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Pour en ins\351rer un, cliquez sur le bouton co rrespondant. Essayez." }}}}{SECT 1 {PARA 4 "" 0 "" {TEXT 216 27 "Ex\35 1cution de commande Maple" }}{EXCHG }{EXCHG {PARA 0 "" 0 "" {TEXT 212 215 "Une fois dans un Input Maple, vous pouvez ex\351cuter des command es. Une commande se termine par ';' si on veut afficher le r\351sultat ou ':' sinon, on l'ex\351cute avec la touche 'Entr\351e'. Ex\351cutez les commandes suivantes." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "1+3*2-7;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 4 "2*3:" }}} {EXCHG {PARA 0 "" 0 "" {TEXT 212 57 "Faites quelques calculs basiques, avec et sans affichage." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 " " }}}{EXCHG {PARA 0 "" 0 "" {TEXT 212 87 "Pour revenir \340 la ligne s ans ex\351cuter, tapez Maj+Entr\351e. Ex\351cutez les lignes suivantes ." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 5 "7*6;\n" }{MPLTEXT 1 0 5 "1-2:\n" }{MPLTEXT 1 0 5 "8/10;" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 212 51 "Reproduisez les lignes pr\351c\351dentes et ex\351cutez-les." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}{SECT 1 {PARA 4 "" 0 "" {TEXT 216 24 "Autres commandes de base" }}{EXCHG }{EXCHG {PARA 0 " " 0 "" {TEXT 212 38 "Pour obtenir de l'aide, tapez '?help'." }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 212 111 "Pour obtenir de l'aide, tapez '?' suivi du nom de la co mmande. Par exemple, ouvrez l'aide de la commande 'irem'" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 212 122 "Pour r\351utiliser le dernier r\351sultat en m\351moire, util isez '%', puis '%%' pour l'avant-dernier. Testez les lignes suivantes. " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 4 "2+3;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 4 "%/2;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 6 "%%-10;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 6 "%%*10;" }}} {EXCHG {PARA 0 "" 0 "" {TEXT 212 173 "Attention ! C'est bien le dernie r r\351sultat en m\351moire qui est utilis\351, pas le r\351sultat de \+ la derni\350re ligne. Pour le voir, ex\351cutez les lignes pr\351c\351 dentes dans le d\351sordre.\n" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 212 142 "Un commentaire est du texte contenu dans une commande Maple mais \+ qui n'est pas ex\351cut\351. Il est introduit par '#'. Testez les lign es suivantes." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 10 "6*7; #3*2; " }}}{EXCHG {PARA 0 "" 0 "" {TEXT 212 125 "Attention, \340 la diff\351 rence de ':', la commande n'est pas ex\351cut\351e, un commentaire peu t ne pas \352tre une commande Maple valide." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 10 "1+1; #2+2;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 2 "%;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 9 "1+1; 2+2:" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 2 "%;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 4 "#1++" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 4 "1 ++;" }}}{EXCHG }}}{SECT 1 {PARA 3 "" 0 "" {TEXT 215 27 "1/ Variables e t affectation" }}{EXCHG }{SECT 1 {PARA 4 "" 0 "" {TEXT 216 9 "Variable s" }}{EXCHG }{EXCHG {PARA 0 "" 0 "" {TEXT 212 144 "Un nom de variable \+ valide commence par une lettre mais peut contenir des chiffres. Attent ion, les majuscules comptent dans les noms de variable." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 3 "t1;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 13 "evalb(t1=t1);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 13 "evalb(T1=t1);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 3 "2t; " }}}{EXCHG {PARA 0 "" 0 "" {TEXT 217 0 "" }}}}{SECT 1 {PARA 4 "" 0 "" {TEXT 216 11 "Affectation" }}{EXCHG }{EXCHG {PARA 0 "" 0 "" {TEXT 212 47 "On affecte une valeur \340 une variable avec ':='." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 5 "a:=2;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 2 "a;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 7 "a:=a+4 ;" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 212 63 "Affecter la valeur a/2 \340 la variable 'a' puis tester sa valeur." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}} {EXCHG {PARA 0 "" 0 "" {TEXT 212 80 "Attention \340 ne pas confondre a vec '=', qui cr\351e une \351quation entre deux membres." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 4 "a=2;" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 212 63 "On teste la valeur (true ou false) d'une \351quation ave c 'evalb'." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 11 "evalb(a=2);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 11 "evalb(a=3);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 212 83 "On peut lib\351rer une variable avec 'un assign' ou en affectant son nom \340 la variable." }}}{EXCHG {PARA 0 " > " 0 "" {MPLTEXT 1 0 14 "unassign('a');" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 2 "a;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 5 "a:=1;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 2 "a;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 7 "a:='a';" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 2 "a;" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 212 127 "La commande 'resta rt' vide toute la m\351moire. Affectez et testez les valeurs de diff\3 51rentes variables avant et apr\350s un restart:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 " " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "restart:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}}{SECT 1 {PARA 3 "" 0 "" {TEXT 215 10 "2/ Nombre s" }}{EXCHG }{SECT 1 {PARA 4 "" 0 "" {TEXT 216 29 "Nombres entiers et \+ rationnels" }}{EXCHG }{EXCHG {PARA 0 "" 0 "" {TEXT 212 57 "Maple sait \+ faire du calcul exact sur les nombres entiers." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 4 "50!;" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 212 24 "Le ur type est 'integer'." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 32 "i s(12,integer); is(1/2,integer);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 212 263 "Les op\351rations \351l\351mentaires sur les entiers sont l'addit ion '+', la soustraction '-', la multiplication '*', la division eucli dienne : quotient 'iquo' et reste 'irem', la puissance '^', le plus gr and diviseur commun 'igcd' et le plus petit multiple commun 'ilcm'." } }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 11 "iquo(59,3);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 212 64 "Calculez le reste dans la division eucli dienne de 2^1003 par 31." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 " " }}}{EXCHG {PARA 0 "" 0 "" {TEXT 212 56 "Calculez le plus grand divis eur commun de 20! et 2^31-3." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 212 94 "Maple sait faire du cal cul exact sur les nombres rationnels. Il les simplifie automatiquement ." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 7 "150/42;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "1/3+1/2;" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 212 71 "Leur type est 'rational', et \351galement 'fraction' pou r les non entiers." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 33 "is(1/ 2,rational); is(2,rational);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 33 "is(1/2,fraction); is(2,fraction);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 212 52 "Les op\351rations \351l\351mentaires sont '+', '-', '*', '/'." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 13 "14/(2/3+4/5);" }}} }{SECT 1 {PARA 4 "" 0 "" {TEXT 216 16 "Nombres d\351cimaux" }}{EXCHG } {EXCHG {PARA 0 "" 0 "" {TEXT 212 73 "Maple sait faire du calcul approc h\351 sur des nombres en \351criture d\351cimale." }}}{EXCHG {PARA 0 " > " 0 "" {MPLTEXT 1 0 8 "1.4*0.7;" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 212 62 "Attention, on utilise un point '.' et non pas une virgule ','. " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 10 "1.2 + 3.7;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 10 "1,2 + 3,7;" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 212 117 "Les nombre d\351cimaux sont repr\351sent\351s par de ux entiers, la mantisse et l'exposant; sous la forme mantisse*10^expos ant." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "12345e6;" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 212 22 "Leur type est 'float'." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 30 "is(0.2,float); is(2/10,float);" }}} {EXCHG {PARA 0 "" 0 "" {TEXT 212 79 "On peut obtenir une valeur approc h\351e d'une expression avec la fonction 'evalf'." }}}{EXCHG {PARA 0 " > " 0 "" {MPLTEXT 1 0 11 "evalf(1/3);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 212 129 "Maple travaille avec un nombre de chiffres fixe, contenu dan s la variable 'Digits'. Affichez le nombres de chiffres actuellement " }{TEXT 212 9 "utilis\351s " }{TEXT 212 10 "par Maple." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 212 37 "Calculez une valeur approch\351e de 5/7." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 212 58 "Modi fiez la variable 'Digits' pour augmenter la pr\351cision." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 212 47 "Calculez \340 nouveau une valeur approch\351e de 5/7." }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}{SECT 1 {PARA 4 "" 0 "" {TEXT 216 12 "Irrationnels" }}{EXCHG }{EXCHG {PARA 0 "" 0 "" {TEXT 212 105 "Maple peut faire du calcul avec certains irrationnels. Par ex emple il connait les racines carr\351es 'sqrt'." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "sqrt(3);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 212 111 "On peut toujours obtenir une valeur approch\351e avec 'evalf' ou \+ en calculant directement sur un nombre \340 virgule." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 25 "evalf(sqrt(3)); sqrt(3.);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 212 133 "Il est souvent pr\351f\351rable de fair e du calcul exact. Par exemple, affectez \340 'x' la valeur 1+sqrt(2) \+ et \340 'y' la valeur 1/(sqrt(2)-1)." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}} {EXCHG {PARA 0 "" 0 "" {TEXT 212 13 "Calculez x-y." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 212 158 "P our que Maple tente de simplifier une expression, il faut lui demander explicitement, avec la fonction 'simplify'. Calculez une expression s implifi\351e de x-y:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }} }{EXCHG {PARA 0 "" 0 "" {TEXT 212 161 "Voyons maintenant ce qui peut s e passer avec un calcul approch\351 : affectez \340 'X' une valeur app roch\351e de x et \340 'Y' une valeur approch\351e de y, puis calculez X-Y." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 11 "Digits:=10;" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}} {EXCHG {PARA 0 "" 0 "" {TEXT 212 54 "Maple connait \351galement quelqu es constantes, comme Pi." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 10 "evalf(Pi);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 212 39 "Attention, la maj uscule est importante." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 10 "e valf(pi);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 212 77 "Comme c'est une con stante de Maple, on ne peut pas l'utiliser comme variable." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 9 "Pi:=3.14;" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 212 78 "On peut obtenir e avec l'exponentielle, ou bien comme s olution d'une \351quation." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 7 "exp(1);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "evalf(exp(1)) ;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "solve(ln(u)=1,u);" }}} }{SECT 1 {PARA 4 "" 0 "" {TEXT 216 17 "Nombres complexes" }}{EXCHG } {EXCHG {PARA 0 "" 0 "" {TEXT 212 160 "Maple n'a pas de type particulie r pour les nombres complexes, on les utilise avec la constante i telle que i^2=-1, qui est not\351e 'I' (attention \340 la majuscule)." }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 6 "5+I*8;" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 212 206 "Les op\351ration particuli\350res aux nombres comp lexes sont la partie r\351elle 'Re', la partie imaginaire 'Im', le mod ule 'abs', un argument 'argument', l'exponentielle complexe 'exp', la \+ conjuguaison 'conjugate'." }}}{EXCHG {PARA 0 "" 0 "" {TEXT 212 44 "Cal culer le module et un argument de 7+0.5i." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}} {EXCHG {PARA 0 "" 0 "" {TEXT 212 64 "Calculer la partie r\351elle et l a partie imaginaire de e^(7+0.5i)." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}} {EXCHG }{EXCHG }{SECT 1 {PARA 3 "" 0 "" {TEXT 215 27 "3/ Fonctions et \+ expressions" }}{EXCHG }{SECT 1 {PARA 4 "" 0 "" {TEXT 216 11 "Expressio ns" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "restart:" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 212 139 "Une expression est un assemblage de var iables li\351es par des op\351rateurs. Elle peut \352tre \351valu\351e en rempla\347ant les variables par des valeurs." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 55 "expr1:=(x^2+x*y)*(y^2-2*x)+x*y^4-2*x^2*y^2+3* y^3-6*x*y;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 34 "expr2:=(exp(u *v)-u*v)/(ln(1+u)-u);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 212 115 "Formez une expression 'expr3' avec pour variables 'r', 's', 't' et utilisant au moins les fonctions 'sin' et 'exp'." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 212 162 "L'op\351rat ion de base sur une expression est l'\351valuation : eval(expression, \+ [variable1=valeur1, variable2=valeur2, ...]) ou bien subs(variable=val eur, expression)." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 23 "eval(e xpr1, [x=1,y=2]);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 22 "subs([ u=1,v=2],expr2);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 212 46 "Evaluez expr 3 au point [r = 1, s = 2, t = -1]." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 212 57 "Calculez une valeur approch\351e de l'\351valuation pr\351c\351dente." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 212 162 "Maple dispose de plusieurs fonctions pour manipuler des expre ssions. La commande 'expand' d\351veloppe l'expression. Testez-la sur \+ les trois expressions pr\351c\351dentes." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 212 66 "La commande 'factor' essaie de factoriser l'expression. \+ Testez-la." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 212 158 "Pour les ex pressions polynomiales, collect(expression, variable) regroupe par pui ssances de 'variable'. Testez-la sur expr1, en prenant x ou y comme va riable." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 18 "collect(expr1, x );" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 212 56 "La commande 'simplify' tente de simplifier l'expre ssion." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 28 "expr4 := exp(y)*e xp(-y) - 1;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 15 "evalb(expr4= 0);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 16 "simplify(expr4);" }} }{EXCHG {PARA 0 "" 0 "" {TEXT 212 162 "Maple peut calculer une d\351ri v\351e par rapport \340 une variable avec diff(expression, variable). \+ Testez sur les expressions pr\351c\351dentes avec les diff\351rentes v ariables." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "diff(expr1,x); " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }} }{EXCHG {PARA 0 "" 0 "" {TEXT 212 152 "Maple peut r\351soudre certaine s \351quations : commandes 'solve(expr1=expr2, variable)' pour une r\3 51solution exacte et 'fsolve' pour une r\351solution approch\351e." }} }{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 41 "P:=x^4-2*x^3-5*x^2-2*x-1; Q :=x^3-46*x+21;" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 212 67 "Calculez exact ement, puis de fa\347on approch\351e les racines de P et Q." }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 212 183 "Maple peut calculer certaines int\351grales : c'est la \+ commande int(expression, variable=borne1..borne2). Calculez l'int\351g rale de P/Q entre 1 et 2, puis calculez-en une valeur approch\351e." } }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 212 110 "Parfois, Maple ne trouve pas d'expression pour l'int\351grale, et on est forc \351s de calculer une valeur approch\351e." }}}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 31 "expr5 := exp(x^2)*ln(1+cos(x));" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 212 53 "Calculez l'int\351grale de expr5 pour x allant d e 0 \340 1." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}{SECT 1 {PARA 4 "" 0 "" {TEXT 216 9 "Fonctions" }}{EXCHG {PARA 0 "" 0 "" {TEXT 212 136 "Une fonction est un objet qui prend une ou plusieurs valeurs en entr\351e et renvo ie une valeur de sortie. Elle s'\351crit en Maple x -> f(x)." }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "f1:=x->x^3+sin(x)/x;" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 22 "f2:=y->exp(y^2-y-1)+1;" }}} {EXCHG {PARA 0 "" 0 "" {TEXT 212 57 "Cr\351ez une fonction 'f3' utilis ant au moins 'ln' et 'cos'." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 212 79 "L'op\351ration de base su r une fonction f est l'\351valuation, qui s'\351crit f(valeur)." }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 6 "f1(7);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "f2(1.5);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 212 77 "Evaluez la fonction f3 en Pi, puis calculez une valeur approch\351 e du r\351sultat." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 212 68 "Maple peut parfois calculer la d\351riv\351e d'une fonct ion f, not\351e D(f)." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 6 "D(f 1);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 212 45 "Calculez les d\351riv\351 es des fonctions f2 et f3." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 " " 0 "" {TEXT 212 196 "Maple peut calculer les int\351grales de certain es fonctions f, la commande est int(f, borne1..borne2). Calculez une v aleur exacte puis une valeur approch\351e des int\351grales entre 0 et 1 de f1, f2, f3." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}{SECT 1 {PARA 4 "" 0 "" {TEXT 216 42 "Comparais on entre fonctions et expressions" }}{EXCHG {PARA 0 "" 0 "" {TEXT 212 267 "Attention, il s'agit de bien faire la diff\351rence entre fonctio n et expression. M\352me si on peut souvent utiliser l'un ou l'autre i ndiff\351remment, ce sont des objets de nature diff\351rente et les fo nctions Maple qui s'appliquent \340 l'un ou l'autre sont souvent diff \351rentes." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 27 "expre1 := u^ 2-sin(u)/ln(u);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 27 "expre2 : = v^2-sin(v)/ln(v);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 21 "eval b(expre1=expre2);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 212 91 "Les express ions expre1 et expre2 sont diff\351rentes car elles n'ont pas les m\35 2mes variables. " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 7 "g1:=u->" }{MPLTEXT 1 0 16 "u^2-sin(u)/ln(u)" }{MPLTEXT 1 0 1 ";" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 7 "g2:=v->" }{MPLTEXT 1 0 16 "v^2-sin(v )/ln(v)" }{MPLTEXT 1 0 1 ";" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 212 168 " Les fonctions g1 et g2 sont les m\352me au sens o\371 elles prennent l es m\352mes valeurs en tout point. (Cependant Maple n'est pas capable \+ de d\351terminer l'\351galit\351 de fonctions)" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 22 "expre3:=(u-v)/(u*v^2);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 212 30 "On a ici une seule expression." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 11 "g3:=(u,v)->" }{MPLTEXT 1 0 13 "(u-v)/(u*v^2)" }{MPLTEXT 1 0 1 ";" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 11 "g4:=( v,u)->" }{MPLTEXT 1 0 13 "(u-v)/(u*v^2)" }{MPLTEXT 1 0 1 ";" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "g3(1,2);" }}}{EXCHG {PARA 0 " > " 0 "" {MPLTEXT 1 0 8 "g4(1,2);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 212 102 "Les fonctions g3 et g4 sont diff\351rentes au sens o\371 elle s prennent des valeurs diff\351rentes en un point." }}}}{SECT 1 {PARA 4 "" 0 "" {TEXT 216 10 "Graphiques" }}{EXCHG {PARA 0 "" 0 "" {TEXT 217 323 "Maple peut produire des graphes de fonctions/expressions. Enc ore une fois, la commande est l\351g\350rement diff\351rente selon qu' on travaille avec une fonction ou une expression. On utilise plot(f,a. .b) pour tracer le graphe d'une fonction sur l'intervalle [a,b] et plo t(expr, x=a..b) pour une expression dont la variable est 'x'." }}} {EXCHG {PARA 0 "" 0 "" {TEXT 212 28 "D\351finissez l'expression f = " }{TEXT 212 61 "(x^2+x+1)x / (x^2-x-1), puis tracer son graphe entre -3 et 8." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 212 87 " D\351finissez la fonction g(x) = 1/(x-1) + cos(x), puis tracer son gra phe entre -20 et 20." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }} }{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 212 87 "Modifiez les commandes des trac\351s pr\351c\351dents po ur que les graphes soit mieux visibles. " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 212 84 "Observez l'e ffet de l'option 'discont = true' dans les commandes de trac\351 de f \+ et g." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 212 165 " En utilisant l'aide sur la fonction 'plot', tracez les courbes de f et g sur un m\352me graphique en utilisant des couleurs et des styles di ff\351rents pour chaque courbe." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 212 32 "Consid\351rez la fonc tion suivante." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "g:=(x,y)- >x*y;" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 212 73 "En utilisant l'aide sur la fonction 'plot3d', repr\351sentez le graphe de g." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}}{EXCHG }{SECT 1 {PARA 3 "" 0 "" {TEXT 215 12 "4/ Exercices" }}{SECT 1 {PARA 4 "" 0 "" {TEXT 216 12 "Affectations" }}{EXCHG {PARA 0 "" 0 "" {TEXT 212 26 "Affectez \340 y \+ la valeur 2x." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}} {EXCHG {PARA 0 "" 0 "" {TEXT 212 60 "Affectez \340 x la valeur 2, puis testez les valeurs de x et y." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 212 51 "R\351soudre l'\351quation x^3+x+1=0. Que remarquez-vous ?" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}} {EXCHG {PARA 0 "" 0 "" {TEXT 212 71 "Lib\351rez la variable x puis r\3 51essayer de r\351soudre l'\351quation. Commentez." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 212 40 "Testez les valeurs de x e t y. Commentez." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}} {SECT 1 {PARA 4 "" 0 "" {TEXT 216 13 "Calcul formel" }}{EXCHG {PARA 0 "" 0 "" {TEXT 212 116 "Montrez par un calcul Maple que cos(x)sin(x)^4 \+ = (cos(5x) - 3cos(3x) + 2cos(x)) / 16. (Utilisez l'aide de 'combine')" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 212 159 "Montrez par un calcul Maple que pour tous complexes \+ z1,z2 on a l'identit\351 |z1+z2|^2 + |z1-z2|^2 = 2 (|z1|^2 + |z2|^2). \+ Interpr\351tez g\351om\351triquement ce r\351sultat." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 212 39 " D\351finir l'expression formelle F= x |x|." }}}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 212 25 "Calculez l a d\351riv\351e de F." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" } }}{EXCHG {PARA 0 "" 0 "" {TEXT 212 121 "En utilisant l'aide sur la fon ction 'assume', ajoutez l'hypoth\350se que x est r\351el, puis simplif iez le r\351sultat pr\351c\351dent. " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}{SECT 1 {PARA 4 "" 0 "" {TEXT 216 7 "Blocage" }} {EXCHG {PARA 0 "" 0 "" {TEXT 212 79 "En utilisant l'aide sur la foncti on 'isprime', testez si 1 000 003 est premier." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 212 26 "Sauveg ardez votre travail." }}}{EXCHG {PARA 0 "" 0 "" {TEXT 212 36 "Testez s i 2^1000003 - 1 est premier." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 212 140 "Essayez d'arr\352ter l e calcul en cliquant sur le bouton STOP. Si le blocage persiste, appui yez sur CTRL+ALT+SUPPR, fermez puis relancez Maple." }}}}{SECT 1 {PARA 4 "" 0 "" {TEXT 216 17 "Etude de fonction" }}{EXCHG {PARA 0 "" 0 "" {TEXT 212 36 "D\351finir f = (x^3+7x^2+5)/(x^2+3x-1)." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 212 53 "Tracez le graphe de f dans un intervalle bien choisi." }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 212 71 "En utilisant un calcul Maple, d\351terminez le domaine d e d\351finition de f." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" } }}{EXCHG {PARA 0 "" 0 "" {TEXT 212 73 "En utilisant des calculs Maple, d\351terminez le tableau de variations de f." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 212 86 "Consult ez l'aide Maple sur la fonction 'limit'. Calculez la limite de f-ax en +infini." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 212 37 "Affectez une valeur pertinente \340 'a'. " }{TEXT 212 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}} {EXCHG {PARA 0 "" 0 "" {TEXT 212 42 "Calculez la limite de f-(ax+b) en +infini." }{TEXT 212 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 212 88 "Commentez le premier calcul de limite. Le graphe de f a-t-il une asymptote en l'infini ?" }{TEXT 212 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}}} {MARK "0 0 0" 0 }{VIEWOPTS 1 1 0 1 1 1803 1 1 1 1 }{PAGENUMBERS 0 1 2 33 1 1 }