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}1 1 0 0 8 2 2 0 2 0 2 2 0 1 }{PSTYLE "_pstyle40 " -1 242 1 {CSTYLE "" -1 -1 "Times" 1 18 0 0 0 1 2 1 2 2 2 2 1 1 1 1 } 3 1 0 0 8 2 2 0 2 0 2 2 0 1 }{PSTYLE "_pstyle41" -1 243 1 {CSTYLE "" -1 -1 "Times" 1 12 0 0 0 1 2 2 2 2 2 2 1 1 1 1 }1 1 0 0 0 0 2 0 2 0 2 2 0 1 }{PSTYLE "_pstyle42" -1 244 1 {CSTYLE "" -1 -1 "Times" 1 12 0 0 0 1 2 2 2 2 2 2 1 1 1 1 }1 1 0 0 0 0 2 0 2 0 2 2 0 1 }{PSTYLE "_pstyle 43" -1 245 1 {CSTYLE "" -1 -1 "Times" 1 12 0 0 0 1 2 2 2 2 2 2 1 1 1 1 }1 1 0 0 0 0 1 0 1 0 2 2 0 1 }} {SECT 0 {EXCHG {PARA 225 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 225 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 226 "" 0 "" {TEXT -1 0 "" }}} {EXCHG {PARA 227 "" 0 "" {TEXT 205 20 "Introduction \340 Maple" }}} {EXCHG {PARA 226 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 226 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 228 "" 0 "" {TEXT 204 20 "Ma\356trise el ementaire" }}}{EXCHG {PARA 226 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 226 "" 0 "" {TEXT -1 0 "" }}}{SECT 0 {PARA 229 "" 0 "" {TEXT 209 16 "E lements de base" }}{SECT 0 {PARA 230 "" 0 "" {TEXT 208 21 "Premiere pr \351sentation" }}{SECT 0 {PARA 5 "" 0 "" {TEXT -1 36 "Operations num \351riques et alg\351briques" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 50 "2+5;2/5;2*5;2^2;2^(1/2);\nm*m*m;m*m/m;(m+n)*(m+n);\n" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 88 "Noter le point-virgule apr\350s chaque op \351ration et majuscule-retour pour passer \340 la ligne" }}{PARA 0 " " 0 "" {TEXT -1 33 "Noter l'\351toile pour tout produit\n" }}}}{SECT 0 {PARA 231 "" 0 "" {TEXT 207 11 "Les nombres" }}{EXCHG {PARA 232 "> \+ " 0 "" {MPLTEXT 1 0 55 "restart;\n6543;\n6.543e3;\n6.543E3;\n6.543E6; \n6.0e2;\n6.e2;\n" }}}}{SECT 0 {PARA 5 "" 0 "" {TEXT -1 33 "Les comman des et leur utilisation" }}{EXCHG {PARA 233 "" 0 "" {TEXT 206 147 "Str ucture d'une cellule : restart, majuscule-retour pour passer a la lign e, affectation de variables, commandes, retour pour declancher les cal culs" }}{PARA 0 "" 0 "" {TEXT -1 54 "Prendre l'habitude de nommer les \+ resultats (variables)" }}{PARA 233 "" 0 "" {TEXT 206 9 "Les zones" }}} {EXCHG {PARA 232 "> " 0 "" {MPLTEXT 1 0 90 "restart;\ne1:=(a+b)^3;\ne2 :=(a+b)^500;\nres1:=expand(e1);\nres2:=factor(e1);\nres3:=expand(e2); " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 34 "restart;\nevalf(Pi,1000 0);\nsqrt(2);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 26 "Noter le P majus cule de Pi" }}}{EXCHG {PARA 232 "> " 0 "" {MPLTEXT 1 0 53 "restart;\na :=5;b:=15;c:=11;\nP:=a*b/c;\nPN:=evalf(P,10);" }}}}}{SECT 0 {PARA 230 "" 0 "" {TEXT 208 27 "Suites, ensembles et listes" }}{SECT 0 {PARA 5 " " 0 "" {TEXT -1 11 "Definitions" }}{EXCHG {PARA 234 "" 0 "" {TEXT 203 116 "Un ensemble a des elements non ordonnes sans duplication, une lis te a des elements ordonnes. Extraction d'un element" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 65 "restart;\nsu:=1,2,3,3,4;\nen:=\{1,2,3,3,4 \};\nli:=[1,2,3,3,4];\nli[4];\n" }}}}{SECT 0 {PARA 5 "" 0 "" {TEXT -1 25 "Composition et extraction" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 54 "restart;\nsu:=a,b,c,d,e;\nen:=\{su\};\nli:=[su];\nli[1..3];\n" } }}}{SECT 0 {PARA 5 "" 0 "" {TEXT -1 14 "La commande op" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 75 "restart;\nsu:=a,b,c,d,e;\nen:=\{su \};\nli:=[su];\nop(li);\nop(2,li);\nop(1..3,li);\n" }}}}{SECT 0 {PARA 5 "" 0 "" {TEXT -1 35 "La commande nops et le denombrement" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 103 "restart;\nli:=[[a,b,2],[c,[d,e]]]; \nen:=\{a,b,c,a,c,d,b\};\nnops(li);\nnops(li[1]);\nnops(li[2,2]);\nnop s(en);\n" }}}}}}{SECT 0 {PARA 3 "" 0 "" {TEXT -1 16 "Aide et packages " }}{SECT 0 {PARA 4 "" 0 "" {TEXT -1 12 "Le menu Help" }}}{SECT 0 {PARA 4 "" 0 "" {TEXT -1 14 "L'aide directe" }}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }{TEXT 203 70 "Avoir des renseignements sur une commande sans passer par le menu Help" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 6 "?evalf" }}}}{SECT 0 {PARA 4 "" 0 "" {TEXT -1 12 "Les packages" }} {EXCHG {PARA 0 "" 0 "" {TEXT -1 25 "Des commande specialis\351es" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "?index,package" }}}}{SECT 0 {PARA 4 "" 0 "" {TEXT -1 12 "Des packages" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 57 "restart;\nwith(plots);\nwith(linalg);\nwith(LinearAlg ebra);\n" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 23 "restart;\nwith( student);" }}}}}{SECT 0 {PARA 235 "" 0 "" {TEXT 202 17 "Calcul algebri que" }}{SECT 0 {PARA 231 "" 0 "" {TEXT 207 34 "Des commandes de calcul algebrique" }}{EXCHG {PARA 234 "" 0 "" {TEXT 203 49 "Des fonctions pr edefinies. Pi avec une majuscule." }}}{EXCHG {PARA 232 "> " 0 "" {MPLTEXT 1 0 87 "restart;\na:=Pi/3;\ncos(a);cos(-a);sin(a);sin(a+Pi/3) ;\nln(1);log[10](10);exp(1);evalf(%);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 48 "Remarque : % pour utiliser le r\351sultat pr\351c\351dent " }}}{EXCHG {PARA 234 "" 0 "" {TEXT 203 39 "Quelques commandes de calc ul algebrique" }}}{EXCHG {PARA 232 "> " 0 "" {MPLTEXT 1 0 211 "restart ;\ne1:=(a+b)^3;\ne2:=expand(e1);\ne3:=factor(%);\nr1:=expand(cos(a+b)) ;\nr2:=factor(a^3-b^3);\nr3:=simplify(sin(a)^2+cos(a)^2);\nr4:=combine (n*ln(a)-m*ln(b),ln);\nr5:=convert(sin(x),exp);\nr6:=normal(2/x-3/(x+1 ));" }}}}{SECT 0 {PARA 236 "" 0 "" {TEXT 201 13 "Les equations" }} {SECT 0 {PARA 237 "" 0 "" {TEXT 212 22 "Resolution d'equations" }} {EXCHG {PARA 232 "> " 0 "" {MPLTEXT 1 0 125 "restart;\neqn1:=x^2-3*x+2 =0;\neqn2:=x^2+1=0;\neqn3:=2*x^2+11*x-7=0;\nsolve(eqn1,x);\nsolve(eqn2 ,x);\nsolve(eqn3,x);\nfsolve(eqn3,x);" }}}{EXCHG {PARA 234 "" 0 "" {TEXT 203 19 "Systeme d'equations" }}}{EXCHG {PARA 232 "> " 0 "" {MPLTEXT 1 0 61 "restart;\neq1:=x+2*y=5;\neq2:=3*x-y=1;\nsolve(\{eq1,e q2\},\{x,y\});\n" }}}{EXCHG {PARA 234 "" 0 "" {TEXT 203 35 "Recuperati on d'une solution (liste)" }}}{EXCHG {PARA 232 "> " 0 "" {MPLTEXT 1 0 83 "restart;\neqn:=x^2-3*x+2=0;\nsol:=[solve(eqn,x)];\nsol[1];\npreuve :=subs(x=sol[1],eqn);" }}}}{SECT 0 {PARA 237 "" 0 "" {TEXT 212 15 "Les inequations" }}{EXCHG {PARA 232 "> " 0 "" {MPLTEXT 1 0 37 "restart;\n iqn:=x^2-1>=0;\nsolve(iqn,x);" }}}}{SECT 0 {PARA 5 "" 0 "" {TEXT -1 11 "Exercices 1" }}{EXCHG {PARA 0 "" 0 "" {TEXT -1 117 "1) Resoudre l' equation x^2+x-6=0, pr\351senter les solutions sous forme d'une liste \+ et en extraire la seconde solution\n\n" }}}}}{SECT 0 {PARA 236 "" 0 " " {TEXT 201 36 "Calcul repetitfif: la commande seq()" }}{EXCHG {PARA 234 "" 0 "" {TEXT 203 24 "Commnade tres importante" }}}{SECT 0 {PARA 237 "" 0 "" {TEXT 212 21 "Iteration par defaut " }}{EXCHG {PARA 234 " " 0 "" {TEXT 203 97 "Liste des racines cubiques des nombres x (surd(x, 3)) compris entre 1 et 10 (iteration de 1 en 1)." }}}{EXCHG {PARA 232 "> " 0 "" {MPLTEXT 1 0 59 "restart;\na:=surd(x,3);\nsuite:=seq(a,x=1.. 10);\nevalf(suite);" }}}}{SECT 0 {PARA 237 "" 0 "" {TEXT 212 22 "Itera tion predetermine" }}{EXCHG {PARA 234 "" 0 "" {TEXT 203 49 "Iteration \+ selon des indices prealablement choisis" }}}{EXCHG {PARA 232 "> " 0 " " {MPLTEXT 1 0 92 "restart;\na:=sin(x);\nangles:=[0,Pi/6,Pi/4,Pi/3,Pi/ 2];\nsuite:=seq(a,x=angles);\nevalf(suite,3);" }}}}{SECT 0 {PARA 237 " " 0 "" {TEXT 212 7 "Tableau" }}{EXCHG {PARA 232 "> " 0 "" {MPLTEXT 1 0 76 "restart;\nrac:=sqrt(x);\nliste:=evalf([seq([x,rac],x=1..10)],3); \nevalm(liste);" }}}}{SECT 0 {PARA 5 "" 0 "" {TEXT -1 29 "Les commande s add, mul et sum" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 155 "restar t:\nli:=[1,5,10];\nln1_10:=seq(i,i=1..10);\nadd_10:=add(i,i=1..10);\nm ul_10:=mul(i,i=1..10);\n10!;\naddli:=add(i,i=li);\nmulli:=mul(i,i=li); \nsum(i,i=1..n);\n" }}}}}{SECT 0 {PARA 236 "" 0 "" {TEXT 201 24 "Expre ssions et fonctions" }}{EXCHG {PARA 234 "" 0 "" {TEXT 203 65 "Il est t res important de distinguer les expressions des fonctions" }}}{SECT 0 {PARA 237 "" 0 "" {TEXT 212 15 "Les definitions" }}{EXCHG {PARA 234 " " 0 "" {TEXT 203 44 "Notez le symbole # pour des commentaires off" }}} {EXCHG {PARA 232 "> " 0 "" {MPLTEXT 1 0 80 "restart;\n#fe expression; \nfe:=x^2;\nfe;\nfe(2);\n#ff fonction\nff:=x->x^2;\nff;\nff(5);" }}}} {SECT 0 {PARA 237 "" 0 "" {TEXT 212 10 "Le passage" }}{EXCHG {PARA 234 "" 0 "" {TEXT 203 53 "D'expression a fonction puis de fonction a e xpression" }}}{EXCHG {PARA 232 "> " 0 "" {MPLTEXT 1 0 123 "restart;\n# expression vers fonction\nfe:=x^2;\nfef:=unapply(fe,x);\nfef(5);\n#fon ction vers expression\nff:=x->x^2;\nff(x);\nff(5);" }}}}{SECT 0 {PARA 237 "" 0 "" {TEXT 212 19 "Plusieurs variables" }}{EXCHG {PARA 232 "> \+ " 0 "" {MPLTEXT 1 0 36 "restart;\nf:=(x,y)->x^2-y^2;\nf(10,5);" }}}} {SECT 0 {PARA 5 "" 0 "" {TEXT -1 24 "Composition de fonctions" }} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 67 "restart;\nf:=x->2*x^2;\ng:=x ->sin(x);\n(g@f)(x);\n(f@g)(x);\n(f@@3)(x);\n" }}}}{SECT 0 {PARA 5 "" 0 "" {TEXT -1 25 "Des fonctions predefinies" }}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 107 "restart;\nlog(100);exp(1);sqrt(16);surd(81,4);sin( Pi/2);tan(Pi/2);sec(Pi/4);\ncot(Pi/3);arcsin(1);csc(Pi/6);\n" }}}} {SECT 0 {PARA 5 "" 0 "" {TEXT -1 11 "Exercices 2" }}{EXCHG {PARA 0 "" 0 "" {TEXT -1 401 "1) Utilisez la commande seq() pour calculer la list e des racines carrees des entiers de 1 \340 10 sous forme d\351cimale \n2) Definissez le sinus comme une fonction au sens de Maple et avec l a commande seq() dressez une liste des valeurs de sin(x) pour x valant 0, Pi/6, Pi/4, Pi/3 et Pi/2 et pr\351sentez cette liste sous forme d' un tableau \340 deux colonnes, l'angle et son sinus\n3) Resolvez l'equ ation cos(x)=x\n" }}}}}}{SECT 0 {PARA 235 "" 0 "" {TEXT 202 14 "Les gr aphiques" }}{SECT 0 {PARA 236 "" 0 "" {TEXT 201 18 "La commande plot() " }}{EXCHG {PARA 234 "" 0 "" {TEXT 203 57 "Commande tres importante. E n selectionnant le graphique, " }}{PARA 234 "" 0 "" {TEXT 203 37 "une \+ barre de menu specialise apparait" }}}{SECT 0 {PARA 237 "" 0 "" {TEXT 212 26 "Graphique d'une expression" }}{EXCHG {PARA 232 "> " 0 "" {MPLTEXT 1 0 114 "restart;\nf:=x^2;\n#Commande de base\nplot(f,x=-5..5 );\n#Commande avec une option\nplot(f,x=-5..5,scaling=constrained);" } }}}{SECT 0 {PARA 237 "" 0 "" {TEXT 212 24 "Graphique d'une fonction" } }{EXCHG {PARA 232 "> " 0 "" {MPLTEXT 1 0 110 "restart;\nf:=x->x^4-x^2; \n#Commande avec une option sur l'image\nplot(f,-5..5,-1..2);\nplot(f( x),x=-5..5,y=-1..2);" }}}}{SECT 0 {PARA 237 "" 0 "" {TEXT 212 20 "Plus ieurs graphiques" }}{EXCHG {PARA 232 "> " 0 "" {MPLTEXT 1 0 121 "resta rt;\nf:=sin(x);\ng:=cos(x);\n#Commande avec une option sur la couleur \+ (liste)\nplot([f,g],x=-Pi..3*Pi,color=[red,blue]);" }}}{EXCHG {PARA 234 "" 0 "" {TEXT 203 57 "Un grand nombre d'exemples pour un grand nom bre d'options" }}}{EXCHG {PARA 232 "> " 0 "" {MPLTEXT 1 0 5 "?plot" }} }}}{SECT 0 {PARA 236 "" 0 "" {TEXT 201 27 "Les graphiques dans le plan " }}{SECT 0 {PARA 237 "" 0 "" {TEXT 212 24 "Les fonctions implicites" }}{EXCHG {PARA 0 "" 0 "" {TEXT -1 71 "La commande implicitplot() est d ans le package plots qu'il faut charger" }}}{EXCHG {PARA 232 "> " 0 " " {MPLTEXT 1 0 91 "restart;\nwith(plots):\neq:=x^2/3+y^2/12=1;\nimplic itplot(eq,x=-5..5,y=-5..5,title=`ellipse`);" }}}}{SECT 0 {PARA 237 "" 0 "" {TEXT 212 27 "Les fonctions parametriques" }}{EXCHG {PARA 232 "> \+ " 0 "" {MPLTEXT 1 0 142 "restart;\nx:=t->1+2*cos(t);\ny:=t->2+2*sin(t) ;\nplot([x(t),y(t),t=0..2*Pi],\n x=-2..4,y=-1..5,\n title=\"ce rcle\",\n scaling=constrained);" }}}}{SECT 0 {PARA 5 "" 0 "" {TEXT -1 35 "Les fonctions definies par morceaux" }}{EXCHG {PARA 0 "> \+ " 0 "" {MPLTEXT 1 0 148 "restart;\nf:=x->piecewise(x<-2,-x,\n \+ x<1,x^2-4,\n x-2);\nplot(f(x),x=-5..5,y=-5..5,\n discont=true,\n color=red);\n" }}}}{SECT 0 {PARA 5 "" 0 "" {TEXT -1 15 "Les inequations" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 223 "restart;\nwith(plots):\niq1:=x>0;\niq2:=y>0;\niq3:=4*y+x-16<0;\ni q4:=y+x-5<0;\niq5:=y+2*x-8<0;\ninequal(\{iq1,iq2,iq3,iq4,iq5\},\n \+ x=-1..5,y=-1..5,\n optionsexcluded=(color=yellow),\n \+ optionsfeasible=(color=red));\n" }}}}{SECT 0 {PARA 237 "" 0 "" {TEXT 212 28 "Differents objets graphiques" }}{EXCHG {PARA 238 "" 0 "" {TEXT 210 107 "La commande display permet de prsenter sur un meme grap hique des objets graphiques de differentes natures. " }}{PARA 238 "" 0 "" {TEXT 210 50 "Elle est dans le package plots qu'il faut charger. " }}}{EXCHG {PARA 232 "> " 0 "" {MPLTEXT 1 0 237 "restart;\nwith(plots ):\nliste:=[[1,1],[5,3],[3,6],[1,1]];\ng1:=plot(liste,style=line):\nx: =t->1+2*cos(t);\ny:=t->2+2*sin(t);\ng2:=plot([x(t),y(t),t=0..2*Pi],\n \+ x=-2..7,y=-1..7,\n title=\"cercle\",\n scaling=constrained ):\ndisplay(g1,g2);" }}}}}{SECT 0 {PARA 236 "" 0 "" {TEXT 201 28 "Les \+ graphiques dans l'espace" }}{SECT 0 {PARA 237 "" 0 "" {TEXT 212 19 "La commane plot3d()" }}{EXCHG {PARA 238 "" 0 "" {TEXT 210 127 "L'option \+ view permet de definir l'intervalle en z, tandis que l'option numpoint s donne une meilleure precision (par defaut 500)" }}}{EXCHG {PARA 232 "> " 0 "" {MPLTEXT 1 0 129 "restart;\nf:=(x,y)->sin(x+y)*sin(x);\nplot 3d(f(x,y),x=-Pi..Pi,y=-Pi..Pi,\n view=-2..2,\n \+ numpoints=2000);" }}}}{SECT 0 {PARA 237 "" 0 "" {TEXT 212 21 "Les courbes de niveau" }}{EXCHG {PARA 234 "" 0 "" {TEXT 203 143 "La comma nde contourplot est dans le package plots qu'il faut charger au \nprea lable avec la commande with\navec: les resultats n'apparaissent pas" } }}{EXCHG {PARA 232 "> " 0 "" {MPLTEXT 1 0 190 "restart;\nwith(plots): \nf:=(x,y)->cos(x+y);\nplot3d(f(x,y),x=-Pi..Pi,y=-Pi..Pi,\n \+ view=-2..2,\n numpoints=2000);\ncontourplot(f(x,y), \n x=-Pi..Pi,y=-Pi..Pi);" }}}}{SECT 0 {PARA 237 "" 0 "" {TEXT 212 27 "Les fonctions implicites 3d" }}{EXCHG {PARA 232 "> " 0 " " {MPLTEXT 1 0 103 "restart;\nwith(plots):\neq:=x^2/2-y^2/5-z^2/10=10; \nimplicitplot3d(eq,x=-10..10,\n y=-10..10,z=-10..10);" }}}}{SECT 0 {PARA 237 "" 0 "" {TEXT 212 27 "Les fonctions parametriques" }} {EXCHG {PARA 232 "> " 0 "" {MPLTEXT 1 0 119 "restart;\nx:=(r,t)->r*cos (t);\ny:=(r,t)->r*sin(t);\nz:=(r,t)->r^2;\nplot3d([x(r,t),y(r,t),z(r,t )],\n r=0..2,t=0..2*Pi);" }}}}{SECT 0 {PARA 237 "" 0 "" {TEXT 212 25 "Les courbes dans l'espace" }}{EXCHG {PARA 232 "> " 0 "" {MPLTEXT 1 0 115 "restart;\nwith(plots):\nx:=t->t*cos(t);\ny:=t->t*sin (t);\nz:=t->t;\nspacecurve([x(t),y(t),z(t)],\n t=0..8*Pi);\n " }}}}{SECT 0 {PARA 5 "" 0 "" {TEXT -1 11 "Exercices 3" }}{EXCHG {PARA 0 "" 0 "" {TEXT -1 183 "1) Representez sur une meme figure y=sin (x) et y=tan(x)\n2) Resolvez les equations x+2y=5 et 2x+y=4 et avec la commande implicitplot() repr\351sentez ces deux droites sur une meme \+ figure\n" }}}}}{SECT 0 {PARA 236 "" 0 "" {TEXT 201 15 "Les simulations " }}{SECT 0 {PARA 237 "" 0 "" {TEXT 212 15 "L'animation 2D " }}{EXCHG {PARA 232 "> " 0 "" {MPLTEXT 1 0 73 "restart;\nwith(plots):\nf:=x->sin (n*x);\nanimate(f(x),x=-2*Pi..2*Pi,n=0..5);" }}}{EXCHG {PARA 232 "> " 0 "" {MPLTEXT 1 0 71 "restart;\nwith(plots):\nf:=sin(n*x);\nanimate(pl ot,[f,x=-10..10],n=1..2);\n" }}}}{SECT 0 {PARA 5 "" 0 "" {TEXT -1 14 " L'animation 3D" }}{EXCHG {PARA 232 "> " 0 "" {MPLTEXT 1 0 106 "restart ;\nwith(plots):\nf:=(x,y)->cos(n*x)*sin(n*y);\nanimate3d(f(x,y),x=-Pi. .Pi,\n y=-Pi..Pi,n=-2..2);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 86 "restart;\nwith(plots):\nf:=cos(k*x+y);\nanimate(plot3 d,,[f,x=-10..10,y=-10..10],k=1..3);\n" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 84 "restart;\nwith(plots):\nf:=x->sin(x);\nanimatecurve(f (x),x=-Pi..Pi,\n frames=40);\n" }}}}{SECT 0 {PARA 237 "" 0 "" {TEXT 212 18 "Les simulations 2d" }}{EXCHG {PARA 232 "> " 0 "" {MPLTEXT 1 0 96 "restart;\nf:=x->m*x+2;\nliste:=[seq(f(x),m=-2..2)];\n plot(liste,x=-1..6,-2..7,scaling=constrained);" }}}{EXCHG {PARA 232 "> " 0 "" {MPLTEXT 1 0 108 "restart;\nwith(plots):\nf:=a*sin(x);\ngraphe s:=seq(plot(f,x=-5..5),a=1..5):\ndisplay(graphes,insequence=true);\n\n " }}}}{SECT 0 {PARA 5 "" 0 "" {TEXT -1 17 "Courbes de niveau" }} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 140 "restart;\nwith(plots):\nf:= x^2+y^2=n;\ngph:=seq(implicitplot(f,x=-5..5,y=-5..5,title=convert(n,st ring)),n=1..5):\ndisplay(gph,insequence=true);\n" }}}}}}{SECT 0 {PARA 235 "" 0 "" {TEXT 202 31 "Calcul differentiel et integral" }}{SECT 0 {PARA 236 "" 0 "" {TEXT 201 9 "La limite" }}{EXCHG {PARA 232 "> " 0 " " {MPLTEXT 1 0 174 "restart;\nf1:=x->(3*x^2+4)/(2*x^2+7);\nf2:=x->sin( x);\nf3:=x->2/(x-1);\nl1:=limit(f1(x),x=infinity);\nl2:=limit(f2(x),x= infinity);\nl3:=limit(f3(x),x=1);\nl4:=limit(f3(x),x=1,left);" }}}} {SECT 0 {PARA 236 "" 0 "" {TEXT 201 9 "La derive" }}{SECT 0 {PARA 237 "" 0 "" {TEXT 212 15 "Derive premiere" }}{EXCHG {PARA 234 "" 0 "" {TEXT 203 23 "Derive d'une expression" }}}{EXCHG {PARA 232 "> " 0 "" {MPLTEXT 1 0 32 "restart;\nf:=1/x;\nder:=diff(f,x);" }}}{EXCHG {PARA 234 "" 0 "" {TEXT 203 21 "Derive d'une fonction" }}}{EXCHG {PARA 232 " > " 0 "" {MPLTEXT 1 0 54 "restart;\nf:=x->(x^2-3)^10;\nder:=D(f)(x);\n der:=D(f)(2);" }}}}{SECT 0 {PARA 237 "" 0 "" {TEXT 212 19 "Derives suc cessives" }}{EXCHG {PARA 234 "" 0 "" {TEXT 203 20 "Pour une expression :" }}}{EXCHG {PARA 232 "> " 0 "" {MPLTEXT 1 0 37 "restart;\nf:=x^10;\n der4:=diff(f,x$4);\n" }}}{EXCHG {PARA 234 "" 0 "" {TEXT 203 17 "Pour u ne fonction" }}}{EXCHG {PARA 232 "> " 0 "" {MPLTEXT 1 0 40 "restart;\n f:=x->x^10;\nder5:=(D@@5)(f)(x);" }}}}{SECT 0 {PARA 5 "" 0 "" {TEXT -1 32 "Deriv\351e d'une fonction implicite" }}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 59 "restart;\neqn:=x^2+y^3+2*x*y;\nderyx:=implicitdiff( eqn,y,x);\n" }}}}{SECT 0 {PARA 237 "" 0 "" {TEXT 212 41 "Derive de fon ctions a plusieurs variables" }}{EXCHG {PARA 234 "" 0 "" {TEXT 203 19 "Pour une expression" }}}{EXCHG {PARA 232 "> " 0 "" {MPLTEXT 1 0 61 "r estart;\nf:=x*exp(y);\nderxy:=diff(f,x,y);\nderyx:=diff(f,y,x);" }}} {EXCHG {PARA 234 "" 0 "" {TEXT 203 17 "Pour une fonction" }}}{EXCHG {PARA 232 "> " 0 "" {MPLTEXT 1 0 176 "restart;\nf:=(x,y)->x*exp(y);\ng :=(x,y)->x^5*y^5;\nderx:=D[1](f);\ndery:=D[2](f);\nderxy:=D[1,2](f);\n deryx:=D[2,1](f);\nder2x3y2x:=D[1,1,1,2,2,1,1](g);\nder2x3y2x:=D[1$3,2 $2,1$2](g);\n" }}}}}{SECT 0 {PARA 236 "" 0 "" {TEXT 201 11 "L'integral e" }}{SECT 0 {PARA 237 "" 0 "" {TEXT 212 21 "L'integrale indefinie" }} {EXCHG {PARA 232 "> " 0 "" {MPLTEXT 1 0 40 "restart;\nf:=x->1/(x^2+a^2 );\nint(f(x),x);" }}}}{SECT 0 {PARA 237 "" 0 "" {TEXT 212 19 "L'integr ale definie" }}{EXCHG {PARA 232 "> " 0 "" {MPLTEXT 1 0 61 "restart;\nf :=sin(2*x);\nfind:=int(f,x);\nfdef:=int(f,x=0..Pi/2);" }}}{EXCHG {PARA 234 "" 0 "" {TEXT 203 20 "Integrale divergente" }}}{EXCHG {PARA 232 "> " 0 "" {MPLTEXT 1 0 38 "restart;\nf:=x->1/x;\nint(f(x),x=-1..1) ;" }}}}}{SECT 0 {PARA 4 "" 0 "" {TEXT -1 9 "Exercices" }}{EXCHG {PARA 0 "" 0 "" {TEXT -1 222 "Soit la fonction y=x^3\n1) D\351finissez la co mme une expression et derivez la deux fois\n2) D\351finissez la comme \+ une fonction et d\351rivez la deux fois\n3) Int\351grez la et d\351fin issez la primitive comme une fonction au sens de Maple" }}{PARA 0 "" 0 "" {TEXT -1 49 "4) D\351terminez son int\351grale d\351finie entre 2 et 5\n" }}}}{SECT 0 {PARA 236 "" 0 "" {TEXT 201 29 "Les equations dif ferentielles" }}{EXCHG {PARA 234 "" 0 "" {TEXT 203 76 "Les symboles ut ilises rapprochent l'ecriture de l'ecriture habituelle des ED" }} {PARA 234 "" 0 "" {TEXT 203 45 "Noter le titrage compris entre des gui llemets" }}{PARA 234 "" 0 "" {TEXT 203 38 "Exemple d'une recuperation \+ de solution" }}}{SECT 0 {PARA 237 "" 0 "" {TEXT 212 10 "Resolution" }} {EXCHG {PARA 232 "> " 0 "" {MPLTEXT 1 0 269 "restart;\n\"Symboles\";\n y0:=y(t);y1:=diff(y0,t);y2:=diff(y1,t);\n\"Conditions imitiales\";\nci 1:=y(0)=1;\nci2:=D(y)(0)=0;\n\"Equation\";\neqd:=y2+y1+y0=0;\n\"Resolu tion\";\nsol:=dsolve(\{eqd,ci1,ci2\},y0);\n\"Recuperation\";\nf:=rhs(s ol);\nxt:=unapply(f,t);\n\"Graphique\";\nplot(xt(t),t=0..10);\n" }}}} {SECT 0 {PARA 237 "" 0 "" {TEXT 212 11 "Simulations" }}{EXCHG {PARA 232 "> " 0 "" {MPLTEXT 1 0 314 "restart;\n\"Symboles\";\ny0:=y(t);y1:= diff(y0,t);y2:=diff(y1,t);\n\"Conditions imitiales\";\nci1:=y(0)=n;\nc i2:=D(y)(0)=0;\n\"Equation\";\neqd:=y2+y1+y0=0;\n\"Resolution\";\nsol: =dsolve(\{eqd,ci1,ci2\},y0);\n\"Recup\}ration\";\nf:=rhs(sol);\nxt:=un apply(f,t);\n\"Famille\";\nliste_xt:=[seq(xt(t),n=0..5)];\n\"Graphique \";\nplot(liste_xt,t=0..10);\n" }}}}{SECT 0 {PARA 5 "" 0 "" {TEXT -1 18 "Le package DEtools" }}{EXCHG {PARA 0 "" 0 "" {TEXT -1 56 "Solution avec champ vectoriel pour famille de solutions\n" }}}{EXCHG {PARA 0 " > " 0 "" {MPLTEXT 1 0 140 "restart;\nwith(DEtools);\ny0:=y(t);y1:=diff (y0,t);\neqd:=y1=-0.5*y0;\nci1:=y(0)=1;\nDEplot(eqd,y(t),-5..5,[[ci1]] ,arrows=small,linecolor=black);\n" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 8 "Solution" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 203 "restart;\nw ith(plots):\ny0:=y(t):y1:=diff(y0,t):y2:=diff(y1,t):\neqd:=0.5*y1*y2-3 *y1*sin(y0)+3*y0*y1=0;\nci1:=y(0)=Pi/3;\nci2:=D(y)(0)=0;\nsol:=dsolve( \{eqd,ci1,ci2\},y(t),numeric);\nodeplot(sol,[t,y(t)],-5..0);\n" }}}} {SECT 0 {PARA 5 "" 0 "" {TEXT -1 19 "Oscillatoire amorti" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 208 "restart;\nwith(plots):\ny0:=y(t);y 1:=diff(y0,t);y2:=diff(y1,t);\na:=1;b:=1;\neqd:=y2+a*y1+b*y0=0;\nci1:= y(0)=1;\nci2:=D(y)(0)=0;\nsol:=dsolve(\{eqd,ci1,ci2\},y(t));\nfy:=rhs( sol);\nf:=unapply(fy,t);\nplot(f(t),t=0..20);\n" }}}}{SECT 0 {PARA 5 " " 0 "" {TEXT -1 78 "Oscillatoire amorti, simulation selon le coefficie nt d'amortissement (courbes)" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 260 "restart;\nwith(plots):\ny0:=y(t);y1:=diff(y0,t);y2:=diff(y1,t);\n b:=1;\neqd:=y2+a*y1+b*y0=0;\nci1:=y(0)=1;\nci2:=D(y)(0)=0;\nsol:=dsolv e(\{eqd,ci1,ci2\},y(t));\nfy:=rhs(sol);\nf:=unapply(fy,t);\nlistea:=[0 .1,0.4,0.7,1];\nlisteg:=[seq(f(t),a=listea)]:\nplot(listeg,t=0..30);\n " }}}}{SECT 0 {PARA 5 "" 0 "" {TEXT -1 78 "Oscillatoire amorti, simula tion selon le coefficient d'amortissement (surface)" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 219 "restart;\nwith(plots):\ny0:=y(t);y1:=diff( y0,t);y2:=diff(y1,t);\nb:=1;\neqd:=y2+a*y1+b*y0=0;\nci1:=y(0)=1;\nci2: =D(y)(0)=0;\nsol:=dsolve(\{eqd,ci1,ci2\},y(t));\nfy:=rhs(sol);\nf:=una pply(fy,t,a);\n\nplot3d(f(t,a),t=0..30,a=0.1..2);\n" }}}}{SECT 0 {PARA 5 "" 0 "" {TEXT -1 9 "Entretenu" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 242 "restart;\nwith(plots):\ny0:=y(t);y1:=diff(y0,t);y2:= diff(y1,t);\na:=1;b:=4;b1:=0.1;\neqd:=y2+a*y1+b*y0=sin(b1*t);\nci1:=y( 0)=1;\nci2:=D(y)(0)=0;\nsol:=dsolve(\{eqd,ci1,ci2\},y(t));\nfy:=rhs(so l);\nf:=unapply(fy,t);\nplot(f(t,a),t=0..100,numpoints=2000);\n" }}}} {SECT 0 {PARA 5 "" 0 "" {TEXT -1 20 "Entretenu resonnance" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 240 "restart;\nwith(plots):\ny0:=y(t);y 1:=diff(y0,t);y2:=diff(y1,t);\na:=1;b:=4;b1:=2;\neqd:=y2+a*y1+b*y0=sin (b1*t);\nci1:=y(0)=1;\nci2:=D(y)(0)=0;\nsol:=dsolve(\{eqd,ci1,ci2\},y( t));\nfy:=rhs(sol);\nf:=unapply(fy,t);\nplot(f(t,a),t=0..100,numpoints =2000);\n" }}}}{SECT 0 {PARA 5 "" 0 "" {TEXT -1 62 "Entretenu resonnan ce simulations selon excitation (graphiques)" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 291 "restart;\nwith(plots):\ny0:=y(t);y1:=diff(y0,t);y 2:=diff(y1,t);\na:=1;b:=4;\neqd:=y2+a*y1+b*y0=sin(b1*t);\nci1:=y(0)=1; \nci2:=D(y)(0)=0;\nsol:=dsolve(\{eqd,ci1,ci2\},y(t));\nfy:=rhs(sol);\n f:=unapply(fy,t);\nlisteb1:=[1,1.5,2,2.5,3];\nlisteg:=[seq(f(t),b1=lis teb1)];\nplot(listeg,t=0..50,numpoints=2000);\n" }}}}{SECT 0 {PARA 5 " " 0 "" {TEXT -1 59 "Entretenu resonnance simulations selon excitation \+ (surface)" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 250 "restart;\nwith (plots):\ny0:=y(t);y1:=diff(y0,t);y2:=diff(y1,t);\na:=0.1;b:=4;\neqd:= y2+a*y1+b*y0=sin(b1*t);\nci1:=y(0)=1;\nci2:=D(y)(0)=0;\nsol:=dsolve(\{ eqd,ci1,ci2\},y(t));\nfy:=rhs(sol);\nf:=unapply(fy,t,b1);\n\nplot3d(f( t,b1),t=0..20,b1=0..4,numpoints=5000);\n" }}}}}{SECT 0 {PARA 236 "" 0 "" {TEXT 201 10 "Les series" }}{SECT 0 {PARA 237 "" 0 "" {TEXT 212 17 "La commande sum()" }}{EXCHG {PARA 232 "> " 0 "" {MPLTEXT 1 0 77 "rest art;\nu:=a*(1/3)^i;\ns10:=sum(u,i=0..99);\nsn:=sum(u,i=1..n);\nsum(i,i =1..n);" }}}}{SECT 0 {PARA 237 "" 0 "" {TEXT 212 20 "La commande serie s()" }}{EXCHG {PARA 234 "" 0 "" {TEXT 203 53 "Exemples de developpemen t de Mc Laurin puis de Taylor" }}}{EXCHG {PARA 232 "> " 0 "" {MPLTEXT 1 0 146 "restart;\nf1:=sin(x);\nf2:=exp(x);\nser_f1_Ml:=series(f1,x=0, 7);\nser_f2_Tay:=series(f2,x=1,6);\nserT_f1:=taylor(f1,x=0,7);\nserT_f 2:=taylor(f2,x=1,6);\n" }}}{EXCHG {PARA 234 "" 0 "" {TEXT 203 36 "Tran sformation en polynome de Taylor" }}}{EXCHG {PARA 232 "> " 0 "" {MPLTEXT 1 0 82 "restart;\nf:=1/(1-x);\nser_f:=series(f,x=0,8);\npolTa ylor_f:=convert(ser_f,polynom);\n" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 241 "restart;\nf:=x\255>sin(x):\nser:=n->taylor(f(x),x=0, n):\npoly:=n->convert(ser(n),polynom):\nlisten:=[2,6,10,12];\nliste:=s eq(poly(n),n=listen):\nplot([liste,f(x)],x=-2*Pi..2*Pi,y=-2..2,\n co lor=[gold,red,blue,magenta,black],\nthickness=[0,0,1,2,3]);\n" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 255 "restart;\nwith(plots):\nf:= x->sin(x):\nser:=n->taylor(f(x),x=0,n):\npoly:=n->convert(ser(n),polyn om):\ngraphes:=seq(plot([poly(n),f(x)],x=-2*Pi..2*Pi,-2..2,color=[red, black],thickness=[0,2],\ntitle=convert(n,string)),\nn=1..6):\ndisplay( graphes,insequence=true);\n" }}}}}}{SECT 0 {PARA 235 "" 0 "" {TEXT 202 19 "Algebre avec linalg" }}{EXCHG {PARA 234 "" 0 "" {TEXT 203 65 " Les deux principales manieres de traiter les vecteurs et matrices" }}} {SECT 0 {PARA 236 "" 0 "" {TEXT 201 27 "Les matrices comme tableaux" } }{EXCHG {PARA 232 "> " 0 "" {MPLTEXT 1 0 116 "restart;\nA:=[[1,2],[3,4 ]];\nB:=[[2,-3],[-1,4]];\nso:=evalm(A+B);\npr:=evalm(A&*B);\ninvA:=eva lm(A^(-1));\nevalm(A&*invA);" }}}}{SECT 0 {PARA 236 "" 0 "" {TEXT 201 17 "Le package linalg" }}{EXCHG {PARA 238 "" 0 "" {TEXT 210 58 "Les ma trices dfinies par matrix et les oprations associees" }}}{EXCHG {PARA 232 "> " 0 "" {MPLTEXT 1 0 244 "restart;\nwith(linalg);\nA:=matrix([[1 ,2],[3,4]]);\nB:=matrix([[2,3],[4,6]]);\nso:=matadd(A,B);\nadjA:=adjoi nt(A);\ntransA:=transpose(A);\ninvA:=inverse(A);\npreuve:=multiply(A,i nvA);\ndetA:=det(A);\ndetB:=det(B);\nvalp:=eigenvals(A);\nvecp:=eigenv ects(A);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 135 "restart;\nwith (linalg):\nA:=matrix([[1,2],[3,4]]);\nadjA:=adjoint(A);\ntranspoA:=tra nspose(A);\ninvA:=inverse(A);\npreuve:=multiply(A,invA);\n" }}}}{SECT 0 {PARA 236 "" 0 "" {TEXT 201 12 "Les vecteurs" }}{EXCHG {PARA 234 "" 0 "" {TEXT 203 73 "Les operations de base sur les vecteurs, produits s calaires et vectoriels" }}}{EXCHG {PARA 232 "> " 0 "" {MPLTEXT 1 0 144 "restart;\nwith(linalg):\nu:=vector([1,2,3]);\nv:=vector([4,5,6]); \nso:=matadd(u,v);\npdscal:=dotprod(u,v);\npdvec:=crossprod(u,v);\nku: =scalarmul(u,k);" }}}}{SECT 0 {PARA 4 "" 0 "" {TEXT -1 34 "Les systeme s d'equations lineaires" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 202 " restart;\nwith(linalg):\neq1:=2*x-y+z=3;\neq2:=x+3*y-2*z=1;\neq3:=5*x- y-3*z=-6;\nA0:=genmatrix([eq1,eq2,eq3],[x,y,z]);\nA1:=genmatrix([eq1,e q2,eq3],[x,y,z],flag);\ngausselim(A0);\ngausselim(A1);\ngaussjord(A1); \n" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 158 "restart;\nwith(linal g):\neq1:=2*x-y+z=3;\neq2:=x+3*y-2*z=1;\neq3:=5*x-y-3*z=-6;\nA0:=genma trix([eq1,eq2,eq3],[x,y,z]);\nB:=matrix(3,1,[3,1,-6]);\nX:=linsolve(A0 ,B);\n" }}}}{SECT 0 {PARA 236 "" 0 "" {TEXT 201 21 "Les champs vectori els" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 101 "restart;\nwith(plots ):\nvx:=x/sqrt(x^2+y^2);\nvy:=-y/sqrt(x^2+y^2);\nfieldplot([vx,vy],x=- 5..5,y=-5..5);\n" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 125 "restar t;\nwith(plots):\nwith(linalg):\nz:=(x,y)->sqrt(x^2+y^2+1);\ngrad(z(x, y),vector([x,y]));\ngradplot(z(x,y),x=-2..2,y=-2..2);\n" }}}{EXCHG {PARA 232 "> " 0 "" {MPLTEXT 1 0 211 "restart;\nwith(plots):\nwith(lin alg):\nz:=(x,y)->x^2-y^2;\ngrad(z(x,y),vector([x,y]));\nplot3d(z(x,y), x=-2..2,y=-2..2);\ng1:=gradplot(z(x,y),x=-2..2,y=-2..2):\ng2:=contourp lot(z(x,y),x=-2..2,y=-2..2):\ndisplay3d(g1,g2);" }}}}}{SECT 0 {PARA 239 "" 0 "" {TEXT 217 25 "Algbre avec LinearAlgebra" }}{SECT 0 {PARA 240 "" 0 "" {TEXT 218 13 "Les commandes" }}{EXCHG {PARA 232 "> " 0 "" {MPLTEXT 1 0 29 "restart;\nwith(LinearAlgebra);" }}}}{SECT 0 {PARA 240 "" 0 "" {TEXT 218 20 "Matrices et vecteurs" }}{EXCHG {PARA 232 "> \+ " 0 "" {MPLTEXT 1 0 147 "restart;\nwith(LinearAlgebra):\nV1:=anglebrac ket(1,2,3);\nV2:=<1|2|3>;\nV3:=<2,1,2>;\nV1+V2;\nDotProduct(V1,V2);\nD otProduct(V1,V3);\nCrossProduct(V1,V2);\n" }}}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 154 "restart;\nwith(LinearAlgebra):\nV1:=anglebracket(1 ,2,3);\nV2:=<1|2|3>;\nV3:=<2,1,2>;\nV1+V2;\n2*V1;\nDotProduct(V1,V2); \nDotProduct(V1,V3);\nCrossProduct(V1,V2);\n\n" }}}{EXCHG {PARA 0 "> \+ " 0 "" {MPLTEXT 1 0 196 "restart;\nwith(LinearAlgebra):\nA:=|<5,6>>;\nB:=<<1|2>,<3|2>,<3|1>>;\nC:=<<3|2>,<5|1>>;\nPd AB:=A.B;\nPdBA:=B.A;\nTranspose(A);\nPc:=C^2;\nCi1:=C^(-1);\nCi2:=Matr ixInverse(C);\nC.Ci1;\n" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 215 "On re marque que les barres verticales | s\351parent les objets selon des co lonnes differentes tandis que les virgules les s\351parent selon des l ignes differentes. Pour les operations, on peut consulter le terme ope rator\n" }}}}{SECT 0 {PARA 4 "" 0 "" {TEXT -1 30 "Syst\350mes d'\351qu ations lineaires" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 107 "restart ;\nwith(LinearAlgebra);\nA := |<7,8,0>>;\n b := <3,2,-2>;\nLinearSolve(A,b);\n" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 194 "restart;\nwith(LinearAlgebra):\n\nA := |<2,-1,1>>;\nb := <9,-3,8>;\nGaussianElimination(A);\n GaussianElimination(A,'method'='FractionFree');\nReducedRowEchelonForm ();\n" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 21 "with(LinearAl gebra);\n" }}}}}{EXCHG {PARA 225 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 226 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 226 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 226 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 226 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 226 "" 0 "" {TEXT -1 0 "" }}} {EXCHG {PARA 226 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 242 "" 0 "" {TEXT 211 14 "Maple en cours" }}}{EXCHG {PARA 226 "" 0 "" {TEXT -1 0 " " }}}{EXCHG {PARA 226 "" 0 "" {TEXT -1 0 "" }}}{SECT 0 {PARA 235 "" 0 "" {TEXT 202 19 "Calcul differentiel" }}{EXCHG {PARA 234 "" 0 "" {TEXT 203 37 "Demarche algorithmique et initiation " }}{PARA 234 "" 0 "" {TEXT 203 48 "?a la resolution de probleme par la modelisation" }}} {SECT 0 {PARA 236 "" 0 "" {TEXT 201 11 "Les droites" }}{EXCHG {PARA 234 "" 0 "" {TEXT 203 39 "Serie de procedures proposes aux eleves" }}} {SECT 0 {PARA 237 "" 0 "" {TEXT 212 30 "Droite passant per deux points " }}{EXCHG {PARA 232 "> " 0 "" {MPLTEXT 1 0 158 "restart;\n\"Les donne es\";\nx1:=2;x2:=4;y1:=1;y2:=-3;\n\"La mathematisation\";\nm:=(y2-y1)/ (x2-x1);\nb:=y2-m*x2;\n\"Les reponses\";\ny:=x->m*x+b;\ny(x);\nplot(y( x),x=-5..5);" }}}}{SECT 0 {PARA 237 "" 0 "" {TEXT 212 10 "La secante" }}{EXCHG {PARA 232 "> " 0 "" {MPLTEXT 1 0 214 "restart;\n\"Les donnees \";\nf:=x->x^4-10*x^2+9;\nx1:=2;x2:=4;\n\"La mathematisation\";\nm:=(f (x2)-f(x1))/(x2-x1);\nb:=f(x2)-m*x2;\n\"Les reponses\";\ny:=x->m*x+b; \ny(x);\nplot([f(x),y(x)],x=-5..5,-20..150,\n color=[red,blue]); " }}}}{SECT 0 {PARA 237 "" 0 "" {TEXT 212 11 "La tangente" }}{EXCHG {PARA 232 "> " 0 "" {MPLTEXT 1 0 173 "restart;\n\"Les donn\}es\";\nf:= x->x^4-10*x^2+9;\nx1:=2;\n\"La mathematisation\";\nm:=D(f)(x1);\nb:=f( x1)-m*x1;\n\"Les reponses\";\ny:=x->m*x+b;\nplot([f(x),y(x)],x=-5..5,c olor=[red,blue]);" }}}}{SECT 0 {PARA 237 "" 0 "" {TEXT 212 19 "L'asymp tote oblique" }}{EXCHG {PARA 232 "> " 0 "" {MPLTEXT 1 0 263 "restart; \n\"Les donnees\";\nf:=x->(x^3-2*x+5)/(x^2-2);\n\"La mathematisation\" ;\nm:=limit(f(x)/x,x=infinity);;\nb:=limit(f(x)-m*x,x=infinity);\n\"Le s resultats\";\n`L'asymptote`;\ny:=x->m*x+b;\n`Le graphique`;\nplot([f (x),y(x)],x=-5..5,-5..5,\n color=[red,blue],discont=true);" }}}} {SECT 0 {PARA 237 "" 0 "" {TEXT 212 16 "La lin?arisation" }}{EXCHG {PARA 232 "> " 0 "" {MPLTEXT 1 0 284 "restart;\n\"Les donnees\";\nf:=x ->sqrt(x);\nx1:=10;\n\"La mathematisation\";\nm:=D(f)(x1);\nb:=f(x1)-m *x1;\n\"Les reponses\";\ny:=x->m*x+b;\nplot([f(x),y(x)],x=-1..15,color =[red,blue]);\n`differentielle`;\ndx:=1;\ndy:=D(f)(x1)*dx;\ndy:=evalf( %);\n`variation fonction`;\nf(x1+dx)-f(x1);\ndeltay:=evalf(%);\n\n" }} }}}}{EXCHG {PARA 226 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 226 "" 0 " " {TEXT -1 0 "" }}}{EXCHG {PARA 226 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 226 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 226 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 226 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 226 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 225 "" 0 "" {TEXT -1 0 "" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 0 "" }}}{SECT 0 {PARA 3 "" 0 "" {TEXT -1 12 "Les packag es" }}{EXCHG {PARA 0 "" 0 "" {TEXT -1 106 "La version 9 contient 3 sou s package destin\351s \340 l'enseignement d'un niveau equivalent au ni veau collegial\n" }}}{SECT 0 {PARA 4 "" 0 "" {TEXT -1 11 "Precalculus " }}{EXCHG {PARA 0 "" 0 "" {TEXT -1 124 "Ce package contient des d\351 mos pour mieux comprendre des elements de base. Ce sont des Maple Mapl et (Tutor). Deux exemples :\n" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 80 "with(Student[Precalculus]):\nCompositionTutor();\nCompositionTut or(x^3+2, 1/x^2);\n" }}{PARA 8 "" 1 "" {TEXT -1 54 "Error, (in pacman: -pexports) Student is not a package\n" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#-%1CompositionTutorG6\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#-%1Compo sitionTutorG6$,&*$)%\"xG\"\"$\"\"\"F+\"\"#F+*&F+F+*$)F)F,F+!\"\"" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}{SECT 0 {PARA 4 "" 0 " " {TEXT -1 8 "Calculus" }}{EXCHG {PARA 0 "" 0 "" {TEXT -1 232 "Ce pack age contient les commandes de base du calcul differentiel et integral. Il y a trois types de ressources : les commandes de visualisation (de s d\351mos), celles interactives (des Maple Maplet de type Tutor) et c elles de calcul. \n" }}}{SECT 0 {PARA 5 "" 0 "" {TEXT -1 13 "Visualisa tion" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 163 "restart;\nwith(Stud ent[Calculus1]):\nRiemannSum(sin(x), x=0.0..5.0, method = lower,\n ou tput=plot);\nRiemannSum(ln(x), x=1..100, method = right, output = anim ation);\n" }}{PARA 8 "" 1 "" {TEXT -1 54 "Error, (in pacman:-pexports) Student is not a package\n" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#-%+Riem annSumG6&-%$sinG6#%\"xG/F);$\"\"!F-$\"#]!\"\"/%'methodG%&lowerG/%'outp utG%%plotG" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#-%+RiemannSumG6&-%#lnG6# %\"xG/F);\"\"\"\"$+\"/%'methodG%&rightG/%'outputG%*animationG" }}}} {SECT 0 {PARA 5 "" 0 "" {TEXT -1 11 "Interactive" }}{EXCHG {PARA 0 "> \+ " 0 "" {MPLTEXT 1 0 142 "restart;\nwith(Student[Calculus1]):\nTangentS ecantTutor();\nTangentSecantTutor(x^3-2);\nTangentSecantTutor(x^2, 4); \nTangentSecantTutor(x^2, x=4);\n" }}}}{SECT 0 {PARA 5 "" 0 "" {TEXT -1 16 "Calcul pas a pas" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 69 "r estart;\nwith(Student:-Calculus1):\nRule[`*`](Diff(x^2*sin(x^2), x)); \n" }}}}}{SECT 0 {PARA 4 "" 0 "" {TEXT -1 7 "Algebre" }}{EXCHG {PARA 0 "" 0 "" {TEXT -1 215 "Ce package contient les commandes de base d'al gebre lineaire sur le modele du package LinearAlgebra. Il y a aussi tr ois types de ressources : les commandes de visualisation, celles inter actives et celles de calcul \n" }}}{SECT 0 {PARA 5 "" 0 "" {TEXT -1 13 "Visualisation" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 84 "restart ;\nwith(Student[LinearAlgebra]):\nPlanePlot( anglebracket(1,1,1), show basis );\n" }}}}{SECT 0 {PARA 5 "" 0 "" {TEXT -1 11 "Interactive" }} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 102 "restart;\nwith(Student[Line arAlgebra]):\nM := |<0,2,1>>;\nInverseTuto r( M );\n" }}}}{SECT 0 {PARA 5 "" 0 "" {TEXT -1 6 "Calcul" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 101 "restart;\nwith(Student[LinearAlgeb ra]):\nA := |<0,8,1>>;\nC := Adjoint(A); \n" }}}}}}{EXCHG {PARA 225 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 225 " " 0 "" {TEXT -1 0 "" }}}{PARA 243 "" 0 "" {TEXT -1 0 "" }}{PARA 244 " " 0 "" {TEXT -1 0 "" }}{PARA 245 "" 0 "" {TEXT -1 0 "" }}}{MARK "40 0 " 0 }{VIEWOPTS 1 1 0 1 1 1803 1 1 1 1 }{PAGENUMBERS 0 1 2 33 1 1 }