }{TEXT 23 12 " \n" } {HYPERLNK 17 "lattice" 2 "lattice" "" }{TEXT 23 6 " " }{HYPERLNK 17 "lcm" 2 "gcd" "" }{TEXT 23 15 " " }{HYPERLNK 17 "lcoe ff" 2 "lcoeff" "" }{TEXT 23 11 " " }{HYPERLNK 17 "leadterm" 2 "leadterm" "" }{TEXT 23 9 " \n" }{HYPERLNK 17 "length" 2 "len gth" "" }{TEXT 23 7 " " }{HYPERLNK 17 "lexorder" 2 "lexorder" " " }{TEXT 23 10 " " }{HYPERLNK 17 "lhs" 2 "lhs" "" }{TEXT 23 14 " " }{HYPERLNK 17 "limit" 2 "limit" "" }{TEXT 23 12 " \+ \n" }{HYPERLNK 17 "ln" 2 "ln" "" }{TEXT 23 11 " " }{HYPERLNK 17 "lnGAMMA" 2 "GAMMA" "" }{TEXT 23 11 " " } {HYPERLNK 17 "log" 2 "ln" "" }{TEXT 23 14 " " }{HYPERLNK 17 "log10" 2 "ln" "" }{TEXT 23 12 " \n" }{HYPERLNK 17 "lprin t" 2 "lprint" "" }{TEXT 23 7 " " }{HYPERLNK 17 "map" 2 "map" "" }{TEXT 23 15 " " }{HYPERLNK 17 "map2" 2 "map" "" }{TEXT 23 13 " " }{HYPERLNK 17 "match" 2 "match" "" }{TEXT 23 12 " \n" }{HYPERLNK 17 "matrix" 2 "matrix" "" }{TEXT 23 7 " \+ " }{HYPERLNK 17 "max" 2 "max" "" }{TEXT 23 15 " " } {HYPERLNK 17 "maximize" 2 "minimize" "" }{TEXT 23 9 " " } {HYPERLNK 17 "maxnorm" 2 "maxnorm" "" }{TEXT 23 10 " \n" } {HYPERLNK 17 "maxorder" 2 "maxorder" "" }{TEXT 23 5 " " } {HYPERLNK 17 "member" 2 "member" "" }{TEXT 23 12 " " } {HYPERLNK 17 "min" 2 "max" "" }{TEXT 23 14 " " } {HYPERLNK 17 "minimize" 2 "minimize" "" }{TEXT 23 9 " \n" } {HYPERLNK 17 "minpoly" 2 "minpoly" "" }{TEXT 23 6 " " }{HYPERLNK 17 "modp" 2 "mod" "" }{TEXT 23 14 " " }{HYPERLNK 17 "modp 1" 2 "modp1" "" }{TEXT 23 12 " " }{HYPERLNK 17 "modp2" 2 "m odp2" "" }{TEXT 23 12 " \n" }{HYPERLNK 17 "modpol" 2 "modpol " "" }{TEXT 23 7 " " }{HYPERLNK 17 "mods" 2 "mod" "" }{TEXT 23 14 " " }{HYPERLNK 17 "msolve" 2 "msolve" "" }{TEXT 23 11 " " }{HYPERLNK 17 "mtaylor" 2 "mtaylor" "" }{TEXT 23 10 " \+ \n" }{HYPERLNK 17 "mul" 2 "add" "" }{TEXT 23 10 " " } {HYPERLNK 17 "nextprime" 2 "nextprime" "" }{TEXT 23 9 " " } {HYPERLNK 17 "nops" 2 "op" "" }{TEXT 23 13 " " }{HYPERLNK 17 "norm" 2 "norm" "" }{TEXT 23 13 " \n" }{HYPERLNK 17 "nor mal" 2 "normal" "" }{TEXT 23 7 " " }{HYPERLNK 17 "numboccur" 2 " numboccur" "" }{TEXT 23 9 " " }{HYPERLNK 17 "numer" 2 "numer" "" }{TEXT 23 12 " " }{HYPERLNK 17 "op" 2 "op" "" }{TEXT 23 15 " \n" }{HYPERLNK 17 "open" 2 "open" "" }{TEXT 23 9 " \+ " }{HYPERLNK 17 "optimize" 2 "optimize" "" }{TEXT 23 10 " \+ " }{HYPERLNK 17 "order" 2 "order" "" }{TEXT 23 12 " " } {HYPERLNK 17 "parse" 2 "parse" "" }{TEXT 23 12 " \n" } {HYPERLNK 17 "pclose" 2 "fclose" "" }{TEXT 23 7 " " }{HYPERLNK 17 "pclose" 2 "fflush" "" }{TEXT 23 12 " " }{HYPERLNK 17 "p desolve" 2 "pdesolve" "" }{TEXT 23 9 " " }{HYPERLNK 17 "piecew ise" 2 "piecewise" "" }{TEXT 23 8 " \n" }{HYPERLNK 17 "plot" 2 " plot" "" }{TEXT 23 9 " " }{HYPERLNK 17 "plot3d" 2 "plot3d" "" }{TEXT 23 12 " " }{HYPERLNK 17 "plotsetup" 2 "plotsetup" " " }{TEXT 23 8 " " }{HYPERLNK 17 "pochhammer" 2 "pochhammer" "" }{TEXT 23 7 " \n" }{HYPERLNK 17 "pointto" 2 "assemble" "" }{TEXT 23 6 " " }{HYPERLNK 17 "poisson" 2 "poisson" "" }{TEXT 23 11 " \+ " }{HYPERLNK 17 "polar" 2 "polar" "" }{TEXT 23 12 " \+ " }{HYPERLNK 17 "polylog" 2 "polylog" "" }{TEXT 23 10 " \n" } {HYPERLNK 17 "polynom" 2 "polynom" "" }{TEXT 23 6 " " }{HYPERLNK 17 "powmod" 2 "powmod" "" }{TEXT 23 12 " " }{HYPERLNK 17 "p rem" 2 "prem" "" }{TEXT 23 13 " " }{HYPERLNK 17 "prevprime " 2 "nextprime" "" }{TEXT 23 8 " \n" }{HYPERLNK 17 "primpart" 2 "content" "" }{TEXT 23 5 " " }{HYPERLNK 17 "print" 2 "print" "" } {TEXT 23 13 " " }{HYPERLNK 17 "printf" 2 "printf" "" } {TEXT 23 11 " " }{HYPERLNK 17 "procbody" 2 "procbody" "" } {TEXT 23 9 " \n" }{HYPERLNK 17 "procmake" 2 "procmake" "" } {TEXT 23 5 " " }{HYPERLNK 17 "product" 2 "product" "" }{TEXT 23 11 " " }{HYPERLNK 17 "proot" 2 "psqrt" "" }{TEXT 23 12 " \+ " }{HYPERLNK 17 "property" 2 "property" "" }{TEXT 23 9 " \+ \n" }{HYPERLNK 17 "protect" 2 "protect" "" }{TEXT 23 6 " " } {HYPERLNK 17 "psqrt" 2 "psqrt" "" }{TEXT 23 13 " " } {HYPERLNK 17 "quo" 2 "rem" "" }{TEXT 23 14 " " } {HYPERLNK 17 "radnormal" 2 "radnormal" "" }{TEXT 23 8 " \n" } {HYPERLNK 17 "radsimp" 2 "radsimp" "" }{TEXT 23 6 " " }{HYPERLNK 17 "rand" 2 "rand" "" }{TEXT 23 14 " " }{HYPERLNK 17 "ran domize" 2 "randomize" "" }{TEXT 23 8 " " }{HYPERLNK 17 "randpol y" 2 "randpoly" "" }{TEXT 23 9 " \n" }{HYPERLNK 17 "range" 2 "r ange" "" }{TEXT 23 8 " " }{HYPERLNK 17 "rationalize" 2 "rationa lize" "" }{TEXT 23 7 " " }{HYPERLNK 17 "ratrecon" 2 "ratrecon" " " }{TEXT 23 9 " " }{HYPERLNK 17 "readbytes" 2 "readbytes" "" } {TEXT 23 8 " \n" }{HYPERLNK 17 "readdata" 2 "readdata" "" } {TEXT 23 5 " " }{HYPERLNK 17 "readlib" 2 "readlib" "" }{TEXT 23 11 " " }{HYPERLNK 17 "readline" 2 "readline" "" }{TEXT 23 9 " " }{HYPERLNK 17 "readstat" 2 "readstat" "" }{TEXT 23 9 " \+ \n" }{HYPERLNK 17 "realroot" 2 "realroot" "" }{TEXT 23 5 " " } {HYPERLNK 17 "recipoly" 2 "recipoly" "" }{TEXT 23 10 " " } {HYPERLNK 17 "rem" 2 "rem" "" }{TEXT 23 14 " " } {HYPERLNK 17 "remove" 2 "select" "" }{TEXT 23 11 " \n" } {HYPERLNK 17 "residue" 2 "residue" "" }{TEXT 23 6 " " }{HYPERLNK 17 "resultant" 2 "resultant" "" }{TEXT 23 9 " " }{HYPERLNK 17 "rhs" 2 "lhs" "" }{TEXT 23 14 " " }{HYPERLNK 17 "root" 2 "root" "" }{TEXT 23 13 " \n" }{HYPERLNK 17 "roots" 2 "roots " "" }{TEXT 23 8 " " }{HYPERLNK 17 "round" 2 "trunc" "" }{TEXT 23 13 " " }{HYPERLNK 17 "rsolve" 2 "rsolve" "" }{TEXT 23 11 " " }{HYPERLNK 17 "savelib" 2 "savelib" "" }{TEXT 23 10 " \n" }{HYPERLNK 17 "scanf" 2 "sscanf" "" }{TEXT 23 8 " \+ " }{HYPERLNK 17 "searchtext" 2 "searchtext" "" }{TEXT 23 8 " " }{HYPERLNK 17 "sec" 2 "trig" "" }{TEXT 23 14 " " } {HYPERLNK 17 "sech" 2 "trig" "" }{TEXT 23 13 " \n" } {HYPERLNK 17 "select" 2 "select" "" }{TEXT 23 7 " " }{HYPERLNK 17 "seq" 2 "seq" "" }{TEXT 23 15 " " }{HYPERLNK 17 "seri es" 2 "series" "" }{TEXT 23 11 " " }{HYPERLNK 17 "setattribu te" 2 "attributes" "" }{TEXT 23 5 " \n" }{HYPERLNK 17 "shake" 2 "ev alr" "" }{TEXT 23 8 " " }{HYPERLNK 17 "showprofile" 2 "showprof ile" "" }{TEXT 23 7 " " }{HYPERLNK 17 "showtime" 2 "showtime" " " }{TEXT 23 9 " " }{HYPERLNK 17 "sign" 2 "sign" "" }{TEXT 23 13 " \n" }{HYPERLNK 17 "signum" 2 "signum" "" }{TEXT 23 7 " " }{HYPERLNK 17 "simplify" 2 "simplify" "" }{TEXT 23 10 " \+ " }{HYPERLNK 17 "sin" 2 "trig" "" }{TEXT 23 14 " " } {HYPERLNK 17 "singular" 2 "singular" "" }{TEXT 23 9 " \n" } {HYPERLNK 17 "sinh" 2 "trig" "" }{TEXT 23 9 " " }{HYPERLNK 17 "sinterp" 2 "sinterp" "" }{TEXT 23 11 " " }{HYPERLNK 17 "sol ve" 2 "solve" "" }{TEXT 23 12 " " }{HYPERLNK 17 "sort" 2 "s ort" "" }{TEXT 23 13 " \n" }{HYPERLNK 17 "sparse" 2 "sparse " "" }{TEXT 23 7 " " }{HYPERLNK 17 "spline" 2 "spline" "" } {TEXT 23 12 " " }{HYPERLNK 17 "split" 2 "split" "" }{TEXT 23 12 " " }{HYPERLNK 17 "splits" 2 "splits" "" }{TEXT 23 11 " \n" }{HYPERLNK 17 "sprem" 2 "prem" "" }{TEXT 23 8 " \+ " }{HYPERLNK 17 "sprintf" 2 "printf" "" }{TEXT 23 11 " " }{HYPERLNK 17 "sqrfree" 2 "sqrfree" "" }{TEXT 23 10 " " } {HYPERLNK 17 "sqrt" 2 "sqrt" "" }{TEXT 23 13 " \n" } {HYPERLNK 17 "sscanf" 2 "sscanf" "" }{TEXT 23 7 " " }{HYPERLNK 17 "ssystem" 2 "ssystem" "" }{TEXT 23 11 " " }{HYPERLNK 17 " stack" 2 "stack" "" }{TEXT 23 12 " " }{HYPERLNK 17 "sturm" 2 "sturm" "" }{TEXT 23 12 " \n" }{HYPERLNK 17 "sturmseq" 2 " sturm" "" }{TEXT 23 5 " " }{HYPERLNK 17 "subs" 2 "subs" "" }{TEXT 23 14 " " }{HYPERLNK 17 "subsop" 2 "subsop" "" }{TEXT 23 11 " " }{HYPERLNK 17 "substring" 2 "substring" "" }{TEXT 23 8 " \n" }{HYPERLNK 17 "sum" 2 "sum" "" }{TEXT 23 10 " \+ " }{HYPERLNK 17 "surd" 2 "surd" "" }{TEXT 23 14 " " } {HYPERLNK 17 "symmdiff" 2 "symmdiff" "" }{TEXT 23 9 " " } {HYPERLNK 17 "symmetric" 2 "symmetric" "" }{TEXT 23 8 " \n" } {HYPERLNK 17 "system" 2 "system" "" }{TEXT 23 7 " " }{HYPERLNK 17 "table" 2 "table" "" }{TEXT 23 13 " " }{HYPERLNK 17 "ta n" 2 "trig" "" }{TEXT 23 14 " " }{HYPERLNK 17 "tanh" 2 "t rig" "" }{TEXT 23 13 " \n" }{HYPERLNK 17 "testeq" 2 "testeq " "" }{TEXT 23 7 " " }{HYPERLNK 17 "testfloat" 2 "testfloat" "" }{TEXT 23 9 " " }{HYPERLNK 17 "thaw" 2 "freeze" "" }{TEXT 23 13 " " }{HYPERLNK 17 "thiele" 2 "thiele" "" }{TEXT 23 11 " \n" }{HYPERLNK 17 "time" 2 "time" "" }{TEXT 23 9 " \+ " }{HYPERLNK 17 "translate" 2 "translate" "" }{TEXT 23 9 " " } {HYPERLNK 17 "traperror" 2 "traperror" "" }{TEXT 23 8 " " } {HYPERLNK 17 "trigsubs" 2 "trigsubs" "" }{TEXT 23 9 " \n" } {HYPERLNK 17 "trunc" 2 "trunc" "" }{TEXT 23 8 " " }{HYPERLNK 17 "type" 2 "type" "" }{TEXT 23 14 " " }{HYPERLNK 17 "typ ematch" 2 "typematch" "" }{TEXT 23 8 " " }{HYPERLNK 17 "unames " 2 "unames" "" }{TEXT 23 11 " \n" }{HYPERLNK 17 "unapply" 2 "unapply" "" }{TEXT 23 6 " " }{HYPERLNK 17 "unassign" 2 "unassign " "" }{TEXT 23 10 " " }{HYPERLNK 17 "unload" 2 "unload" "" } {TEXT 23 11 " " }{HYPERLNK 17 "unprotect" 2 "protect" "" } {TEXT 23 8 " \n" }{HYPERLNK 17 "updatesR4" 2 "updatesR4" "" } {TEXT 23 4 " " }{HYPERLNK 17 "userinfo" 2 "userinfo" "" }{TEXT 23 10 " " }{HYPERLNK 17 "value" 2 "value" "" }{TEXT 23 12 " \+ " }{HYPERLNK 17 "vector" 2 "vector" "" }{TEXT 23 11 " \+ \n" }{HYPERLNK 17 "verify" 2 "verify" "" }{TEXT 23 7 " " } {HYPERLNK 17 "whattype" 2 "whattype" "" }{TEXT 23 10 " " } {HYPERLNK 17 "with" 2 "with" "" }{TEXT 23 13 " " } {HYPERLNK 17 "writebytes" 2 "writebytes" "" }{TEXT 23 7 " \n" } {HYPERLNK 17 "writedata" 2 "writedata" "" }{TEXT 23 4 " " } {HYPERLNK 17 "writeline" 2 "writeline" "" }{TEXT 23 9 " " } {HYPERLNK 17 "writestat" 2 "writestat" "" }{TEXT 23 8 " " } {HYPERLNK 17 "writeto" 2 "writeto" "" }{TEXT 23 10 " \n" } {HYPERLNK 17 "zip" 2 "zip" "" }{TEXT 23 10 " " }{HYPERLNK 17 "ztrans" 2 "ztrans" "" }{TEXT 23 46 " \+ " }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 5 "# FIM" }}}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}} {MARK "5 0" 7 }{VIEWOPTS 1 1 0 1 1 1803 }