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}0 0 0 -1 -1 -1 1 0 1 0 2 2 -1 1 }} {SECT 0 {EXCHG {PARA 231 "" 0 "" {TEXT 379 27 "DEUG -- MASS1 en 2004- 2005" }}{PARA 231 "" 0 "" {TEXT 379 35 "Premiers pas dans le syst\350m e Maple " }}}{SECT 0 {PARA 232 "" 0 "" {TEXT 380 28 "Premieres command es en Maple" }}{EXCHG {PARA 233 "> " 0 "" {MPLTEXT 1 381 8 "restart;" }}}{EXCHG {PARA 234 "" 0 "" {TEXT 382 74 "Vous etes sous Windows, vous trouverez Maple dans le menu Demarrer. Clic! " }{TEXT 382 1 "\n" }} {PARA 235 "" 0 "" {TEXT 383 81 "Vous vous trouvez dans une \"Maple Wor ksheet\", sous Windows l'extension est .mws." }}{PARA 236 "" 0 "" {TEXT 384 86 "C'est une feuille de travail, structur\351e en paragrap hes, pouvant contenir des calculs" }}{PARA 237 "" 0 "" {TEXT 385 86 "m ath\351matiques, des graphiques 2D ou 3D, des animations, etc. et pouv ant \352tre imprim\351e." }{TEXT 385 87 "\nLe document que vous avez s ous les mains en est un exemple, il a \351t\351 compos\351 \340 partir " }{TEXT 385 57 "\nde documents semblables \351labor\351s les annees \+ pr\351c\351dentes." }{TEXT 385 39 "\nLisez-le et relisez-le attentivem ent !" }{TEXT 385 95 "\nPour la session suivante, vous devez rediger u n compte rendu avec les solutions des exercices." }}{PARA 238 "" 0 "" {TEXT 386 88 "Une commande s'\351crit sur une ligne o\371 se trouve l e \"prompt\" de Maple qui est le signe " }{TEXT 386 3 "\n> " }{TEXT 386 84 "\nvous devez la terminer par un point-virgule (pour que l'exe cution s'affiche) ou un" }}{PARA 239 "" 0 "" {TEXT 387 91 "deux-points pour une execution que l'on veut cacher (par exemple si elle est vol umineuse)." }{TEXT 387 97 "\nElle s'execute quand on appuie sur la tou che Retour. Si on veut aller \340 la ligne pour taper une " }}{PARA 240 "" 0 "" {TEXT 388 89 "commande plus longue, il faut appuyer en m\3 52me temps sur les touches Majuscule et Retour. " }}{PARA 241 "" 0 "" {TEXT 389 83 "Dans les documents que l'on vous distribue, les lignes d e commande se terminent en " }}{PARA 233 "" 0 "" {TEXT 390 83 "g\351n \351ral par un deux-points. A vous de remettre le point-virgule quand \+ c'est utile. " }}{PARA 242 "" 0 "" {TEXT 391 91 "Normalement votre com mande apparait en rouge tandis que la r\351ponse du syst\350me est en \+ bleu. " }}{PARA 243 "" 0 "" {TEXT 392 86 "On peut \351crire plusieurs \+ commandes sur une m\352me ligne ou bien \351crire plusieurs lignes " } {TEXT 392 32 "\ndans un meme bloc de commandes." }{TEXT 392 99 "\nOn p eut faire du copier/coller , mais attention aux differents formats de \+ copier (voir dans Edit)." }}{PARA 244 "" 0 "" {TEXT 393 40 "Un comment aire s'\351crit apres le signe #." }{TEXT 393 84 "\nPour passer \340 l a ligne sans executer les commandes, faire shift(majuscule)+return :" }}}{EXCHG {PARA 233 "> " 0 "" {MPLTEXT 1 381 16 "1999*2000*2001: " }}} {EXCHG {PARA 233 "> " 0 "" {MPLTEXT 1 381 49 "1999*a: #remarquer que \+ l'on n'indique rien sur a" }{MPLTEXT 1 381 11 "\n2000+2001:" }}} {EXCHG {PARA 245 "" 0 "" {TEXT 394 11 "Au secours!" }}{PARA 246 "" 0 " " {TEXT 395 51 "Maple reconnait beaucoup de fonctions, par exemple " } {TEXT 396 13 "sin, cos, exp" }{TEXT 395 45 ", etc., mais il se peut qu e vous ne savez pas" }}{PARA 247 "" 0 "" {TEXT 397 69 "comment se nomm e (en Maple) la fonction que vous souhaitez utiliser. " }}{PARA 248 "" 0 "" {TEXT 398 58 "Ne demandez pas tout de suite au prof ! Vous pouv ez vous " }{TEXT 398 43 "d\351brouiller tout seul avec l'aide en ligne ." }}{PARA 249 "" 0 "" {TEXT 399 96 "Dans le menu \"Help\", optez pour \"Topic search\" et tapez lentement les lettres de la fonction que" } }{PARA 250 "" 0 "" {TEXT 400 88 "vous cherchez. N'oubliez pas de ferme z les fen\352tres d'aide dont vous n'avez plus besoin." }{TEXT 400 56 "\nVous pouvez aussi utiliser la commande \"?\" comme ceci :" }}} {EXCHG {PARA 233 "> " 0 "" {MPLTEXT 1 381 11 "? worksheet" }}}{EXCHG {PARA 233 "" 0 "" {TEXT 401 11 "Exercice 1:" }{TEXT 402 1 " " }{TEXT 403 48 "Calculez une valeur numerique de racine de 0,3. " }{TEXT 403 47 "\nDevinez comment ...faites le, puis expliquez !" }{TEXT 403 69 " \nPouvez vous effectuer en Maple tous les calculs num\351riques que vo us " }{TEXT 403 44 "effectuez d'habitude avec votre calculette ?" }}} {EXCHG {PARA 233 "" 0 "" {TEXT 404 20 "Variables sous Maple" }}{PARA 233 "" 0 "" {TEXT 390 1 "O" }{TEXT 402 73 "n affecte une valeur ou une expression \340 une variable par le signe \":=\" " }{TEXT 402 87 "\n c'est \340 dire que cette valeur est conserv\351e dans la m\351moire d e Maple et associ\351e \340 ce " }{TEXT 402 5 "nom. " }}}{EXCHG {PARA 233 "> " 0 "" {MPLTEXT 1 381 6 "u:=50:" }}}{EXCHG {PARA 233 "> " 0 "" {MPLTEXT 1 381 7 "v:=5*a:" }}}{EXCHG {PARA 251 "" 0 "" {TEXT 405 98 "C haque variable est identifi\351e par son nom, c'est-a-dire une cha\356 ne de caract\350res et de chiffres. " }}{PARA 252 "" 0 "" {TEXT 406 105 "Seule contrainte: il faut que le nom commence par une lettre. Ma ple distingue majuscules et minuscules. " }}{PARA 253 "" 0 "" {TEXT 407 61 "Pour connaitre la valeur d'une variable, tapez son nom suivi " }{TEXT 408 19 "d'un point-virgule." }}}{EXCHG {PARA 233 "> " 0 "" {MPLTEXT 1 381 11 "toto:=3.11:" }{MPLTEXT 1 381 6 "\ntoto:" }}}{EXCHG {PARA 233 "" 0 "" {TEXT 402 90 "Attention: le signe \351gal \"=\" n'a ffecte pas de valeur \340 la variable !! on verra plus loin " }{TEXT 402 121 "\nqu'il sert \340 exprimer des conditions d'\351galit\351 uti lis\351s dans les tests.Certains noms comme Pi ou I ou exp, sont prot \351g\351s" }{TEXT 390 2 ". " }}}{EXCHG {PARA 233 "" 0 "" {TEXT 401 11 "Exercice 2:" }{TEXT 402 1 " " }{TEXT 402 66 "Entrez ces trois aff ectations et expliquez les reponses de Maple." }{TEXT 402 91 "\nQuelle diff\351rence y a-t-il entre ces affectations et les \351galit\351s q ue l'on \351crit en math ?" }}}{EXCHG {PARA 233 "> " 0 "" {MPLTEXT 1 381 9 "Pi:=3.14:" }}{PARA 254 "" 1 "" {TEXT 409 54 "Error, attempting \+ to assign to `Pi` which is protected" }{TEXT 409 1 "\n" }}}{EXCHG {PARA 233 "> " 0 "" {MPLTEXT 1 381 7 "exp(1):" }}{PARA 233 "> " 0 "" {MPLTEXT 1 381 10 "pi:=3.14: " }}}{EXCHG {PARA 255 "" 0 "" {TEXT 410 79 "On peut aussi \"prot\351ger\" une variable pour \351viter les r\35 1affectations abusives :" }}}{EXCHG {PARA 233 "> " 0 "" {MPLTEXT 1 381 13 "protect('n'):" }{MPLTEXT 1 402 1 " " }{MPLTEXT 1 390 1 "#" } {MPLTEXT 1 403 1 " " }{MPLTEXT 1 390 64 "ATTENTION : ce sont des apos trophes 'n' est diff\351rent de `n` " }{MPLTEXT 1 390 30 "\nsi on te nte une affectation " }{MPLTEXT 1 381 7 "\nn:=0; " }{MPLTEXT 1 390 20 "\nMaple vous r\351pond :" }}{PARA 254 "" 1 "" {TEXT 409 53 "Error, attempting to assign to `n` which is protected" }{TEXT 409 1 "\n" }}} {EXCHG {PARA 233 "" 0 "" {TEXT 402 91 "Pour rendre \340 nouveau \"inde termin\351e\" une variable, on l'affecte \340 son nom mis entre deux \+ '" }{TEXT 402 59 "\n(le lien qui existait dans la m\351moire de Maple \+ est \351ffac\351)" }{TEXT 390 1 ":" }}}{EXCHG {PARA 233 "> " 0 "" {MPLTEXT 1 381 3 "u: " }}}{EXCHG {PARA 233 "> " 0 "" {MPLTEXT 1 381 7 "u:='u':" }}}{EXCHG {PARA 233 "> " 0 "" {MPLTEXT 1 381 2 "u:" }}}} {SECT 0 {PARA 232 "" 0 "" {TEXT 380 18 "Les types en Maple" }}{SECT 0 {PARA 256 "" 0 "" {TEXT 411 11 "Les entiers" }}{EXCHG {PARA 257 "" 0 " " {TEXT 412 72 "Affectation avec affichage , les entiers sont aussi gr ands qu'on veut : " }}{PARA 257 "> " 0 "" {MPLTEXT 1 413 9 "n:= 34!: " }}}{PARA 258 "" 0 "" }}{SECT 0 {PARA 256 "" 0 "" {TEXT 411 14 "Les ra tionnels" }}{EXCHG {PARA 255 "" 0 "" {TEXT 410 70 "Les expressions rat ionnelles sont \351valu\351es sous forme de fractions :" }}}{EXCHG {PARA 233 "> " 0 "" {MPLTEXT 1 381 24 "u:= 1/2 +1/3 +1/4 +1/7; " }} {PARA 258 "" 1 "" {XPPMATH 20 "6#>%\"uG#\"$.\"\"#%)" }{TEXT 414 1 " " }}}{EXCHG {PARA 255 "" 0 "" {TEXT 410 95 "Si vous voulez une approxima tion en decimales, utilisez evalf [f pour float = nombre flottant]" } }}{EXCHG {PARA 233 "> " 0 "" {MPLTEXT 1 381 9 "evalf(u);" }}{PARA 258 "" 1 "" {XPPMATH 20 "6#$\"+w/>E7!\"*" }{TEXT 414 1 " " }}}}{SECT 0 {PARA 245 "" 0 "" {TEXT 394 25 " Les r\351els (ou flottants)" }{TEXT 415 1 " " }}{EXCHG {PARA 257 "" 0 "" {TEXT 412 79 " Pi est le nombre bien connu , il est \351value comme une lettre (formellement):" }}} {EXCHG {PARA 257 "> " 0 "" {MPLTEXT 1 413 18 "p:= Pi: q:=1.2*p:" }}} {EXCHG {PARA 255 "" 0 "" {TEXT 410 67 "Evaluation des r\351els par des nombres flottants (nombres decimaux) :" }}}{EXCHG {PARA 257 "> " 0 "" {MPLTEXT 1 413 27 "r:= evalf(p): s:= evalf(q):" }}}{EXCHG {PARA 233 " " 0 "" {TEXT 390 81 "Noter la diff\351rence entre l'entier 5 et le nom bre flottant 5. (qui signifie 5.0)." }{TEXT 390 91 "\nL'\351valuation \+ se fait par defaut avec 10 chiffres en tout. Si vous en voulez plus ou moins," }{TEXT 390 47 "\nvous pouvez le preciser (mais il arrondit !) :" }}}{EXCHG {PARA 233 "> " 0 "" {MPLTEXT 1 381 42 "5: 5.:5+5.:t:=eva lf(p,4): s:=evalf(q,15): " }}}{PARA 233 "" 0 "" {TEXT 402 81 " Si vous voulez changer la precision pour tous les calculs, utiliser la comman de:" }}{EXCHG {PARA 233 "> " 0 "" {MPLTEXT 1 381 12 "Digits:= 30:" } {MPLTEXT 1 381 15 "\nevalf(1.2*Pi):" }}}{EXCHG {PARA 233 "" 0 "" {TEXT 402 79 "La commande round renvoie l'entier le plus proche, tandi s que la commande trunc" }}{PARA 233 "" 0 "" {TEXT 402 90 "renvoie la \+ partie enti\350re. On peut l'utiliser pour \351crire les d\351cimales \+ de Pi, expliquez !" }}}{EXCHG {PARA 233 "> " 0 "" {MPLTEXT 1 381 22 "t runc(10^4*evalf(Pi)):" }{MPLTEXT 1 381 48 "\ntrunc(10^4*evalf(Pi))-10* trunc(10^3*evalf(Pi)):" }}}}{SECT 0 {PARA 245 "" 0 "" {TEXT 394 13 "Le s complexes" }}{EXCHG {PARA 233 "> " 0 "" {MPLTEXT 1 381 28 "z:=1+I: w :=2+I: v:=z*w: 1/v:" }{MPLTEXT 1 381 72 "\n# I v\351rifie la relation \+ I^2 = -1 et tous les calculs en tiennent compte" }}}}{SECT 0 {PARA 245 "" 0 "" {TEXT 394 13 "Les fonctions" }}{EXCHG {PARA 233 "" 0 "" {TEXT 390 77 "La d\351finition d'une fonction se fait par la notation \+ \"fl\351che\" (suivi de ->):" }}}{EXCHG {PARA 233 "> " 0 "" {MPLTEXT 1 381 26 "f:= x -> x^3/(x^2+3*x+3): " }}{PARA 233 "" 0 "" {TEXT 416 57 "\n# il faut \351crire tous les operateurs: 3*x au lieu de 3x " }}} {EXCHG {PARA 233 "" 0 "" {TEXT 402 125 "Evaluation d'une fonction en u n point (noter la diff\351rence entre l'\351valuation de f au nombre \+ entier \"7\" et au flottant \"7.\")" }{TEXT 390 2 " :" }}}{EXCHG {PARA 233 "> " 0 "" {MPLTEXT 1 381 12 "f(7):f(7.): " }}}{EXCHG {PARA 233 "> " 0 "" {MPLTEXT 1 381 30 "g:=x->x: h:=f+g: h(2):f(g(2)):" }}} {EXCHG {PARA 233 "" 0 "" {TEXT 402 71 "On peut additionner, multiplier , diviser, d\351river, ... des expressions:" }}}{EXCHG {PARA 233 "> " 0 "" {MPLTEXT 1 381 13 "diff(h(x),x):" }}}{EXCHG {PARA 233 "" 0 "" {TEXT 390 32 "Fonctions \340 plusieurs variables:" }}}{EXCHG {PARA 233 "> " 0 "" {MPLTEXT 1 381 47 "norme:=(x,y) -> (x^2+y^2)^(1/2): norm e(1.,-5.):" }}}{EXCHG {PARA 233 "" 0 "" {TEXT 401 11 "Exercice 3:" } {TEXT 402 62 " Expliquez la diff\351rence entre une fonction et une ex pression." }}{PARA 233 "" 0 "" {TEXT 402 84 "Peut-on par exemple les a dditionner ? Comment fait-on pour composer deux fonctions ?" }{TEXT 402 44 "\nComment s'effectue l'\351valuation en chaine ?" }}}}{SECT 0 {PARA 259 "" 0 "" {TEXT 417 16 "Listes et suites" }}{EXCHG {PARA 233 " " 0 "" {TEXT 402 72 "Une liste est un ensemble ordonn\351 de valeurs ( notez bien la syntaxe !) :" }{TEXT 390 1 " " }}}{EXCHG {PARA 233 "> " 0 "" {MPLTEXT 1 381 21 "liste1:=[1,2,a, 5,9]:" }}}{EXCHG {PARA 233 "" 0 "" {TEXT 390 61 "Pour acc\351der aux \351lements d'une liste, on ind ique le num\351ro :" }}}{EXCHG {PARA 233 "> " 0 "" {MPLTEXT 1 381 31 " liste1[3]: liste1[5]:liste1[6]:" }}{PARA 254 "" 1 "" {TEXT 409 33 "Err or, invalid subscript selector" }{TEXT 409 1 "\n" }}}{EXCHG {PARA 233 "" 0 "" {TEXT 390 70 "La fonction nops permet de connaitre le nombre d '\351lements d'une liste:" }}}{EXCHG {PARA 233 "> " 0 "" {MPLTEXT 1 381 13 "nops(liste1):" }}}{EXCHG {PARA 233 "" 0 "" {TEXT 402 107 "Pour former rapidement une liste, il est commode de construire une suite \+ (\"sequence\" pour les anglophones)" }{TEXT 402 28 "\n\340 l'aide de l a commande seq" }{TEXT 390 1 " " }}{PARA 233 "> " 0 "" {MPLTEXT 1 381 18 "S:=seq(j,j=1..17):" }}}{EXCHG {PARA 233 "> " 0 "" {MPLTEXT 1 381 26 "T:=seq(cos(j*Pi), j=1..4):" }}}{EXCHG {PARA 233 "" 0 "" {TEXT 390 13 "Remarquer que" }{TEXT 402 1 " " }{TEXT 390 64 "une autre syntaxe ( plus courte) est \351galement accept\351e par Maple" }{TEXT 402 2 " :" }}}{EXCHG {PARA 233 "> " 0 "" {MPLTEXT 1 381 31 "j $j=1..17: cos(j*P i) $j=1..4:" }}}{EXCHG {PARA 233 "" 0 "" {TEXT 402 60 "Pour ajouter un \351l\351ment \340 une suite, on utilise une virgule." }{TEXT 402 30 "\nLa suitre vide se nomme NULL." }{TEXT 402 94 "\nOn peut aussi trans former une suite en liste (\347a sert par exemple pour tracer des gra phiques" }{TEXT 390 1 ")" }}}{EXCHG {PARA 233 "> " 0 "" {MPLTEXT 1 381 21 "S2:=S,a: S3:NULL,a,b:" }{MPLTEXT 1 381 9 "\nLS:=[S]:" }}}} {EXCHG {PARA 233 "" 0 "" {TEXT 402 96 "Vous pouvez consulter l'Aide en ligne \"Help\" pour effectuer des manipulations plus compliquees. " } {TEXT 402 69 "\nIl existe aussi un type ensemble cherchez \"? set \" ou \"? union\"." }}}{EXCHG {PARA 233 "" 0 "" {TEXT 401 11 "Exercice 4:" }{TEXT 402 42 " Expliquez la diff\351rence, en Maple, entre " } {TEXT 402 38 "une liste et un ensemble, comparer les" }}{PARA 233 "" 0 "" {TEXT 402 39 "r\351sultats des commandes [S,T] et \{S,T\}." }}} {SECT 0 {PARA 245 "" 0 "" {TEXT 394 12 "Les tableaux" }}{EXCHG {PARA 233 "" 0 "" {TEXT 390 47 "Voici comment les d\351clarer et les initial iser :" }}}{EXCHG {PARA 257 "> " 0 "" {MPLTEXT 1 413 23 "A1:= array(0. .2,1..5): " }{MPLTEXT 1 412 51 "# d\351claration d'un tableau \340 3 l ignes et 5 colonnes" }{MPLTEXT 1 413 44 "\nA2:= array(1..3,1..2,[[1,0] ,[4,2],[1,3]]): " }{MPLTEXT 1 412 31 "# declaration et initialisation" }}}{PARA 233 "" 0 "" {TEXT 402 56 "Remarquer que les tableaux sont re mplis ligne par ligne." }}}{SECT 0 {PARA 256 "" 0 "" {TEXT 411 25 "Les matrices et vecteurs " }{TEXT 418 2 ": " }{TEXT 419 33 "on doit consu lter la biblioth\350que" }{TEXT 420 2 " (" }{TEXT 419 25 "on dit aussi librairie) " }{TEXT 420 7 " linalg" }}{EXCHG {PARA 233 "> " 0 "" {MPLTEXT 1 381 13 "with(linalg):" }{MPLTEXT 1 403 2 "# " }{MPLTEXT 1 390 65 "on \"charge\" la librairie linalg , ici sans afficher son con tenu " }}{PARA 260 "" 1 "" {TEXT 421 32 "Warning, new definition for n orm" }}{PARA 260 "" 1 "" {TEXT 421 33 "Warning, new definition for tra ce" }}}{EXCHG {PARA 257 "" 0 "" {TEXT 422 47 "D\351claration, initial isation, calcul matriciel " }{TEXT 412 3 " " }}{PARA 257 "> " 0 "" {MPLTEXT 1 413 31 "A:=matrix(2,3,[seq(i,i=1..6)]):" }{MPLTEXT 1 413 34 "\nB:=matrix(2,3,[seq(6-i,i=1..6)]):" }{MPLTEXT 1 413 9 "\nC:= A+B: " }}}{EXCHG {PARA 257 "" 0 "" {TEXT 412 47 "On \"force\" l'\351valuat ion de C par la commande " }{TEXT 422 5 "evalm" }{TEXT 423 1 " " } {TEXT 412 1 ":" }}{PARA 257 "> " 0 "" {MPLTEXT 1 413 14 "C:=evalm(A+B) :" }}}{EXCHG {PARA 233 "" 0 "" {TEXT 402 76 "voici un autre exemple d' affectation de matrices et de calcul d'un produit :" }}}{EXCHG {PARA 233 "> " 0 "" {MPLTEXT 1 381 33 "AA:= matrix(2,3, [a,b,c,d,e,f]): " } {MPLTEXT 1 381 48 "\nBB:= matrix(3,1,[x1,x2,x3]): # c'est un vecteur" }}}{EXCHG {PARA 233 "> " 0 "" {MPLTEXT 1 381 55 "evalm(AA&*BB): # cec i effectue le produit de matrices " }}}}{PARA 245 "" 0 "" }{EXCHG {PARA 233 "" 0 "" {TEXT 402 78 "Remarque : Les op\351rations sur les m atrices seront \351galement \351tudi\351es en Math. " }}}}{SECT 0 {PARA 261 "" 0 "" {TEXT 424 43 "Le langage de programmation (par l'exe mple)" }}{PARA 233 "" 0 "" {TEXT 402 99 "Maple ne se r\351duit pas \34 0 une calculette sophistiqu\351e. Il contient aussi un langage de prog rammation" }{TEXT 390 1 " " }}{PARA 233 "" 0 "" {TEXT 390 1 " " } {TEXT 402 87 "specialis\351 en math\351matiques. Voici d'abord deux s tructures de contr\364le: \"IF\" et \"FOR\"," }}{PARA 233 "" 0 "" {TEXT 402 83 "les mots r\351serv\351s sont \351crits en gras , n'oubli ez pas fi \340 la fin de l'instruction " }{TEXT 390 2 ": " }}{SECT 0 {PARA 259 "" 0 "" {TEXT 417 32 "L'instruction conditionnelle IF " }} {PARA 257 "" 0 "" {TEXT 425 7 "Syntaxe" }{TEXT 412 12 "\n " }{TEXT 422 3 " if" }{TEXT 412 11 " condition " }{TEXT 422 4 "then" } {TEXT 412 15 " instructions " }{TEXT 422 3 "fi " }{TEXT 412 1 ";" }} {PARA 257 "" 0 "" {TEXT 412 7 "ou bien" }}{PARA 257 "" 0 "" {TEXT 412 11 " " }{TEXT 422 2 "if" }{TEXT 412 11 " condition " }{TEXT 422 4 "then" }{TEXT 412 19 " instructions_1 " }{TEXT 412 12 "\n \+ " }{TEXT 422 6 "else " }{TEXT 412 14 "insructions_2 " }{TEXT 422 12 "\n " }{TEXT 422 2 "fi" }{TEXT 422 1 ";" }{TEXT 412 9 "\nou bien " }{TEXT 412 10 "\n " }{TEXT 422 7 "if " } {TEXT 412 12 "condition_1 " }{TEXT 422 4 "then" }{TEXT 412 18 " instr uctions_1 " }{TEXT 412 12 "\n " }{TEXT 422 5 "elif " } {TEXT 412 13 " condition_2 " }{TEXT 422 4 "then" }{TEXT 412 16 " instr uctions_2 " }{TEXT 412 17 "\n ....." }{TEXT 412 12 "\n \+ " }{TEXT 422 5 "elif " }{TEXT 412 13 " condition_n " }{TEXT 422 4 "then" }{TEXT 412 16 " instructions_n" }{TEXT 422 18 "\n \+ else " }{TEXT 412 15 " insructions " }{TEXT 412 12 "\n " }{TEXT 422 2 "fi" }{TEXT 412 1 ";" }{TEXT 426 62 "\nles conditions son t exprim\351es par exemple \340 l'aide de =, >,<." }}{PARA 262 "" 0 "" {TEXT 427 7 "Exemple" }}{EXCHG {PARA 257 "> " 0 "" {MPLTEXT 1 413 38 "m:=3: x:=1:y:=1: # valeurs initiales " }{MPLTEXT 1 413 1 "\n" } {MPLTEXT 1 413 19 "\nif x > y then m:=x" }{MPLTEXT 1 413 12 "\nelse m \+ := 0" }{MPLTEXT 1 412 4 " " }{MPLTEXT 1 413 4 "\nfi;" }}{PARA 258 " " 1 "" {XPPMATH 20 "6#>%\"mG\"\"!" }{TEXT 414 1 " " }}}{PARA 233 "" 0 "" {TEXT 402 78 "Faire attention aux ponctuations ; ou : pour pr\351vo ir ce qui doit \352tre affich\351." }{TEXT 402 55 "\nNe pas oublier le \"fi\" \340 la fin de l'instruction IF !" }{TEXT 390 1 "!" }}}{SECT 0 {PARA 259 "" 0 "" {TEXT 417 28 "L'instruction it\351rative FOR " }} {EXCHG {PARA 257 "" 0 "" {TEXT 425 8 "Syntaxe " }{TEXT 412 1 ":" } {TEXT 412 9 "\n " }{TEXT 422 6 " for " }{TEXT 412 7 " j " }{TEXT 422 5 "from " }{TEXT 412 9 " debut " }{TEXT 422 2 "to" } {TEXT 412 8 " fin " }{TEXT 422 2 "by" }{TEXT 412 8 " pas " } {TEXT 422 2 "do" }{TEXT 412 15 " instructions " }{TEXT 422 3 "od;" } {TEXT 412 8 "\nou bien" }}{PARA 257 "" 0 "" {TEXT 412 6 " " } {TEXT 422 5 "for " }{TEXT 412 7 " j " }{TEXT 422 3 " in" }{TEXT 412 17 " Quelquechose " }{TEXT 422 2 "do" }{TEXT 412 15 " instruct ions " }{TEXT 422 3 "od;" }{TEXT 412 1 "\n" }{TEXT 412 2 "\n\"" } {TEXT 422 2 "by" }{TEXT 412 71 "\" est facultatif, la lettre j peut \3 52tre remplac\351e par une autre lettre." }{TEXT 412 53 "\nNe pas oubl ier le \"od\" \340 la fin de l'instruction !!" }}}{EXCHG {PARA 262 "" 0 "" {TEXT 427 8 "Exemples" }}}{EXCHG {PARA 233 "> " 0 "" {MPLTEXT 1 381 19 "for k from 1 to 10 " }{MPLTEXT 1 381 5 "\n do" }{MPLTEXT 1 381 16 "\n evalf(Pi,k)" }{MPLTEXT 1 381 6 "\n od:" }}}{EXCHG {PARA 233 "> " 0 "" {MPLTEXT 1 381 46 "L:=[seq(j^2,j=1..4)]: #il s'ag it d'une liste " }{MPLTEXT 1 381 52 "\ns:=0: # on initialise s \340 0 \+ pour calculer une somme" }{MPLTEXT 1 381 14 "\nfor k in L do" } {MPLTEXT 1 381 17 "\n s:=s+k od : " }{MPLTEXT 1 381 45 "\n# on cach e les calculs interm\351diaires avec :" }{MPLTEXT 1 381 59 "\ns; # ce ci donne la valeur de la somme des \351l\351ments de L. " }}{PARA 258 "" 1 "" {XPPMATH 20 "6#\"#I" }{TEXT 414 1 " " }}}{EXCHG {PARA 233 "" 0 "" {TEXT 402 81 "Remarque : Les expressions interm\351diaires peuvent \352tre tres volumineuses, il vaut" }}{PARA 233 "" 0 "" {TEXT 402 42 "mieux ne pas les afficher ni les imprimer." }}}{EXCHG {PARA 233 "" 0 "" {TEXT 401 11 "Exercice 5:" }{TEXT 402 1 " " }{TEXT 402 79 "Ecrire u ne boucle qui remplit une suite avec les 100 premi\350res d\351cimales de Pi." }{TEXT 402 54 "\n(Utiliser la commande trunc comme indiqu\351 plus haut)." }{TEXT 402 107 "\nPuis \351crire une autre boucle qui co mpte combien de fois 0 apparait dans les 100 premi\350res d\351cimales de Pi." }}}}{SECT 0 {PARA 245 "" 0 "" {TEXT 394 14 "Les procedures" } {TEXT 428 105 "\nOn cr\351e une proc\351dure pour ne pas avoir \340 \3 51crire plusieurs fois la m\352me suite d'instructions de calculs." }} {EXCHG {PARA 257 "" 0 "" {TEXT 425 7 "Syntaxe" }{TEXT 412 1 ":" } {TEXT 412 18 "\nnom_de_fonction:=" }{TEXT 422 4 "proc" }{TEXT 412 22 " (suite des parametres)" }{TEXT 413 2 "\n " }{TEXT 422 5 "local" } {TEXT 412 27 " nom_des_variables_locales;" }{TEXT 412 20 "\n Ins tructions" }}{PARA 233 "" 0 "" {TEXT 390 7 " " }{TEXT 429 6 "RET URN" }{TEXT 390 11 "(r\351sultat);" }{TEXT 429 5 "\nend:" }}}{EXCHG {PARA 233 "" 0 "" {TEXT 404 10 "Remarque: " }{TEXT 402 70 "Il n'y a pa s forc\351ment de variables locales, dans ce cas on ecrit pas " } {TEXT 404 5 "local" }{TEXT 402 1 "." }{TEXT 404 10 "\nExemple: " } {TEXT 402 103 "calcul de la somme des carr\351s jusqu'\340 n, ceci g \351n\351ralise le calcul effectu\351 dans l'exemple pre\351c\351dent. " }}}{EXCHG {PARA 233 "> " 0 "" {MPLTEXT 1 381 20 "somCarre:=proc(n) \+ " }{MPLTEXT 1 404 51 "# nom de la proc\351dure et variable globale (v isible)" }{MPLTEXT 1 381 14 "\nlocal k,s; " }{MPLTEXT 1 404 42 "# va riables locales (c'est \340 dire cach\351es)" }{MPLTEXT 1 381 14 "\n \+ s:=0; " }{MPLTEXT 1 404 15 "# instruction 1" }{MPLTEXT 1 381 25 " \n for k from 1 to n do " }{MPLTEXT 1 404 16 "# instruction 2 " } {MPLTEXT 1 381 18 "\n s:=s+k^2 od:" }{MPLTEXT 1 381 10 "\nRETURN(s )" }{MPLTEXT 1 381 9 "\nend: " }{MPLTEXT 1 404 39 "# attention aux \+ majuscules pour RETURN" }}{PARA 233 "" 0 "" {TEXT 404 46 " \+ # fin de la procedure" }{TEXT 381 1 " " }}}{EXCHG {PARA 233 "> " 0 "" {MPLTEXT 1 381 28 "somCarre(4): somCarre(1000):" }}}} {SECT 0 {PARA 256 "" 0 "" {TEXT 411 34 "Quelques fonctions utiles de M aple" }}{SECT 0 {PARA 263 "" 0 "" {TEXT 430 9 "restart: " }{TEXT 431 76 "met \340 z\351ro la m\351moire de Maple. Cela peut servir lorsque \+ les r\351sultats sont " }{TEXT 431 81 "\ninattendus...: mettez l'ordre restart en premi\350re ligne de la feuille de calcul." }{TEXT 431 90 "\nVous pouvez refaire les calculs d'un seul coup par Edit/Execute/Wo rksheet, ou pas a pas." }}}{SECT 0 {PARA 264 "" 0 "" {TEXT 432 6 "time :" }{TEXT 433 85 " le chronom\350tre pour une estimation du temps de \+ calcul , voici un exemple dans lequel" }{TEXT 433 95 "\non mesure le t emps mis pour calculer combien il y a de nombres premiers inf\351rieur s \340 1 0 000 :" }}{EXCHG {PARA 233 "> " 0 "" {MPLTEXT 1 381 8 "resta rt:" }{MPLTEXT 1 381 13 "\nt_0:=time():" }{MPLTEXT 1 381 10 "\n s := 0 :" }{MPLTEXT 1 381 25 "\nfor j from 1 to 10000 do" }{MPLTEXT 1 381 51 "\n if isprime(j) # ceci v\351rifie si j est premier " } {MPLTEXT 1 381 16 "\n then s:=s+1 " }{MPLTEXT 1 381 26 "\n fi \+ od:" }{MPLTEXT 1 381 3 "\ns:" }{MPLTEXT 1 381 43 "\nduree: = time() - t_0: # temps en secondes" }}}}}}{EXCHG {PARA 233 "" 0 "" {TEXT 401 11 "Exercice 6:" }{TEXT 402 1 " " }{TEXT 402 176 "Ecrire une proc\351dure qui calcule les d\351riv\351es partielles de (sin x*y)^n pour n entier positif, puis les range dans une liste L (d\351pendant de n) et fournit le temps du calcul. " }}}{SECT 0 {PARA 232 "" 0 "" {TEXT 434 9 "Graphique" }{TEXT 435 173 "\nMaple est plus puissant et p lus pr\351cis qu'une calculatrice il permet de tracer des graphiques pr\351cis et aussi des animations. Cependant il faut bien apprendre l a syntaxe." }}{SECT 0 {PARA 245 "" 0 "" {TEXT 394 31 "Tracer le graphe d'une fonction" }}}{EXCHG {PARA 233 "> " 0 "" {MPLTEXT 1 381 36 "f:=x ->(0.5*x^3-1.5*x+1)/(x^2+3*x+2):" }}}{EXCHG {PARA 233 "" 0 "" {TEXT 402 89 "Remarquer que le d\351nominateur s'annule pour x=-1, il y aura donc une asymptote verticale." }{TEXT 402 58 "\nLes commandes suivant es donnent des resultats diff\351rents." }}}{EXCHG {PARA 233 "> " 0 "" {MPLTEXT 1 381 23 "plot(f(x),x=-5 .. 5): " }{MPLTEXT 1 381 60 "\n# o n n'impose pas le cadre en y, on voit mal le graphe de f" }}}{EXCHG {PARA 233 "> " 0 "" {MPLTEXT 1 381 31 "plot(f(x),x=-5 .. 5,y=-5 .. 5): " }{MPLTEXT 1 381 64 "\n# le cadre est bon mais Maple trace aussi l'as ymptote verticale" }}}{EXCHG {PARA 233 "> " 0 "" {MPLTEXT 1 381 45 "pl ot(f(x),x=-5 .. 5,y=-5 .. 5,discont=true): " }{MPLTEXT 1 381 45 "\n# o n \351vite le trac\351 de l'asymptote verticale" }}}{EXCHG {PARA 233 " " 0 "" {TEXT 402 62 "Pour tracer plusieurs courbes, on met les \351qua tions entre \{ \}:" }}}{EXCHG {PARA 233 "> " 0 "" {MPLTEXT 1 381 61 "a :=x->0.5*x-1.5: # \351quation donnant l'asymptote oblique de f " }}} {EXCHG {PARA 233 "> " 0 "" {MPLTEXT 1 381 51 "plot(\{f(x),a(x)\},x=-5 \+ .. 5,y=-5 .. 5,discont=true):" }}}{EXCHG {PARA 233 "" 0 "" {TEXT 402 153 "Remarquer que les 2 graphes sont de couleurs diff\351rentes. On p eut choisir ces couleurs et aussi mettre du texte... mais il faut ind iquer o\371 on le place." }{TEXT 402 120 "\nIci on va \351crire asympt ote en bas \340 gauche de l'ecran et align\351 \340 la hauteur de x=-2 et y=-2,6 puis ajouter un titre. " }{TEXT 404 14 "\nExercice 7 : " } {TEXT 402 71 "changer de cadre et de couleurs et \351crire y=f(x) \340 cot\351 du graphe de f." }}}{EXCHG {PARA 233 "> " 0 "" {MPLTEXT 1 381 13 "with(plots): " }{MPLTEXT 1 404 34 "# on charge la librairie gr aphique" }}{PARA 260 "" 1 "" {TEXT 421 49 "Warning, the name changecoo rds has been redefined" }{TEXT 421 1 "\n" }}}{EXCHG {PARA 233 "" 0 "" {TEXT 402 152 "Pour des dessins plus compliqu\351s, on donne d'abord u n nom au tableau engendr\351 par la commande plot puis on l'affiche \3 40 l'\351cran avec la commande display." }}}{EXCHG {PARA 233 "> " 0 "" {MPLTEXT 1 381 60 "graph_f:=plot(f(x),x=-5..5,y=-5..5,discont=true,co lor=blue):" }{MPLTEXT 1 381 47 "\ngraph_a:=plot(a(x),x=-5..5,y=-5..5,c olor=red):" }{MPLTEXT 1 381 58 "\ntext:=textplot([-2,-2.6,`asymptote`] ,align=\{ABOVE,LEFT\}):" }{MPLTEXT 1 381 59 "\n# l'instruction align p recise la position de l'inscription" }{MPLTEXT 1 381 57 "\ndisplay(\{t ext,graph_f,graph_a\},title=`asymptote oblique " }{MPLTEXT 1 381 30 " \nd'une fonction rationnelle`):" }}}{SECT 0 {PARA 245 "" 0 "" {TEXT 394 33 "Tracer des points ou un polygone" }}}{EXCHG {PARA 233 "> " 0 "" {MPLTEXT 1 381 37 " L:=\{[1,2],[2,3],[3,2],[1,4],[2,4]\}: " } {MPLTEXT 1 381 70 "\n# on donne les coordonnees de 5 points et on les \+ met dans un ensemble" }}}{EXCHG {PARA 233 "" 0 "" {TEXT 390 9 "Compare r:" }}}{EXCHG {PARA 233 "> " 0 "" {MPLTEXT 1 381 8 "plot(L):" }}} {EXCHG {PARA 233 "" 0 "" {TEXT 390 20 "Tracer avec style..." }}} {EXCHG {PARA 233 "> " 0 "" {MPLTEXT 1 381 46 "plot(L,style=point,symbo lsize=30,color=black):" }}}{EXCHG {PARA 233 "" 0 "" {TEXT 390 77 "Pour en savoir plus avant d'expliquer tout cela dans votre compte rendu fa ire" }}}{EXCHG {PARA 233 "> " 0 "" {MPLTEXT 1 381 15 "?plot[options];" }}}{SECT 0 {PARA 245 "" 0 "" {TEXT 415 9 "Animation" }{TEXT 436 126 " \nFaire une animation en 2D : c'est \340 dire tracer une succession d e graphes d'une fonction f_t (x) dependant d'un parametre t." }{TEXT 436 83 "\nVoici un exemple avec la fonction y=sin(x+t), frames indiqu e le nombres d'images." }{TEXT 436 112 "\nQuand le graphique apparait, il faut cliquer sur la figure. Alors une ligne de commande apparait d ans la barre " }{TEXT 436 57 "\nd'outils et la commande \"Play\" met e n route l'animation." }}{EXCHG {PARA 233 "> " 0 "" {MPLTEXT 1 381 12 " with(plots):" }{MPLTEXT 1 381 46 "\nanimate(sin(x+t),x=-10..10,t=1..4, frames=50):" }{MPLTEXT 1 381 1 "\n" }}{PARA 260 "" 1 "" {TEXT 421 49 " Warning, the name changecoords has been redefined" }{TEXT 421 1 "\n" } }}}}{SECT 0 {PARA 232 "" 0 "" {TEXT 380 46 "Quelques BONS PRINCIPES po ur la programmation " }{TEXT 380 2 "\n(" }{TEXT 435 100 "i) Il est con seill\351 de r\351fl\351chir avant d'\351crire la moindre ligne de cod e, de tester sur un exemple " }{TEXT 435 52 "\n et eventuellement \+ d'ameliorer ce qu'on a \351crit." }{TEXT 435 105 "\n \+ \+ " }{TEXT 435 50 "\n(ii) Voici les d\351coupages qu'il \+ faut rechercher :" }}{PARA 265 "" 0 "" {TEXT 437 11 " un " } {TEXT 438 36 "calcul tres simple = une commande; " }{TEXT 437 1 " " } {TEXT 437 12 "\n un " }{TEXT 438 57 "calcul plut\364t simple = \+ une fonction ou une boucle for; " }{TEXT 437 1 " " }{TEXT 437 12 "\n un " }{TEXT 438 40 "calcul un peu compliqu\351 = une proc\351d ure " }{TEXT 438 73 "\n un calcul compliqu\351 = une successi on maitris\351e de proc\351dures " }{TEXT 437 36 "( donc de fonctions qu'on compose )." }{TEXT 437 1 "\n" }{TEXT 437 104 "\nFaire attention aux noms des variables (globales) : si il est deja pris, les valeurs \+ vont r\351apparaitre." }}{PARA 232 "" 0 "" {TEXT 435 56 "( iii) Trop d e lignes de code nuisent \340 la lisibilit\351 ; " }{TEXT 435 94 "\nun e fonction doit donc \352tre \351crite de mani\350re courte, pensez a ussi \340 a\351rer vos pr\351sentations" }{TEXT 435 100 "\nIl sera so uvent judicieux de d\351composer un proc\351dure longue en plusieurs \+ procedures plus simples " }{TEXT 435 34 "\n( ayant moins de lignes de \+ code )" }{TEXT 439 1 "." }}}{SECT 0 {PARA 232 "" 0 "" {TEXT 434 13 "Po ur conclure" }{TEXT 435 108 "\nMaple contient aussi de tres nombreuses commandes que vous pourrez trouver dans \"Help\" ou dans des manuels. " }{TEXT 435 110 "\nNous en verrons quelques unes dans les prochains c ours. Il faudra aussi vous familiariser avec les commandes " }{TEXT 435 123 "\nassez subtiles qui servent \340 g\351rer la pr\351sentation des expressions et aussi celles qui servent \340 les modifier telles que " }{TEXT 435 56 "\nsimplify, expand, factor, collect, subs, conve rt, ... " }}{PARA 266 "" 0 "" {TEXT 440 114 "Une derni\350re commande de confort : l'operateur dito qui permet de d\351signer la derni\350r e valeur repondue par Maple, " }{TEXT 440 51 "\nil faut utiliser \" s ur Maple V et % sur Maple 7. " }{TEXT 440 63 "\nComme vous voyez il fa ut aussi faire attention au num\351ro de la" }{TEXT 441 1 " " }{TEXT 440 34 "version de Maple que l'on utilise." }}}{PARA 267 "" 0 "" }} {VIEWOPTS 1 1 0 1 1 1803 1 1 1 1 }{PAGENUMBERS 0 1 2 33 1 1 }