{VERSION 3 0 "IBM INTEL NT" "3.0" } {USTYLETAB {CSTYLE "Maple Input" -1 0 "Courier" 0 1 255 0 0 1 0 1 0 0 1 0 0 0 0 }{CSTYLE "" -1 256 "" 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 } {CSTYLE "" -1 257 "" 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 }{CSTYLE "" -1 258 "" 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 }{CSTYLE "" -1 259 "" 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 }{CSTYLE "" -1 260 "" 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 } {CSTYLE "" -1 261 "" 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 }{CSTYLE "" -1 262 "" 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 }{PSTYLE "Normal" -1 0 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 }0 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "" 0 256 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 }3 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }} {SECT 0 {EXCHG {PARA 256 "" 0 "" {TEXT -1 34 "TP maths et Maple N\2601 , ann\351e 2005\n" }}{PARA 0 "" 0 "" {TEXT -1 297 "Ce TP a pour object if de fournir \340 chaque \351l\350ve un mini-guide des principales fo nctions de Maple.\nIl vous est propos\351 de taper un certain nombre d 'instructions, d'en regarder et d'en annoter le r\351sultat pour vous. Vous devez sauvegarder r\351guli\350rement vos r\351sultats pour les \+ retrouver par la suite." }}{PARA 0 "" 0 "" {TEXT -1 109 "Pour avoir un renseignement sur une instruction, il suffit de la s\351lectionner et de cliquer sur le menu Help." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }} {PARA 0 "" 0 "" {TEXT -1 2 "1." }{TEXT 256 22 " Calculs \351l\351menta ires " }{TEXT -1 1 ":" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 4 "2+3 ;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "2/7+2/3;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 19 "1+0,66666;2^3;2**3;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "1-sqrt(2)+2*sqrt(2);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 9 "evalf(%);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 38 "Digits:=12;evalf(1-sqrt(2)+2*sqrt(2));" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 38 "Digits:=20:evalf(1-sqrt(2)+2*sqrt(2 ));" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 145 "On remarque que \";\" et \+ \":\" sont des marqueurs de fin d'instruction, mais Maple ne renvoie q ue les r\351sultats des instructions se terminant par \";\"" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 3 "2. " }{TEXT 257 11 "Affectation" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> \+ " 0 "" {MPLTEXT 1 0 8 "restart;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 5 "x:=2;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 2 "x;" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 4 "x+3;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 7 "y:=x;y;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "restart;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 2 "x;" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "x:=y;y:=z;z:=3;x;" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 22 "t;t=2;t;assign(t=2);t;" }}} {EXCHG {PARA 0 "" 0 "" {TEXT -1 3 "3. " }{TEXT 258 24 "Manipulation de formules" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 8 "restart;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 13 "U:=x+2*y-3*z;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 11 "V:=x-2 +3*z;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "U+V;U/V;U*V;U**V; " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 15 "X:=subs(x=z,V);" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 23 "S:=sum((n-1)^i,i=0..9);" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 34 "simplify(S);S;factor(S);expa nd(S);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 32 "A:=sin(x)^4+sin(x )^2*cos(x)^2-1;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "simplify (A);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 23 "M:=x+1/(x+1);normal (M);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 28 "N:=cos(x)^7;combine (N,trig);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 2 "U;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 22 "subs(\{x=1,z=0,y=1\},U);" }}} {EXCHG {PARA 0 "" 0 "" {TEXT -1 3 "4. " }{TEXT 259 9 "Graphisme" }} {PARA 0 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "restart;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 7 "sin(x);" }} }{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 18 "smartplot(sin(x));" }}} {EXCHG {PARA 0 "" 0 "" {TEXT -1 108 "Cliquez avec le bouton droit de l a souris, sur l'expression sin(x) obtenue, puis choisissez l'option pl ot2d." }}{PARA 0 "" 0 "" {TEXT -1 22 "Un graphisme apparait." }}{PARA 0 "" 0 "" {TEXT -1 110 "Vous pouvez changer les \351chelles de ce grap hisme gr\342ce au bouton droit de la souris, voir \351galement les aut res" }}{PARA 0 "" 0 "" {TEXT -1 20 "options disponibles." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "x-x^3/6;" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 140 "S\351lectionnez le r\351sultat obtenu et faites un gliss er d\351poser dans le graphisme pr\351c\351dent. Adapter le range pour comparer les deux fonctions." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 4 "y=x;" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 64 "De nouveau faire un glisser-d\351poser dans le graphis me pr\351c\351dent." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "x^2+y^2;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 26 "smartplot3d[x,y](x^2+y^2);" }}}{EXCHG {PARA 0 "" 0 " " {TEXT -1 360 "Cliquez toujours avec le bouton droit de la souris pou r s\351lectionner plot3d, puis cliquez avec le bouton droit sur le gra phisme pour voir les diff\351rentes options disponibles. Remarquez \+ \351galement qu'en cliquant avec le bouton gauche sur le graphisme, ma is en dehors de la surface, on peut, en maintenant appuy\351 le bouton , faire tourner la surface dans l'espace." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 6 "2*x*y;" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 63 "Faites un glisser-d\351poser, et comparer ainsi 2*x*y avec x^2+y^2" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 3 "5. " }{TEXT 260 50 "R\351solution d'\351qu ations et de syst\350mes d'\351quations." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "restart;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "solve(x^2-y^3,y);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "solve(x^3-1=0,x);" }}}{EXCHG {PARA 0 "> \+ " 0 "" {MPLTEXT 1 0 28 "eq:=x^5+x^4+x=0;solve(eq,x);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 274 "Lorsque les racines du polyn\364me sont trop c ompliqu\351es ou ne s'\351crivent pas \340 l'aide des fonctions usuell es, Maple donne une r\351ponse \340 l'aide de la fonction RootOf(). Le s solutions de l'\351quation sont alors les racines de la quantit\351 \+ se trouvant en argument de cette fonction." }}}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 35 " fsolve(eq,x);fsolve(eq,x,complex);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 18 "solve(cos(x)=x,x);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 19 "fsolve(cos(x)=x,x);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 31 "S:=\{x^2-y*x=1,(x-y)*(x+y+1)=0\};" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 15 "solve(S,\{x,y\});" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 41 "ED:=diff(f(t),t,t)-diff(f(t) ,t)+f(t)-t^2;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 16 "dsolve(ED, f(t));" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 3 "6. " }{TEXT 261 19 "Fonc tions et suites" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> \+ " 0 "" {MPLTEXT 1 0 8 "restart;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 18 "f:=x->sqrt(1+x^2);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "f;f(x);f(t);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 10 "f(2);f( I);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 26 "evalf(f(pi));evalf(f (Pi));" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "f(f(f(f(f(1))))); " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 10 "(f@@5)(1);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 10 "(f@@n)(0);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 50 "g:=D(f);g(1);diff(f(x),x);int(f(x),x);Int(f(x),x );" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 120 "Remarquez l'importance des majuscules/minuscules. Une constante commence toujours par une maju scule : (I, Digits, Pi)." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 2 "7." }{TEXT 262 38 " Structure : s\351quenc e, liste et table." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "(x,y,z):=(1,2,5);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 2 "y;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 20 " S:=seq(i^2,i=1..10);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 5 "S[3] ;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "T:=[S];T[3];" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "map(t->t-1,T);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 6 "op(T);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 25 "S:=seq(x[i]=i^2,i=1..10);" }}}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 25 "S:=seq(u[i]=i^2,i=1..10);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 5 "u[2];" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 10 "assign(S);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 5 "u[2];" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 10 "assign(S);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 58 "Il est normal d'obtenir une erreur. (comprendre pourquoi)." }}}}{MARK "85" 0 }{VIEWOPTS 1 1 0 1 1 1803 }