<Text-field layout="Heading 1" style="Heading 1"> Rappel: Op\351rateur D et macro-commande diff</Text-field>

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 des d\351riv\351es partielles et des int\351grales doubles

\251 Pierre Lantagne (juin 2001)

Coll\350ge de Maisonneuve

plantag@edu.cmaisonneuve.qc.ca

http://math.cmaisonneuve.qc.ca/plantagne

restart;

<Text-field layout="Heading 1" style="Heading 1"> Rappel: Op\351rateur D et macro-commande diff</Text-field>

Rappelons les deux syntaxes Maple pour le calcul de la d\351riv\351e:

- calcul de la d\351riv\351e avec l'op\351rateur D

- calcul de la d\351riv\351e avec la macro-commande diff

<Text-field layout="Heading 2" style="Heading 2"> L'op\351rateur de d\351rivation D</Text-field>

Soit la fonction f d\351finie par NiMvLSUiZkc2IyUieEcqJkYnIiIjLSUkZXhwRzYjKiRGJ0YpIiIi.

f:= x->x^2*exp(x^2);

Obtenons la fonction d\351riv\351e premi\350re:

D(f);

Et donc, la formule de la fonction d\351riv\351e premi\350re

D(f)(x);

Simplifions ce r\351sultat en factorisant NiMqKCIiIyIiIiUieEdGJS0lJGV4cEc2IyokRiZGJEYl.

factor(D(f)(x));

La fonction d\351riv\351e successive d'ordre n, (D@@n)(f), est obtenu avec l'op\351rateur de composition it\351r\351e @@.

Par exemple, obtenons la formule d\351riv\351e successive d'ordre 3 de la fonction f.

(D@@3)(f)(x,y);

Simplifions ce r\351sultat en factorisant NiMqKCIiJSIiIiUieEdGJS0lJGV4cEc2IyokRiYiIiNGJQ==.

factor(%);

<Text-field layout="Heading 2" style="Heading 2"> La macro-commande de d\351rivation diff</Text-field>

Contrairement \340 l'op\351rateur D, la macro-commande diff est utilis\351e pour d\351river une expression. Le r\351sultat est donc une formule d\351riv\351e et non pas une fonction d\351riv\351e.

Trouver y' si NiMvJSJ5RywmKiQlInhHIiIkIiIiKiYiIiZGKS0lJXNxcnRHNiMtJSRzaW5HNiNGJ0YpISIi.

y:= x^3-5*sqrt(sin(x));

`y'`:= diff(y,x);

On peut, bien s\373r, employer diff pour d\351river la formule f(x) d'une fonction f car, comme on le sait, f(x) d\351signe la formule de la fonction f. Soit alors la fonction f d\351finie par NiMvLSUiZkc2IyUieEcsJi0qJCUkc2VjRyIiI0YmIiIiLSUlc3FydEc2IywmRi1GLSokRidGLCEiIkYt.

f:=x-> (sec^2)(x)+sqrt(1-x^2);

`y'`:= diff(f(x),x);

Avec la macro-commande diff, la d\351riv\351e successive d'ordre n est obtenue en r\351p\351tant n fois la variable x.

Par exemple, calculer la d\351riv\351e successive d'ordre 3 y''' si NiMvJSJ5RyomLCYqJCUieEciIiQiIiIiIiMhIiJGKiwmRipGKiokRihGK0YsRiw=.

y:= (x^3-2)/(1-x^2);

`y'''`:= diff(y,x,x,x);

Utilisons plut\364t l'op\351rateur de cr\351ation de s\351quences $ pour r\351p\351ter la variable le nombre de fois voulu.

`y'''`:= diff(y,x$3);

Simplifions en normalisant cette addition de fractions.

`y'''`:= normal(diff(y,x$3));

Rendons de nouveau la variable y libre.

y:='y':

<Text-field layout="Heading 1" style="Heading 1"> Calcul des d\351riv\351es partielles de fonctions explicites</Text-field>

<Text-field layout="Heading 2" style="Heading 2"> Avec l'op\351rateur de d\351rivation D</Text-field>

Soit la fonction f d\351finie par NiMvLSUiZkc2JCUieEclInlHLSUjbG5HNiMsJi0lJHNpbkc2IyokRiciIiMiIiIqJkYxRjIqJEYoRjFGMkYy.

f:=(x,y)-> ln(sin(x^2)+2*y^2);

La fonction d\351riv\351e partielle par rapport \340 x, NiMtJSVEaWZmRzYkJSJmRyUieEc=, est obtenue ainsi:

D[1](f);

Et donc, la formule de la d\351riv\351e partielle par rapport \340 x de la fonction f:

D[1](f)(x,y);

On a pr\351cis\351, \340 l'op\351rateur D, le nombre 1 entre crochet car, au moment de la cr\351ation de la fonction f, la premi\350re variable pr\351cis\351e a \351t\351 la variable x. Alors, la formule de la d\351riv\351e partielle par rapport \340 y, NiMtJSVEaWZmRzYkJSJmRyUieUc=, sera

D[2](f)(x,y);

Pour le calcul des d\351riv\351es mixtes, il suffit de pr\351ciser entre crochets l'ordre des variables de la d\351rivation.

Par exemple, trouver NiMtJSVEaWZmRzYlJSJmRyUieEclInlH

D[2,1](f)(x,y);

En fait, D[i,j](f) est \351quivalent \340 D[i](D[j](f)).

Alors, le calcul de NiMtJSVEaWZmRzYlLSUiZkc2JCUieEclInlHRipGKQ== est pos\351 comme suit:

D[1,2](f)(x,y);

Pourquoi a-t-on NiMvLSUlRGlmZkc2JS0lImZHNiQlInhHJSJ5R0YqRistRiU2JUYnRitGKg== ? En est-il toujours ainsi ?

Pour calculer la d\351riv\351e partielle (par rapport \340 x) successive d'ordre 3, NiMtJSVEaWZmRzYkLSUiZkc2JCUieEclInlHLSUiJEc2JEYpIiIk, on devra r\351p\351ter trois fois le chiffre 1:

D[1,1,1](f)(x,y);

On peut, bien s\373r, employer l'op\351rateur de cr\351ation de s\351quence $.

D[1$3](f)(x,y);

Voici un autre exemple de calcul.

Trouver la d\351riv\351e partielle d'ordre 5 NiMtJSVEaWZmRzYmLSUiZkc2JCUieEclInlHRiktJSIkRzYkRioiIiMtRiw2JEYpRi4=.

D[1$2,2$2,1](f)(x,y);

<Text-field layout="Heading 2" style="Heading 2">Avec la macro-commande de d\351rivation diff</Text-field>

Soit \340 calculer NiMtJSVEaWZmRzYkKiYtJSVzcXJ0RzYjLCYqJCUieEciIiMiIiIqJCUieUdGLSEiIkYuLCZGLEYuRjBGMUYxRiw=.

Afin de documenter plus clairement les r\351sultats, utilisons la forme inactive de diff, soit Diff et formulons les requ\352tes sous la forme d'une \351quation

Forme inerte = Forme active

Diff(sqrt(x^2-y^2)/(x-y),x)=diff(sqrt(x^2-y^2)/(x-y),x);

Simplifions ce r\351sultat en normalisant la soustraction des deux fractions.

normal(%);

Soit \340 calculer NiMtJSVEaWZmRzYlKiYtJSVzcXJ0RzYjLCYqJCUieEciIiMiIiIqJCUieUdGLSEiIkYuLCZGLEYuRjBGMUYxRixGMA==.

Diff(sqrt(x^2-y^2)/(x-y),x,y)=diff(sqrt(x^2-y^2)/(x-y),x,y);

Simplifions.

normal(%);

En fait, diff(Formule, x, y) est \351quivalent \340 diff(diff (Formule, x), y).

Soit \340 calculer NiMtJSVEaWZmRzYlKiYtJSVzcXJ0RzYjLCYqJCUieEciIiMiIiIqJCUieUdGLSEiIkYuLCZGLEYuRjBGMUYxRiwtJSIkRzYkRjBGLQ==

Diff(sqrt(x^2-y^2)/(x-y),x,y$2)=diff(sqrt(x^2-y^2)/(x-y),x,y$2);

Simplifions.

normal(%);

<Text-field layout="Heading 1" style="Heading 1"> Calcul des d\351riv\351es partielles de fonctions implicites</Text-field>

Soit NiMvJSJ6Ry0lImZHNiQlInhHJSJ5Rw== o\371 z est d\351finie implicitement par la relation NiMvLCYqJiUieEciIiIqJCUieUciIiNGJ0YnKihGJkYnRilGJyUiekdGJ0YnLCZGKkYnKiRGLCIiJCEiIg==. Pour trouver NiMtJSVkaWZmRzYkJSJ6RyUieEc=, il faut d\351river chaque membre de cette \351quation, par rapport \340 x. Dans ce cas, il faut signifier \340 l'\351valuateur que z est d\351finie implicitement en termes de x et y. Pour signifier \340 l'\351valuateur que z est une variable d\351pendante de x et de y, il faut utiliser la syntaxe fonctionnelle NiMtJSJ6RzYkJSJ4RyUieUc= au lieu de taper seulement z.

Cr\351ons l'\351quation \340 d\351river.

Eq:= x*y^2+x*y*z(x,y) = 2-z(x,y)^3;

D\351rivons ensuite chaque membre de cette \351quation par rapport \340 x.

Eq_derivee:=diff(Eq,x);

Reste donc \340 isoler NiMtJSVkaWZmRzYkLSUiekc2JCUieEclInlHRik=. R\351solvons donc Eq_derivee par rapport \340 NiMtJSVkaWZmRzYkLSUiekc2JCUieEclInlHRik=.

solve(Eq_derivee,{diff(z(x,y),x)});

On aurait pu \351galement employer la macro-commande isolate. Depuis Maple 6, cette macro-commande de la biblioth\350que de base est auto-chargeable mais, avec Maple V, nous devons la rendre disponible en ex\351cutant au pr\351alable un readlib sur cette macro-commande.

### WARNING: persistent store makes one-argument readlib obsolete readlib(isolate);

isolate(Eq_derivee,diff(z(x,y),x));

Simplifions en factorisant ce r\351sultat.

factor(%);

Pour obtenir plus directement la formule de NiMtJSVkaWZmRzYkJSJ6RyUieEc=, il est de loin pr\351f\351rable d'employer la macro-commande implicitdiff.

Reformulons Eq en terme de z et non pas en terme de NiMtJSJ6RzYkJSJ4RyUieUc=.

Eq:= x*y^2+x*y*z = 2-z^3;

Le second argument de la macro-commande implicitdiff doit obligatoirement pr\351ciser lesquelles des variables en causes sont les variables d\351pendantes. On emploiera pour cela la syntaxe fonctionnelle.

Diff(z,x)=implicitdiff(Eq,z(x,y),x);

Le r\351sultat pr\351c\351dent est plus conforme \340 la notation habituelle utilis\351e en classe.

Comme dernier exemple, trouvons NiMtJSVkaWZmRzYkJSJ6Ry0lIiRHNiQlInhHIiIj.

Diff(z,x$2)=implicitdiff(Eq,z(x,y),x$2);

Essayons de simplifier ce r\351sulat en factorisant.

factor(%);

<Text-field layout="Heading 1" style="Heading 1"> Rappel: Calcul d'une int\351grale simple</Text-field>

La macro-commande int permet le calcul d'une int\351grale ind\351finie ou le calcul d'une int\351grale d\351finie.

Par exemple, soit le calcul de l'int\351grale ind\351finie NiMtJSRpbnRHNiQqJiUieEciIiItJSRzaW5HNiNGJ0YoRic=.

Ici \351galement, afin de documenter plus clairement les r\351sulats, utilisons la forme inactive de int, soit Int et formulons les requ\352tes sous la forme d'une \351quation

Forme inerte = Forme active

Int(x*sin(x),x)=int(x*sin(x),x)+C;

Rappel: La constante d'int\351gration doit \352tre ajouter manuellement.

Pour le calcul d'une int\351grale d\351finie, il suffit de remplacer la variable d'int\351gration par un intervalle de la variable d'int\351gration.

\311valuer NiMtJSRpbnRHNiQtJSRzaW5HNiMlInhHL0YpOyIiISomIiIjIiIiJSNQaUdGLw==.

Int(sin(x), x=0..2*Pi)=int(sin(x), x=0..2*Pi);

Un dernier exemple. \311valuer NiMtJSRpbnRHNiQqJiIiIkYnKiQlInhHIiIjISIiL0YpO0YnJSlpbmZpbml0eUc=.

Int(1/x^2,x = 1 .. infinity)=int(1/x^2,x = 1 .. infinity);

<Text-field layout="Heading 1" style="Heading 1"> Calcul des int\351grales doubles</Text-field>

Le calcul d'une int\351grale double est, comme vous le savez, un calcul successif de deux int\351grales simples.

Soit le calcul de NiMtJSRpbnRHNiQtRiQ2JComIiIiRikqJCwmJSJ4R0YpJSJ5R0YpIiIjISIiL0YtO0YpRi4vRiw7IiIkIiIl.

Une mani\350re d'effectuer le calcul demand\351 est de calculer successivement les deux int\351grales simples en commen\347ant par l'int\351grale imbriqu\351e. Il faut donc int\351grer d'abord par rapport \340 la variable y.

Posons le calcul demand\351.

Calcul:=Int(Int(1/((x+y)^2),y = 1 .. 2),x = 3 .. 4);

Int\351grons d'abord par rapport \340 y. Posons ce calcul.

yintegrale:=Int(1/(x+y)^2,y=1..2);

Imbriquons ensuite l'\351valuation de yintegrale dans l'int\351gration par rapport \340 x.

Int(value(yintegrale),x=3..4);

Reste donc \340 \351valuer la seconde int\351grale par rapport \340 x.

Calcul=value(%);

Une autre fa\347on de faire est d'imbriquer imm\351diatement ces deux int\351grales simples. Cette mani\350re s'av\350re plus directe et donc plus claire.

Calcul=int(int(1/(x+y)^2,y=1..2),x=3..4);

Simplifions l'\351criture logarithmique de ce r\351sultat \340 l'aide des propri\351t\351s des logarithmes.

combine(%,ln);

Dans une int\351grale double, les bornes d'int\351gration de l'int\351grale imbriqu\351e ne sont pas n\351cessairement des constantes.

Calculer NiMtJSRpbnRHNiQtRiQ2JComJSJyRyIiIi0lJXNxcnRHNiMsJiIiKkYqKiRGKSIiIyEiIkYqL0YpOyIiISomIiIkRiotJSRzaW5HNiMlJnRoZXRhR0YqL0Y7O0Y1JSNQaUc=.

Posons le calcul demand\351.

Calcul:=Int(Int(r*sqrt(9-r^2),r=0..3*sin(theta)),theta=0..Pi);

\311valuons.

Calcul=int(int(r*sqrt(9-r^2),r=0..3*sin(theta)),theta=0..Pi);

Voici un autre exemple de calcul d'une int\351grale double. Calculer NiMtJSRpbnRHNiQtRiQ2JCUickcvJSZ0aGV0YUc7LSUnYXJjY29zRzYjKiYiIiMiIiJGKCEiIi0lJ2FyY3NpbkdGLi9GKDtGMComRjBGMS0lJXNxcnRHNiNGMEYx.

Posons le calcul demand\351.

Calcul:=Int(Int(r,theta=arccos(2/r)..arcsin(2/r)),r=2..2*sqrt(2));

\311valuons.

Calcul=int(int(r,theta=arccos(2/r)..arcsin(2/r)),r=2..2*sqrt(2));

Le r\351sultat obtenu montre que, cette fois-ci, Maple n'a pu compl\351ter automatiquement l'\351valuation demand\351e. Utilisons donc la macro-commande expand afin que Maple puisse, sur demande, effectuer ce dernier calcul en d\351veloppant l'int\351grale d'une somme en la somme de deux int\351grales.

expand(%);

Remarquez que ce sont les deux membres qui ont \351t\351 d\351velopp\351s mais que le membre de gauche, quant \340 lui, l'a \351t\351 dans sa forme inerte.

Les exemples pr\351c\351dents ont montr\351 comment employer Maple dans des calculs formels. On peut, bien s\373r, commander une approximation num\351rique plut\364t qu'une \351valuation symbolique (exacte) lorsqu'on \351value des int\351grales d\351finies. Dans ce cas, il faut employer la macro-commande evalf.

Obtenez une approximation de NiMtJSRpbnRHNiQtRiQ2JCUickcvRig7IiIiKigiIztGKyUmdGhldGFHRislI1BpRyEiIi9GLjsqJkYvRitGLUYwKiZGL0YrIiIpRjA=.

Posons le calcul demand\351.

Calcul:=Int(Int(r,r=1..16*theta/Pi),theta=Pi/16..Pi/8);

Obtenons une approximation avec des calculs impliquant 20 chiffres d\351cimaux.

Calcul=evalf(Calcul,20);

Comme dernier exemple, reprenons le calcul de la page 89 du cahier de notes \253 Int\351grales doubles \273: NiMsJi0lJGludEc2JC1GJTYkKiQlInJHIiIjLyUmdGhldGFHOyIiISomJSNQaUciIiIiIiUhIiIvRio7Ri9GK0YyLUYlNiQtRiU2JEYpL0YtOy0lJ2FyY2Nvc0c2IyomRitGMkYqRjRGMC9GKjtGKyomRitGMi0lJXNxcnRHNiNGK0YyRjI=.

Dans le cahier de notes, le d\351veloppement de ce calcul est fait sur environ trois pages et applique les techniques d'int\351gration par parties (2 fois) et la substitution trigonom\351trique. Voyons le r\351sultat que donnera Maple.

Posons le calcul demand\351.

Calcul:=Int(Int(r^2,theta = 0 .. Pi/4),r = 0 .. 2)+Int(Int(r^2,theta = arccos(2/r) .. Pi/4),r = 2 .. 2*sqrt(2));

\311valuons.

Calcul=int(int(r^2,theta = 0 .. Pi/4),r = 0 .. 2)+int(int(r^2,theta = arccos(2/r) .. Pi/4),r = 2 .. 2*sqrt(2));

Aidons Maple \340 compl\351ter le calcul en employant la macro-commande expand.

``=expand(rhs(%));

Maple a formul\351 symboliquement la r\351ponse \340 l'aide de la partie r\351elle d'une arctangente hyperbolique. Exprimons cette arctangente hyperbolique avec une \351criture logarithmique.

``=convert(rhs(%),ln);

La rapidit\351 du r\351sultat est remarquable mais il a \351t\351 n\351cessaire de convertir le r\351sultat pr\351c\351dent en des termes plus communs pour notre niveau d'enseignement.

Pour terminer cette feuille Maple, montrons que le r\351sultat NiMsKCooIiIlIiIiIiIkISIiLSUlc3FydEc2IyIiI0YmRiYqKEYsRiZGJ0YoLSUjbG5HNiMsJkYpRiZGJkYmRiZGJiooRixGJkYnRigtRi82IywmRilGJkYmRihGJkYo qu'a donn\351 l'\351valuateur est \351quivalent \340 celui du cahier de notes NiMqKCIiJSIiIiwmLSUlc3FydEc2IyIiI0YlLSUjbG5HNiMsJkYnRiVGJUYlRiVGJSIiJCEiIg==.

Reponse_cahier:=4*(sqrt(2)+ln(sqrt(2)+1))/3;

Il suffit donc montrer que NiMvKigiIiUiIiItJSNsbkc2IywmLSUlc3FydEc2IyIiI0YmRiZGJkYmIiIkISIiLCYqKEYuRiZGJ0YmRi9GMEYmKihGLkYmLUYoNiMsJkYrRiZGJkYwRiZGL0YwRjA=

Resultat_1:=2/3*ln(sqrt(2)+1)-2/3*ln(sqrt(2)-1);

### WARNING: note that `I` is no longer of type `radical` Resultat_2:=combine(Resultat_1,[ln,radical]);

Rationalisons l'argument de la fonction ln.

Arg_Rationalise:=rationalize(op(1,Resultat_2));

Substituons cette rationalisation \340 l'argument de la fonction ln.

Resultat_3:=subs(op(1,Resultat_2)=Arg_Rationalise,Resultat_2);

Resultat_1=expand(Resultat_3);

Ce qu'il fallait d\351montrer.

On aurait pu \351galement comparer num\351riquement le calcul demand\351 NiMsJi0lJEludEc2JC1GJTYkKiQlInJHIiIjLyUmdGhldGFHOyIiISooIiIiRjEiIiUhIiIlI1BpR0YxL0YqO0YvRitGMS1GJTYkLUYlNiRGKS9GLTstJSdhcmNjb3NHNiMqKEYrRjFGMUYxRipGM0YwL0YqO0YrKiZGK0YxLSUlc3FydEc2I0YrRjFGMQ== et la r\351ponse du cahier NiMqKCIiJSIiIiwmLSUlc3FydEc2IyIiI0YlLSUjbG5HNiMsJkYnRiVGJUYlRiVGJSIiJCEiIg==.

evalf(Calcul,20);

evalf(Reponse_cahier,20);