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{SECT 0 {EXCHG {PARA 258 "" 0 "" {TEXT -1 124 "\253 Les math\351matiqu
es pures sont cette discipline o\371 on ne sait pas de quoi on parle n
i si ce qu'on dit est vrai  \273 B. Russel." }}}{EXCHG {PARA 261 "" 0 
"" {TEXT -1 34 "Universit\351 Paris 7 - Denis Diderot" }}{PARA 0 "" 0 
"" {TEXT -1 15 "Ann\351e 2000-2001" }}{PARA 259 "" 0 "" {TEXT 280 16 "
MI 101 - Maple V" }}{PARA 260 "" 0 "" {TEXT 280 20 "Groupes A4 - A5 - \+
D5" }}}{EXCHG {PARA 18 "" 0 "" {TEXT -1 30 "3. Repr\351sentations Grap
hiques." }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 8 "Sommaire" }}{PARA 14 "
" 0 "" {TEXT -1 33 "1. Graphiques en deux dimensions." }}{PARA 14 "" 
0 "" {TEXT -1 24 "     1.1 package \"plots\"" }}{PARA 14 "" 0 "" 
{TEXT -1 35 "2. D'autres type de graphes en 2-d." }}{PARA 14 "" 0 "" 
{TEXT -1 29 "     21. courbes parametr\351es." }}{PARA 14 "" 0 "" 
{TEXT -1 35 "     2.2 Champs de vecteurs en 2-d." }}{PARA 14 "" 0 "" 
{TEXT -1 51 "     2.3 Graphes de courbes d\351finies implicitements" }
}{PARA 14 "" 0 "" {TEXT -1 32 "     2.4 Graphes de points.     " }}
{PARA 14 "" 0 "" {TEXT -1 41 "     2.5 D'autres syst\350mes de coordon
\351es." }}{PARA 14 "" 0 "" {TEXT -1 19 "     2.6 Inegalit\351s" }}
{PARA 14 "" 0 "" {TEXT -1 32 "     2.7 Echelles logarithmiques" }}
{PARA 14 "" 0 "" {TEXT -1 49 "3. Graphiques en trois dimensions.\n4. A
nimations." }}}{EXCHG {PARA 0 "" 0 "" {TEXT 281 5 "Note:" }}{PARA 0 "
" 0 "" {TEXT -1 244 "On est pas oblig\351 d'afficher tous les calculs \+
que l'on fait avec Maple. Si on veut effectuer un calcul sans afficher
 le r\351sultat, on peut remplacer le  \";\" final par un \":\". Maple
 effectura le calcul demand\351 mais n'en affichera pas le r\351sultat
." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 56 "z := (3-6*I)^(3*I);\ns
qrt(Re(z)^2 +Im(z)^2);\nsimplify(%);" }{TEXT -1 0 "" }}}{EXCHG {PARA 
0 "> " 0 "" {MPLTEXT 1 0 51 "sqrt(Re(z)^2 +Im(z)^2):\nsimplify(%);\nun
assign('z');" }}}{EXCHG {PARA 4 "" 0 "" {TEXT -1 0 "" }}{PARA 4 "" 0 "
" {TEXT -1 33 "1. Graphiques en deux dimensions." }}{PARA 0 "" 0 "" 
{TEXT -1 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 73 "La syntaxe g\351n
\351rale pour tracer un graphique avec Maple est la suivante :" }}
{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 262 "" 0 "" {TEXT -1 0 "" }
{TEXT 256 10 "plot_type(" }{TEXT 258 34 "expression, intervalle, optio
ns,.." }{TEXT 257 2 ")," }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 
0 "" {TEXT -1 5 "O\371 : " }{TEXT 282 10 "expression" }{TEXT -1 103 " \+
est une expression math\351matique, o\371 un ensemble d'expression d
\351finissant la (les) fonctions \340 tracer. " }{TEXT 283 10 "interva
lle" }{TEXT -1 17 " est de la forme " }{TEXT 284 6 "x=a..b" }{TEXT -1 
34 " avec a et b des nombres r\351els et " }{TEXT 285 3 "a<b" }{TEXT 
-1 175 ", ou une liste d'intervalles de la meme forme.. Option corresp
ont \340 une ou plusieurs sp\351cificatiosn optionnelles qui determine
nt l'apparence du graphe (titre, echelles, etc.)." }{TEXT 286 1 " " }}
{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 65 "    La co
mmande de base poru tracer un graphique est la commande " }{TEXT 287 
4 "plot" }{TEXT -1 88 ". Cependant, de nombreuses commandes existent p
our tracer differents type de graphiques." }}{PARA 0 "" 0 "" {TEXT -1 
85 "    Il existe meme un package pour tracer certains graphiques. Cer
 package s'appelle " }{TEXT 288 5 "plots" }{TEXT -1 78 ", et pour pouv
oir le charger en m\351moire il faut avoir recours \340 la commande : \+
" }{TEXT 289 11 "with(plots)" }{TEXT -1 86 ". Si on charge tout le pac
kage en m\351moire on peut faire appel \340 la commande en tapant " }
{TEXT 290 8 "commande" }{TEXT -1 67 ". Mais si tout le package n'est p
as charg\351 on peut toujours \351crire " }{TEXT 291 6 "plots[" }
{TEXT 292 7 "command" }{TEXT 293 1 "]" }{TEXT -1 30 " qui donnera le m
eme r\351sultat." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" 
{TEXT -1 44 "  N'oubliez pas que l'aide est toujours l\340 :" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 6 "?plots" }{TEXT -1 0 "" }}}
{EXCHG {PARA 0 "" 0 "" {TEXT -1 101 "Le type le plus simple de graphiq
ues en deux dimensions est obtenu par uen expressions de la forme : " 
}{TEXT 295 17 "plot(f(x), x=a..b" }{TEXT 294 25 ", y=c..d, opt1, opt2,
 ..." }{TEXT 296 1 ")" }{TEXT -1 44 " o\371 les terme en italiques son
t optionnels. " }{TEXT 297 4 "f(x)" }{TEXT -1 102 " est une focntion d
\351pendantes de la variable r\351elle x et le domaine o\371 l'on va t
racer la fonction est " }{TEXT 298 6 "x=a..b" }{TEXT -1 15 " (avec a <
 b). " }}{PARA 0 "" 0 "" {TEXT -1 106 "Nous verrons els options les pl
us souvent utilis\351es. Pour les autres options vous pouvez regarder \+
l'aide :" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "?plot[options]
" }{TEXT -1 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 
0 "" {TEXT -1 71 "Et voici un exemple (le plsu simple possible) pour t
racer un graphique." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "plot
(x^2-3,x=-4..4);" }{TEXT -1 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 
104 "Et un autre graphique avec un titre, et la sp\351cification de la
 fonte, du style et de la police utilis\351e." }}}{EXCHG {PARA 0 "> " 
0 "" {MPLTEXT 1 0 78 "plot(x*sin(x),x=-3*Pi..3*Pi, title=\"x*sin(x)\",
titlefont=[HELVETICA, BOLD,18]);" }{TEXT -1 0 "" }}}{EXCHG {PARA 0 "" 
0 "" {TEXT -1 33 "Un autre avec des noms aux axes :" }}}{EXCHG {PARA 
0 "> " 0 "" {MPLTEXT 1 0 53 "plot(exp(-t^2), t=0..4,\n     labels=[ele
ves, notes]);" }{TEXT -1 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" 
}}{PARA 0 "" 0 "" {TEXT -1 168 "Lorsqu'on essaie de tracer une fonctio
n discontinue, Maple va essayer par d\351faut de joindre les points de
 discontinuit\351s. Ce qui peut etre supprim\351 en mettant l'option \+
" }{TEXT 299 12 "discont=true" }{TEXT -1 163 ", ce qui dit \340 Maple \+
de determiner les points de discontinuit\351s de l'expression et s\351
parle l'interval de d\351finition en sous intervales o\371 la fonction
 est continue." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 104 "plot(x-f
loor(x),x=-3..3,scaling=constrained);\nplot(x-floor(x),x=-3..3,discont
=true,scaling=constrained);" }{TEXT -1 0 "" }}}{EXCHG {PARA 0 "" 0 "" 
{TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 146 "Par d\351faut, Maple cal
cule un minimum de 50 points par graphe, mais ilk peut etre utile d'au
gmenter ce nombre de points. on utilise alors l'option " }{TEXT 300 9 
"numpoints" }{TEXT -1 1 "." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 
90 "plot(x^3*sin(exp(1/x)),x=(.2)..(.3));\nplot(x^3*sin(exp(1/x)),x=(.
2)..(.3), numpoints=500);" }{TEXT -1 0 "" }}}{EXCHG {PARA 0 "" 0 "" 
{TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 72 "Voici deux fa\347on de sp
\351cifier la couleur d'un graphe \340 deux dimensions :" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 93 "plot(BesselJ(0,x),x=0..10,color=gre
en);\nplot(BesselJ(1,x),x=0..10,color=COLOR(RGB,.8,.4,.4));" }{TEXT 
-1 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" 
{TEXT -1 22 "En utilisant l'option " }{TEXT 301 11 "style=point" }
{TEXT -1 39 " on trace un graphe de fa\347on discrete :" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 43 "plot(exp(-x)*sin(x^2), x=0..4,style
=point);" }{TEXT -1 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}
{PARA 0 "" 0 "" {TEXT -1 58 "Bien entendu, on peut tracer plusieurs gr
aphes \340 la fois :" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 79 "plo
t(\{x^2-1,sin(x)\},x=-Pi..Pi,y=-1..1);\nplot([x^2-1,sin(x)],x=-Pi..Pi,
y=-1..1);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 88 "\nGrace \340 la seco
nde notation, on peut imposer une couleur particuli\350re \340 chaque \+
graphe :" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 59 "plot([x^2-1,sin
(x)],x=-Pi..Pi,y=-1..1, color=[green,blue]);" }{TEXT -1 0 "" }}}
{EXCHG {PARA 0 "" 0 "" {TEXT -1 187 "\nDe mani\350re g\351n\351rale, p
lusieures courbes peuvent etre trac\351es simultan\351menents avec la \+
commande plot, avec differentes options tels que la couleur, le style \+
etc. pour chacune des courbes." }}{PARA 263 "" 0 "" {TEXT -1 0 "" }
{TEXT 259 4 "plot" }{TEXT -1 1 "(" }{TEXT 260 72 "[expr1,expr2,  ..., \+
exprn], range, color=[c1, c2,...], style=[s1,s2,...]" }{TEXT -1 5 ", .
.)" }}}{EXCHG {PARA 5 "" 0 "" {TEXT -1 0 "" }}{PARA 5 "" 0 "" {TEXT 
-1 19 "1.1 package \"plots\"" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}
{EXCHG {PARA 0 "" 0 "" {TEXT -1 86 "\nUn autre moyen d'afficher plusie
urs graphes en meme temps est d'utilsier la commande " }{TEXT 302 7 "d
isplay" }{TEXT -1 40 ". Cetet commande fait partie du package " }
{TEXT 303 5 "plots" }{TEXT -1 60 ". cette commande peut donc soit etre
 utilis\351e sous la forme " }{TEXT 304 14 "plots[display]" }{TEXT -1 
20 " soit sous la forme " }{TEXT 305 7 "display" }{TEXT -1 56 " en cha
rgeant d'abord en m\351moire le package en entier. \n" }}{PARA 0 "" 0 
"" {TEXT -1 118 "Comme nous allons \351tudier de nombreuses fonctions \+
de ce package, nous choisissons ici de charger le package en entier." 
}}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "with(plots);" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 116 "plot1:=plot(sin(x),x=-2*Pi..2*Pi,c
olor=red):\nplot2:=plot(cos(x), x=-2*Pi..2*Pi,color=green):\ndisplay([
plot1,plot2]);" }{TEXT -1 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "
" }}{PARA 0 "" 0 "" {TEXT -1 90 "On peut aussi placer du texte \340 un
 endroit pr\351cis sur un graphe, en utilisant la commande " }{TEXT 
306 8 "textplot" }{TEXT -1 1 "." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 
1 0 224 "a:=plot(sin(x),x=-Pi..Pi):\nb:=textplot([Pi/2,1,`Local Maximu
m`],font=[TIMES,ITALIC,12]):\nc:=textplot([-Pi/2,-1,`Local Minimum`],f
ont=[TIMES,ITALIC,12]):\ndisplay([a,b,c],title=\"f(x) = sin(x)\",title
font=[HELVETICA, BOLD, 18]);" }{TEXT -1 0 "" }}}{EXCHG {PARA 0 "" 0 "
" {TEXT 348 10 "Exercice 1" }}{PARA 14 "" 0 "" {TEXT -1 22 "a) Tracer \+
la fonction " }{XPPEDIT 18 0 "f(x) = 1-x^n;" "6#/-%\"fG6#%\"xG,&\"\"\"
\"\"\")F'%\"nG!\"\"" }{TEXT -1 103 " sur l'intervale [0,1] pour n=1, 2
 ,5 et 10 le tout sur un seul graphe. Donnez un titre \340 votre graph
e." }}{PARA 14 "" 0 "" {TEXT -1 29 "b) Sur R Tracer les fonction " }
{XPPEDIT 18 0 "y = sqrt(abs(x));" "6#/%\"yG-%%sqrtG6#-%$absG6#%\"xG" }
{TEXT -1 4 " et " }{XPPEDIT 18 0 "y = x^2;" "6#/%\"yG*$%\"xG\"\"#" }
{TEXT -1 112 " sur un meme graphe.\nc) tracez la fonction y = 1-floor(
x) sachant quelle est discontinue.\nd) Tracer la fonction " }{XPPEDIT 
18 0 "f(x) := x*e^(-x);" "6#>-%\"fG6#%\"xG*&F'\"\"\")%\"eG,$F'!\"\"F)
" }{TEXT -1 5 "pour " }{TEXT 347 7 "x > -1." }{TEXT -1 50 " Pensez vou
s que la d\351riv\351e s'annule en un point ?" }}{PARA 14 "" 0 "" 
{TEXT -1 20 "e) Sur l'intervalle " }{XPPEDIT 18 0 "[-2*Pi, 2*Pi];" "6#
7$,$*&\"\"#\"\"\"%#PiGF'!\"\"*&\"\"#F'F(F'" }{TEXT -1 42 ", tracer dan
s un meme graphe les fonction " }{XPPEDIT 18 0 "proc (x) options opera
tor, arrow; x*sin(x) end;" "6#R6#%\"xG7\"6$%)operatorG%&arrowG6\"*&F%
\"\"\"-%$sinG6#F%F,F*F*F*" }{TEXT -1 14 " (en rouge) : " }{XPPEDIT 18 
0 "proc (x) options operator, arrow; x end;" "6#R6#%\"xG7\"6$%)operato
rG%&arrowG6\"F%F*F*F*" }{TEXT -1 14 " (en vert) et " }{XPPEDIT 18 0 "p
roc (x) options operator, arrow; -x end;" "6#R6#%\"xG7\"6$%)operatorG%
&arrowG6\",$F%!\"\"F*F*F*" }{TEXT -1 75 " (en vert). Donnez un titre \+
\340 ce graphe (en hevetica avec une police de 14)" }}}{EXCHG {PARA 4 
"" 0 "" {TEXT -1 0 "" }}{PARA 4 "" 0 "" {TEXT -1 35 "2  D'autres type \+
de graphes en 2-d." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 5 
"" 0 "" {TEXT -1 25 "2.1. courbes parametr\351es." }}{PARA 0 "" 0 "" 
{TEXT -1 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 168 "Nous allons voir
 comment tracer une courbe qui est d\351finie param\351tiquement. La s
yntaxe pour tracer une courbe d\351finie param\351triquement par le ve
cteur (f(t), g(t)) est :" }}{PARA 264 "" 0 "" {TEXT 307 27 "plot([f(t)
, g(t), t=a..b]) " }}{PARA 0 "" 0 "" {TEXT -1 154 "Notez que les croch
ets [...] sont autour de toute l'expression. C'est al seule particular
it\351 qui distingue une expression param\351trique d'un graphe normal
." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 32 "plot([sin(t),cos(t),t=
0..2*Pi]);" }{TEXT -1 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 90 "\nVo
ici ce que donen le graphie de la fonction param\351trique d\351finie \+
par (f(t), g(t)) avec :" }}{PARA 265 "" 0 "" {TEXT -1 1 " " }{XPPEDIT 
18 0 "f(t) = (sin(t)-cos(t))^3-sin(t)+cos(t);" "6#/-%\"fG6#%\"tG,(*$,&
-%$sinG6#F'\"\"\"-%$cosG6#F'!\"\"\"\"$F.-F,6#F'F2-F06#F'F." }}{PARA 
266 "" 0 "" {TEXT -1 1 " " }{XPPEDIT 18 0 "g(t) = cos(t)^2-sin(t)^2;" 
"6#/-%\"gG6#%\"tG,&*$-%$cosG6#F'\"\"#\"\"\"*$-%$sinG6#F'\"\"#!\"\"" }}
{PARA 0 "" 0 "" {TEXT -1 21 "Pour t variant entre " }{XPPEDIT 18 0 "-P
i;" "6#,$%#PiG!\"\"" }{TEXT -1 4 " et " }{XPPEDIT 18 0 "Pi;" "6#%#PiG
" }{TEXT -1 2 " ." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 130 "plot(
[(sin(t)-cos(t))^3-(sin(t)-cos(t)),\n       cos(t)^2-sin(t)^2,\n      \+
 t=-Pi..Pi\n     ],\n     -2..2,-1..1,scaling=constrained);" }{TEXT 
-1 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" 
{TEXT -1 80 "On peut, bien entendu tracer plsuiseurs courbes param\351
tr\351es dans le meme graphe." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 
0 97 "plot([\n      [t^2,t,t=-1..1],\n      [sin(t),cos(t),t=0..2*Pi]
\n     ],\n      scaling=constrained);" }}}{EXCHG {PARA 0 "" 0 "" 
{TEXT -1 102 "\nLes courbes param\351tr\351es et non-param\351tr\351es
 peuvent, bien entendu etre representer sur un seul graphe." }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 164 "plot([\n      x-x^3/3,\n   \+
   [\n       (sin(t)-cos(t))^3-(sin(t)-cos(t)),\n       cos(t)^2-sin(t
)^2,\n       t=-Pi..Pi\n      ]\n     ],\n      x=-2..2, color=[red,bl
ue]);" }{TEXT -1 0 "" }}}{EXCHG {PARA 5 "" 0 "" {TEXT -1 0 "" }}{PARA 
5 "" 0 "" {TEXT -1 30 "2.2 Champs de vecteurs en 2-d." }}{PARA 0 "" 0 
"" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 184 "Un champ de v
ecteurs dans le plan x-y est d\351finie par la paire de fonctions ( f(
x,y), g(x,y) ) qui d\351finissent ses composantes. La commande pour tr
acer un tel champs est d\351finie par : " }}{PARA 267 "" 0 "" {TEXT 
308 9 "fieldplot" }{TEXT 311 1 "(" }{TEXT -1 34 "[f(x,y), g(x,y)], x=a
..b, y=c..d, " }{TEXT 309 6 "option" }{TEXT -1 1 "s" }{TEXT 310 1 ")" 
}}{PARA 0 "" 0 "" {TEXT -1 27 "(field = champs en anglais)" }}{PARA 0 
"" 0 "" {TEXT -1 10 "Notez que " }{TEXT 315 9 "fieldplot" }{TEXT -1 
24 " fait partie du package " }{TEXT 314 5 "plots" }{TEXT -1 39 ". S'i
l n'est pas en m\351moire, remplacez " }{TEXT 313 9 "fieldplot" }
{TEXT -1 5 " par " }{TEXT 312 17 "plots[fieldplot]\n" }{TEXT -1 19 "Vo
ici un exemple :+" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 50 "fieldp
lot([y,-x],x=-10..10,y=-10..10,arrows=SLIM);" }{TEXT -1 0 "" }}}
{EXCHG {PARA 0 "" 0 "" {TEXT -1 16 "\nNote: L'option " }{TEXT 263 11 "
arrows=SLIM" }{TEXT -1 134 ", qui a \351t\351 utilis\351e ici permet d
e specifier le type de fleche (=arrow dans la langue de Dickens). Les \+
autres types de fleches sont : " }{TEXT 264 5 "LINE " }{TEXT -1 9 "(=l
igne)," }{TEXT 317 5 " THIN" }{TEXT -1 15 " (=maigre) and " }{TEXT 
265 6 "THICK " }{TEXT -1 36 "(=\351pais), Par d\351faut c'est l'option
 " }{TEXT 316 4 "THIN" }{TEXT -1 18 " qui est utilis\351e." }}}{EXCHG 
{PARA 5 "" 0 "" {TEXT -1 0 "" }}{PARA 5 "" 0 "" {TEXT -1 46 "2.3 Graph
es de courbes d\351finies implicitements" }}{PARA 0 "" 0 "" {TEXT -1 
0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 101 "Les fonctions implicites \+
en deux dimensions sont les fonctions d\351finies par une relation de \+
la forme " }{TEXT 318 8 "f(x,y)=0" }{TEXT -1 54 ". Elles peuvent etre \+
trac\351es en utilisant la commande " }{TEXT 319 12 "implicitplot" }
{TEXT -1 57 ". Encore une fois, cette commande fait partie du package \+
" }{TEXT 320 5 "plots" }{TEXT -1 49 ", et subit les memes restrictions
 que d'habitude." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 ">
 " 0 "" {MPLTEXT 1 0 87 "implicitplot(x^2 / 25 + y^2 / 9 = 1,\n       \+
      x=-6..6,y=-6..6,scaling=CONSTRAINED);" }{TEXT -1 0 "" }}}{EXCHG 
{PARA 5 "" 0 "" {TEXT -1 0 "" }}{PARA 5 "" 0 "" {TEXT -1 22 "2.4 Graph
es de points." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "" 0 
"" {TEXT -1 102 "La commande plot peut aussi etre utilis\351e pour rel
ier des points entre eux, avec la syntaxe suivante :" }}{PARA 256 "" 
0 "" {TEXT -1 6 "plot([" }{TEXT 266 27 "[a1,b1], [a2,b2],...[an,bn]" }
{TEXT -1 3 ")] " }}{PARA 257 "" 0 "" {TEXT 267 165 "O\371 [a1, b1], [a
2, b2],... represente les deux composantes d'un poit en coordon\351es \+
cart\351siennes.\nEn mettant [a1,b1] = [an,bn], on peut fermer la cour
be ainsi obtenue." }{TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 49 "plot([[-12,-1],[20,7],[21,3],[-11,-5],[-12,-1]]);" }
{TEXT -1 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 94 "\nSi l'on ne veut
 que representer les points sans les rejoindre, il suffit d'utiliser l
'option " }{TEXT 321 11 "style=point" }{TEXT -1 13 " comme suit :" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 62 "plot([[-12,-1],[20,7],[21,3]
,[-11,-5],[-12,-1]], style=point);" }{TEXT -1 0 "" }}}{EXCHG {PARA 5 "
" 0 "" {TEXT -1 37 "\n2.5 D'autres syst\350mes de coordon\351es." }}
{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 179 "
En dehors des coordon\351es cartesiennes,  On peut \351galement tracer
 des graphes dans d'autres coordonn\351es, telles que polaires, hyperb
oliques, elliptiques, etc. En ajoutant l'option\n" }{TEXT 322 6 "coord
s" }{TEXT -1 1 "=" }{TEXT 323 4 "type" }{TEXT -1 49 ". Je vous encoura
ge \340 regarder l'aide \340 ce sujet." }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 14 "?plot[coords];" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 
1 0 7 "?coords" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 
0 "" {TEXT -1 49 "Nous allons voir le cas des coordon\351es polaires :
" }}}{EXCHG {PARA 5 "" 0 "" {TEXT -1 0 "" }}{PARA 5 "" 0 "" {TEXT -1 
30 "Graphes en coordon\351es polaires" }}{PARA 0 "" 0 "" {TEXT -1 0 "
" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 68 "En coordon\351es polaire, la \+
fonction \340 tracer s'exprime sous la forme " }{XPPEDIT 18 0 "r(theta
);" "6#-%\"rG6#%&thetaG" }{TEXT -1 36 ".\nTout d'abord un cercle de ra
yon 2." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 53 "plot(2,t=0..2*Pi,
 coords=polar, scaling=constrained);" }{TEXT -1 0 "" }}}{EXCHG {PARA 
0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 79 "On peut obtenir
 le meme r\351sultat en untilisant une representation parametrique." }
}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 56 "plot([2,t,t=0..2*Pi],coord
s=polar, scaling=constrained);" }}{PARA 13 "" 1 "" {TEXT -1 0 "" }}}
{EXCHG {PARA 0 "" 0 "" {TEXT -1 57 "On cherche maintenant \340 represe
nter la fonction suvante :" }}{PARA 268 "" 0 "" {TEXT -1 1 " " }
{XPPEDIT 18 0 "r(theta) = 6/sqrt(4*cos(theta)^2+9*sin(theta)^2);" "6#/
-%\"rG6#%&thetaG*&\"\"'\"\"\"-%%sqrtG6#,&*&\"\"%F**$-%$cosG6#F'\"\"#F*
F**&\"\"*F**$-%$sinG6#F'\"\"#F*F*!\"\"" }}{PARA 0 "" 0 "" {TEXT -1 0 "
" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 88 "plot(6/sqrt((4*cos(t)^2
+9*sin(t)^2)),\n     t=0..2*Pi, coords=polar,scaling=constrained);" }
{TEXT -1 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "
" {TEXT -1 34 "Il existe egalement une commande  " }{TEXT 324 9 "polar
plot" }{TEXT -1 25 " incluse dans le package " }{TEXT 325 5 "plots" }
{TEXT -1 49 ", qui est pratiquement \351quivalente \340 la commande " 
}{TEXT 327 4 "plot" }{TEXT -1 17 " avec les option " }{TEXT 326 12 "co
ords=polar" }{TEXT -1 4 " et " }{TEXT 328 20 " scaling=constrained" }
{TEXT -1 71 ", (si ce n'est que l'intervale o\371 varie l'angle n'est \+
aps \340 sp\351cifier)." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 41 "
polarplot(6/sqrt(4*cos(t)^2+9*sin(t)^2));" }{TEXT -1 0 "" }}}{EXCHG 
{PARA 0 "" 0 "" {TEXT -1 63 "Des courbes param\351tr\351es peuvent etr
e obtenues avec la comamnde " }{TEXT 329 9 "polarplot" }{TEXT -1 63 ",
 \nmais l'intervale du parametre doit absolument etre specifi\351." }}
}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 42 "polarplot([sin(t),2*Pi*sin(
t),t=0..Pi/2]);" }{TEXT -1 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "
" }}{PARA 0 "" 0 "" {TEXT -1 83 "Ici aussi, els courbes param\351tr
\351s et non parametr\351es peuvent etre trac\351es ensemble." }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 94 "polarplot(\{[sin(t),2*Pi*sin
(t),t=0..Pi/2],sin(2*t)+sin(t)\},t=-Pi/2..Pi/2,scaling=constrained);" 
}{TEXT -1 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 100 "\nNotez qu'on p
eut utiliser la commande display pour afficher plusieurs graphes dans \+
la meme fenetre." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 150 "a:=pol
arplot([sin(t),2*Pi*sin(t),t=0..Pi/2]):\nb:=polarplot(sin(2*t)+sin(t),
t=-Pi/2..Pi/2):\nc:=plot(x-floor(x),x=-3..3,discont=true):\ndisplay(\{
a,b,c\});" }}}{EXCHG {PARA 5 "" 0 "" {TEXT -1 15 "\n2.6 Inegalit\351s
" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 
81 "On peut traces des courbes representatives d'inegalit\351s en util
isant la commande " }{TEXT 330 7 "inequal" }{TEXT -1 13 " comme suit :
" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 94 "inequal(\{x+y<5,0<x,x<4
\},\n         x=-1..5,y=-10..10,\n         optionsexcluded=(color=yell
ow));" }}}{EXCHG {PARA 5 "" 0 "" {TEXT -1 28 "\n2.7 Echelles logarithm
iques" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "" 0 "" 
{TEXT -1 12 "La commande " }{TEXT 331 7 "logplot" }{TEXT -1 62 " perme
t d'obtenir des echelles logarithmiques sur l'axe des y." }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 22 "logplot(10^x,x=0..10);" }{TEXT -1 
0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT 
-1 12 "La commande " }{TEXT 332 11 "semilogplot" }{TEXT -1 37 " permet
 la meme chose sur l'axe des x" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 
1 0 37 "semilogplot(2^(sin(x^1/3)),x=1..100);" }{TEXT -1 0 "" }}}
{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 65 "Et
 la commande loglogplot permet la meme chsoe sur les deux axes." }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 24 "loglogplot(x^17,x=1..7);" }}
}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT 349 10 "
Exercice 2" }}{PARA 14 "" 0 "" {TEXT -1 20 "a) Tracer la courbe " }
{XPPEDIT 18 0 "r = sin(3*theta);" "6#/%\"rG-%$sinG6#*&\"\"$\"\"\"%&the
taGF*" }{TEXT -1 29 " en coordon\351es polaires pour " }{XPPEDIT 18 0 
"theta = 0 .. 2*pi;" "6#/%&thetaG;\"\"!*&\"\"#\"\"\"%#piGF)" }}{PARA 
14 "" 0 "" {TEXT -1 21 "b) Tracer la spirale " }{XPPEDIT 18 0 "r := th
eta;" "6#>%\"rG%&thetaG" }{TEXT -1 6 " pour " }{XPPEDIT 18 0 "theta = \+
-4*Pi .. 4*pi;" "6#/%&thetaG;,$*&\"\"%\"\"\"%#PiGF)!\"\"*&\"\"%F)%#piG
F)" }}{PARA 14 "" 0 "" {TEXT -1 31 "c) Tracer la courbe donn\351e par \+
" }{XPPEDIT 18 0 "y^2 = 2*x+4;" "6#/*$%\"yG\"\"#,&*&\"\"#\"\"\"%\"xGF*
F*\"\"%F*" }{TEXT -1 17 " dans la fenetre " }{XPPEDIT 18 0 "x = -2 .. \+
1.5;" "6#/%\"xG;,$\"\"#!\"\"$\"#:!\"\"" }{TEXT -1 4 " et " }{XPPEDIT 
18 0 "y = -3 .. 3;" "6#/%\"yG;,$\"\"$!\"\"\"\"$" }{TEXT -1 2 "  " }}
{PARA 14 "" 0 "" {TEXT -1 56 "d) Tracer  la courbe (polaire) parametr
\351e donn\351e par : (" }{XPPEDIT 18 0 "r = sin(t);" "6#/%\"rG-%$sinG
6#%\"tG" }{TEXT -1 2 ", " }{XPPEDIT 18 0 "theta = cos(t);" "6#/%&theta
G-%$cosG6#%\"tG" }{TEXT -1 7 ") pour " }{XPPEDIT 18 0 "t = 0 .. 2*Pi;
" "6#/%\"tG;\"\"!*&\"\"#\"\"\"%#PiGF)" }}{PARA 14 "" 0 "" {TEXT -1 45 
"e) tracer la courbes polaire correspondant \340 " }{XPPEDIT 18 0 "the
ta = exp(rho);" "6#/%&thetaG-%$expG6#%$rhoG" }}{PARA 14 "" 0 "" {TEXT 
-1 106 "f) Tracer entre 0 et 4 la fonction qui vaut x pour x <1 ; 1 po
ur 1< x < 2 ; 2*x-4 pour 2< x< 3 et 3 sinon." }}{PARA 14 "" 0 "" 
{TEXT -1 63 "g) Quelle est la r\351gion du plan qui satisfait ces in
\351galit\351s : " }{XPPEDIT 18 0 "x <= 4;" "6#1%\"xG\"\"%" }{TEXT -1 
3 " ; " }{XPPEDIT 18 0 "0 < x;" "6#2\"\"!%\"xG" }{TEXT -1 4 " et " }
{XPPEDIT 18 0 "x+y < 5;" "6#2,&%\"xG\"\"\"%\"yGF&\"\"&" }}{PARA 14 "" 
0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 4 "" 0 "" {TEXT -1 0 "" }}{PARA 4 "
" 0 "" {TEXT -1 34 "3. Graphiques en trois dimensions." }}{PARA 0 "" 
0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 117 "Maple sait \+
aussi bien tracer les graphes en 3-d que les graphes dans le plan. La \+
commande \340 utiliser est la commande " }{TEXT 333 6 "plot3d" }{TEXT 
-1 30 ". La syntaxe est al suivante :" }}{PARA 269 "" 0 "" {TEXT 269 
6 "plot3d" }{TEXT -1 1 "(" }{TEXT 268 23 "f(x,y), x=a..b, y=c..d," }
{TEXT -1 9 " options)" }}{PARA 0 "" 0 "" {TEXT -1 94 "Notez que Maple \+
ne montre pas d'axes par defaut. Mais on peut preciser les options sui
vantes :" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }{TEXT 334 11 "axes= frame" 
}{TEXT -1 2 ", " }{TEXT 335 5 "boxed" }{TEXT -1 6 " , ou " }{TEXT 336 
6 "normal" }{TEXT -1 43 ". Ce qui permet d'avoir differentes rendus." 
}}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 44 "plot3d((x^2-y^2)/(x^2+y^2
),x=-2..2,y=-2..2);" }{TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 55 "plot3d((x^2-y^2)/(x^2+y^2),x=-2..2,y=-2..2,axes=frame
);" }{TEXT -1 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 60 "\nDe meme, o
n peut afficher differents graphes en meme temps." }}}{EXCHG {PARA 0 "
> " 0 "" {MPLTEXT 1 0 50 "plot3d(\{x+y^2,-x-y^2\},x=-2..2,y=-2..2,axes
=frame);" }}{PARA 13 "" 1 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "" 0 "" 
{TEXT -1 2 "  " }}{PARA 0 "" 0 "" {TEXT -1 41 "Ou afficher une courbe \+
parametr\351e en 3-d." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 75 "pl
ot3d([s*sin(s),s*cos(t),s*sin(t)],\n       s=0..2*Pi,t=0..Pi, axes=box
ed);" }}{PARA 13 "" 1 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "" 0 "" 
{TEXT -1 81 "On peut faire des representation de courbes parametr\351e
s en utilisant le commande " }{TEXT 337 10 "spacecurve" }{TEXT -1 26 "
 (qui est dans la package " }{TEXT 338 5 "plots" }{TEXT -1 2 ")." }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 57 "spacecurve([s*sin(s),s*cos(s
),s],s=0..6*Pi, axes=normal);" }{TEXT -1 0 "" }}}{EXCHG {PARA 0 "" 0 "
" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 12 "La commande " }{TEXT 
343 6 "polt3d" }{TEXT -1 76 " utilise les coordon\351es cartesiennes p
ar d\351faut. Mais en utilisant l'option " }{TEXT 344 6 "coords" }
{TEXT -1 151 ", on peut changer ce syst\350me de coordon\351e en un au
tre. Les plus familiers \351tant les coordon\351es cylindriques et sph
\351riques. Regardez l'aide \340 ce sujet :" }}}{EXCHG {PARA 0 "> " 0 
"" {MPLTEXT 1 0 15 "?plot3d[coords]" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 7 "?coords" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 50 "La syt
axe g\351n\351rale d'un commande est de la forme :" }}{PARA 272 "" 0 "
" {TEXT 261 6 "plot3d" }{TEXT -1 1 "(" }{TEXT 270 37 "arguments obliga
toires et optionnels," }{TEXT -1 27 " coords=coordinate_system);" }}
{PARA 0 "" 0 "" {TEXT -1 65 "Lorsque le syt\350me de coordon\351es est
 spherique (coordinat_system =" }{TEXT 341 9 "spherical" }{TEXT -1 22 
") c'est equivalent \340 :" }}{PARA 270 "" 0 "" {TEXT 262 10 "spherepl
ot" }{TEXT -1 1 "(" }{TEXT 339 36 "arguments obligatoires et optionnel
s" }{TEXT -1 1 ")" }}{PARA 0 "" 0 "" {TEXT -1 71 "Ou, lorsque le syst
\350me de coordon\351es est cylindrique (coordinat_system " }{TEXT 
273 12 "=cylindrical" }{TEXT -1 3 ") :" }}{PARA 271 "" 0 "" {TEXT 274 
15 "cylindricalplot" }{TEXT -1 1 "(" }{TEXT 340 36 "arguments obligato
ires et optionnels" }{TEXT -1 1 ")" }}{PARA 0 "" 0 "" {TEXT -1 55 "(le
s deux dernieres commandes appartiennent au package " }{TEXT 342 5 "pl
ots" }{TEXT -1 2 ")." }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 74 "Voici la \+
syntaxe minimale pour trace le graphe de f(x,y) dans la fenetre  " }
{TEXT 271 5 "a<x<b" }{TEXT -1 4 " et " }{TEXT 272 5 "c<y<d" }{TEXT -1 
1 "." }}{PARA 273 "" 0 "" {TEXT 275 6 "plot3d" }{TEXT -1 23 "(f(x,y), \+
x=a..b,y=c..d)" }}{PARA 0 "" 0 "" {TEXT -1 2 "ou" }}{PARA 274 "" 0 "" 
{TEXT 276 6 "plot3d" }{TEXT -1 14 "(f, a..b,c..d)" }}}{EXCHG {PARA 0 "
" 0 "" {TEXT -1 44 "Et la syntaxe pour les courbes param\351tr\351es :
" }}{PARA 275 "" 0 "" {TEXT 277 6 "plot3d" }{TEXT -1 39 "([f(s,t),g(s,
t),h(s,t)], s=a..b,t=c..d)" }}{PARA 0 "" 0 "" {TEXT -1 2 "ou" }}{PARA 
276 "" 0 "" {TEXT 278 7 " plot3d" }{TEXT -1 36 "([f(s,t),g(s,t),h(s,t)
], a..b, c..d)" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 25 "Voici quelques \+
exemples :" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 91 "plot3d( (1.3)
^x*sin(y),\n        x=-1..2*Pi, y=0..Pi,\n        coords=spherical,sty
le=PATCH);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 69 "plot3d( sin(x
*y),\n        x=-Pi..Pi, y=-Pi..Pi,\n        style=PATCH);" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 115 "plot3d([\n         x*sin(x)*cos(y)
,\n         x*cos(x)*cos(y),\n         x*sin(y)\n       ],\n       x=0
..2*Pi,y=0..Pi);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 53 "plot3d(
x*exp(-x^2-y^2),x=-2..2,y=-2..2,grid=[49,49]);" }}}{EXCHG {PARA 0 "" 
0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 36 "Et plusieurs graphes
 en meme temps :" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 45 "plot3d(
\{sin(x*y),x+2*y\},x=-Pi..Pi,y=-Pi..Pi);" }{TEXT -1 0 "" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 281 "c1:=[cos(x)-2*cos(0.4*y),sin(x)-2*
sin(0.4*y),y]:\nc2:=[cos(x)+2*cos(0.4*y),sin(x)+2*sin(0.4*y),y]:\nc3:=
[cos(x)+2*sin(0.4*y),sin(x)-2*cos(0.4*y),y]:\nc4:=[cos(x)-2*sin(0.4*y)
,sin(x)+2*cos(0.4*y),y]:\nplot3d( \{c1,c2,c3,c4\},\n        x=0..2*Pi,
 y=0..10,\n        grid=[25,15],style=PATCH);" }{TEXT -1 0 "" }}}
{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 26 "En
 coordon\351es spheriques :" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 
156 "sphereplot(1,\n           theta=0..2*Pi, phi=0..Pi,\n           s
caling=constrained,\n           title=\"The Sphere\",\n           titl
efont=[HELVETICA,BOLD,24]);" }{TEXT -1 0 "" }}}{EXCHG {PARA 0 "" 0 "" 
{TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 130 "Par defaut, maple n'affi
che pas els axes. Mais si on lui precise d'afficher les axes, on peut \+
meme donenr des noms \340 ces derniers." }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 109 "plot3d(sin(x*y),\n       x=-1..1,y=-1..1,\n       la
bels=[\"longueur\",\"largeur\",\"hauteur\"],\n       axes=FRAMED);" }}
{PARA 13 "" 1 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 57 "
Quelques exemples de graphes en coordon\351es cylindriques :" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 42 "cylinderplot(theta,theta=0..
4*Pi,z=-1..1);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 37 "cylinderp
lot(z,theta=0..2*Pi,z=0..1);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" 
}}{PARA 0 "" 0 "" {TEXT -1 53 "Et une courbe parametr\351e en coordon
\351es cylindriques :" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 47 "cy
linderplot([s*t,s,cos(t^2)],s=0..Pi,t=-2..2);" }}}{EXCHG {PARA 0 "" 0 
"" {TEXT 350 10 "Exercice 3" }}{PARA 14 "" 0 "" {TEXT -1 35 "a) Tracer
 la fonction suivante :   " }{XPPEDIT 18 0 "f(x,y) = exp(-x^2)+exp(-4*
y^2);" "6#/-%\"fG6$%\"xG%\"yG,&-%$expG6#,$*$)F'\"\"#\"\"\"!\"\"F1-F+6#
,$*&\"\"%F1*$)F(\"\"#F1F1F2F1" }}{PARA 14 "" 0 "" {TEXT -1 33 "b) Trac
er la fonction suivante : " }{XPPEDIT 18 0 "f(x,y) = sin(sqrt(x^2+y^2)
);" "6#/-%\"fG6$%\"xG%\"yG-%$sinG6#-%%sqrtG6#,&*$F'\"\"#\"\"\"*$F(\"\"
#F2" }}{PARA 14 "" 0 "" {TEXT -1 33 "c) Tracer la fonction suivante : \+
" }{XPPEDIT 18 0 "f(x,y) = x^2*y^2*exp(-x^2-y^2)/(x^2+y^2);" "6#/-%\"f
G6$%\"xG%\"yG**F'\"\"#F(\"\"#-%$expG6#,&*$)%\"xG\"\"#\"\"\"!\"\"*$)%\"
yG\"\"#F4F5\"\"\",&*$F'\"\"#\"\"\"*$F(\"\"#F>!\"\"" }{TEXT -1 1 " " }}
{PARA 14 "" 0 "" {TEXT -1 31 "d) Tracer la fonction suivante " }
{XPPEDIT 18 0 "f(x,y) = -x*y*exp(-1*x^2/2-1*y^2/2);" "6#/-%\"fG6$%\"xG
%\"yG,$*(F'\"\"\"F(F+-%$expG6#,&*&*&\"\"\"F+)F'\"\"#F+F+\"\"#!\"\"F6*&
*&\"\"\"F+)F(\"\"#F+F+\"\"#F6F6F+F6" }{TEXT -1 24 " autour de l'origin
e.   " }}}{EXCHG {PARA 4 "" 0 "" {TEXT -1 0 "" }}{PARA 4 "" 0 "" 
{TEXT -1 13 "4. Animation." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{EXCHG 
{PARA 0 "" 0 "" {TEXT -1 78 "Une suite de graphes en 2 ou 3 dimensions
 peut etre anim\351 grace \340 la commande " }{TEXT 345 7 "animate" }
{TEXT -1 35 " qui a la syntaxe suivante en 2-d :" }}{PARA 277 "" 0 "" 
{TEXT -1 0 "" }{TEXT 279 7 "animate" }{TEXT -1 23 "(f(x,t),x=a..b, t=c
..d)" }}{PARA 0 "" 0 "" {TEXT -1 3 "O\371 " }{TEXT 346 1 "t" }{TEXT 
-1 21 " represente le temps." }}{PARA 0 "" 0 "" {TEXT -1 3 "   " }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 35 "animate(sin(x*t),x=-10..10,t
=1..2);" }{TEXT -1 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}
{PARA 0 "" 0 "" {TEXT -1 42 "Une animation avec une courbe parametr
\351e :" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 44 "animate([a*cos(u
),sin(u),u=0..2*Pi],a=0..2);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" 
}}{PARA 0 "" 0 "" {TEXT -1 25 "Et une animation en 3-d :" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 56 "animate3d(cos(t*x)*sin(t*y),x=-Pi..
Pi,y=-Pi..Pi,t=1..2);" }}}}{MARK "0 0 0" 0 }{VIEWOPTS 1 1 0 1 1 1803 }