<Text-field style="Heading 1" layout="Heading 1">1. Calcul formel et num\303\251rique</Text-field>

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D\303\251couverte des premi\303\250res fonctionnalit\303\251s de Maple

Maple est un outil pour faire des calculs scientifiques. Ces calculs peuvent \303\252tre men\303\251s d\342\200\231un point de vue symbolique, num\303\251rique, graphique.

Maple est aussi un langage de programmation. Maple peut r\303\251aliser formellement tous les calculs pour lesquels nous avons un algorithme : d\303\251rivation, int\303\251gration de certaines fonctions, r\303\251solution de syst\303\250mes d\342\200\231\303\251quations lin\303\251aires, r\303\251solution de certaines \303\251quations diff\303\251rentielles...

Num\303\251riquement, on peut \303\251valuer des int\303\251grales, des sommes... Maple poss\303\250de \303\251galement un certain nombre de fonctions graphiques, permettant d\342\200\231obtenir des repr\303\251sentations de courbes en 2D et 3D, ainsi que des surfaces. Maple est livr\303\251 avec un syst\303\250me d\342\200\231aide tr\303\250s complet. Il est vital de savoir l'utiliser. On acc\303\250de \303\240 l\342\200\231aide sur la commande \302\253 X \302\273 en tapant \342\200\234?X\342\200\235 ou en utilisant la touche F2 lorsque le curseur est sur le nom de la fonction. En pratique, on regardera toujours les exemples fournis dans l\342\200\231aide.

Et si on commen\303\247ait par l'aide ?

LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbW9HRiQ2LVEiP0YnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGNC8lKXN0cmV0Y2h5R0Y0LyUqc3ltbWV0cmljR0Y0LyUobGFyZ2VvcEdGNC8lLm1vdmFibGVsaW1pdHNHRjQvJSdhY2NlbnRHRjQvJSdsc3BhY2VHUSwwLjExMTExMTFlbUYnLyUncnNwYWNlR0ZDLyUrZXhlY3V0YWJsZUdGNEYv

On peut \303\251crire plusieurs commandes sur une seule ligne pourvu qu'elles soient s\303\251par\303\251es par une virgule, un point-virgule ou par deux points :

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LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=

Un petit tour de Maple

<Text-field style="Heading 1" layout="Heading 1">1. Calcul formel et num\303\251rique</Text-field>

Un petit calcul alg\303\251brique formel puis num\303\251rique :

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

Le symbole % est un raccourci de la derni\303\250re commande ex\303\251cut\303\251e.

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On factorise et on teste la primalit\303\251 d'un entierLUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbW9HRiQ2L1EiOkYnLyUnZmFtaWx5R1EtVHJlYnVjaGV0fk1TRicvJStleGVjdXRhYmxlR1EmZmFsc2VGJy8lLG1hdGh2YXJpYW50R1Enbm9ybWFsRicvJSZmZW5jZUdGNC8lKnNlcGFyYXRvckdGNC8lKXN0cmV0Y2h5R0Y0LyUqc3ltbWV0cmljR0Y0LyUobGFyZ2VvcEdGNC8lLm1vdmFibGVsaW1pdHNHRjQvJSdhY2NlbnRHRjQvJSdsc3BhY2VHUSwwLjI3Nzc3NzhlbUYnLyUncnNwYWNlR0ZIRi9GMi8lMGZvbnRfc3R5bGVfbmFtZUdRKTJEfklucHV0RidGNQ==

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

En cas d'erreurs, Maple nous pr\303\251vient parfois :

LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2I1EhRictRiM2Jy1JJm1mcmFjR0YkNigtRiM2JC1JI21uR0YkNiRRIjFGJy8lLG1hdGh2YXJpYW50R1Enbm9ybWFsRidGOi1GIzYmRistRiM2Ji1GLDYlUSRjb3NGJy8lJ2l0YWxpY0dRJmZhbHNlRidGOi1JI21vR0YkNi1RMCZBcHBseUZ1bmN0aW9uO0YnRjovJSZmZW5jZUdGRi8lKnNlcGFyYXRvckdGRi8lKXN0cmV0Y2h5R0ZGLyUqc3ltbWV0cmljR0ZGLyUobGFyZ2VvcEdGRi8lLm1vdmFibGVsaW1pdHNHRkYvJSdhY2NlbnRHRkYvJSdsc3BhY2VHUSYwLjBlbUYnLyUncnNwYWNlR0Zlbi1JKG1mZW5jZWRHRiQ2JC1GIzYkLUYyNigtRiM2JC1GLDYlUSUmcGk7RidGREY6RjotRiM2JC1GNzYkUSIyRidGOkY6LyUubGluZXRoaWNrbmVzc0dGOS8lK2Rlbm9tYWxpZ25HUSdjZW50ZXJGJy8lKW51bWFsaWduR0ZdcC8lKWJldmVsbGVkR0ZGRjpGOkY6RitGOkZpb0ZbcEZecEZgcC1GSDYtUSI7RidGOkZLL0ZOUSV0cnVlRidGT0ZRRlNGVUZXRlkvRmduUSwwLjI3Nzc3NzhlbUYnLUYsNiVRJHRhbkYnRkRGOkZobkY6RisvJStleGVjdXRhYmxlR0ZGRjo=

On calcule toute une s\303\251rie de coefficients binomiaux :

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

On affecte une valeur \303\240 de nouvelles variables :

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

On peut ensuite r\303\251utiliser ces variables dans d'autres calculs. On d\303\251veloppe LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JlEic0YnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0Yn et on factorise LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JlEidEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0Yn :

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

On \303\251value les 500 premi\303\250res d\303\251cimales du nombre LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JlElJnBpO0YnLyUnaXRhbGljR1EmZmFsc2VGJy8lK2V4ZWN1dGFibGVHRi4vJSxtYXRodmFyaWFudEdRJ25vcm1hbEYn (Pi) :

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

Aucun int\303\251r\303\252t !

Quelques fonctionalit\303\251s sur les complexes :

LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYqLUklbXN1cEdGJDYlLUkobWZlbmNlZEdGJDYkLUYjNictSSNtbkdGJDYkUSIxRicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYnLUkjbW9HRiQ2LVEiK0YnRjcvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRkAvJSlzdHJldGNoeUdGQC8lKnN5bW1ldHJpY0dGQC8lKGxhcmdlb3BHRkAvJS5tb3ZhYmxlbGltaXRzR0ZALyUnYWNjZW50R0ZALyUnbHNwYWNlR1EsMC4yMjIyMjIyZW1GJy8lJ3JzcGFjZUdGTy1JI21pR0YkNiVRIklGJy8lJ2l0YWxpY0dRJXRydWVGJy9GOFEnaXRhbGljRicvJStleGVjdXRhYmxlR0ZARjdGNy1GIzYkLUY0NiRRJDEwNUYnRjdGNy8lMXN1cGVyc2NyaXB0c2hpZnRHUSIwRictRjs2LVEiO0YnRjdGPi9GQkZYRkNGRUZHRklGSy9GTlEmMC4wZW1GJy9GUVEsMC4yNzc3Nzc4ZW1GJy1GUzYlUSZwb2xhckYnL0ZXRkBGNy1GLzYkLUYjNiUtRlM2JVEiJUYnRlZGWUZlbkY3RjdGX28tRlM2I1EhRidGZW5GNw==

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

On calcule maintenant des sommes de rationnels :

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

LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYzLUkjbWlHRiQ2JVEkc3VtRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkobWZlbmNlZEdGJDYkLUYjNiotSSZtZnJhY0dGJDYoLUYjNiQtSSNtbkdGJDYkUSIxRicvRjNRJ25vcm1hbEYnRkMtRiM2JS1GLDYlUSJrRidGL0YyLUkjbW9HRiQ2LVEiIUYnRkMvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRlAvJSlzdHJldGNoeUdGUC8lKnN5bW1ldHJpY0dGUC8lKGxhcmdlb3BHRlAvJS5tb3ZhYmxlbGltaXRzR0ZQLyUnYWNjZW50R0ZQLyUnbHNwYWNlR1EsMC4xMTExMTExZW1GJy8lJ3JzcGFjZUdGaW5GQy8lLmxpbmV0aGlja25lc3NHRkIvJStkZW5vbWFsaWduR1EnY2VudGVyRicvJSludW1hbGlnbkdGYG8vJSliZXZlbGxlZEdGUC1GSzYtUSIsRidGQ0ZOL0ZSRjFGU0ZVRldGWUZlbi9GaG5RJjAuMGVtRicvRltvUSwwLjMzMzMzMzNlbUYnRkctRks2LVEiPUYnRkNGTkZRRlNGVUZXRllGZW4vRmhuUSwwLjI3Nzc3NzhlbUYnL0Zbb0ZhcC1GQDYkUSIwRidGQy1GSzYtUSMuLkYnRkNGTkZRRlNGVUZXRllGZW4vRmhuUSwwLjIyMjIyMjJlbUYnL0Zbb0Zqby1GQDYkUSMzMEYnRkNGQ0ZDLUZLNi1RIjtGJ0ZDRk5GaG9GU0ZVRldGWUZlbkZpb0ZicC1GSzYtUSJ+RidGQ0ZORlFGU0ZVRldGWUZlbkZpb0ZbcS1GSzYtUSInRidGQ0ZORlFGU0ZVRldGWUZlbkZnbkZbcS1GLDYlUSsmIzIzMztjYXJ0RidGL0YyRmJxLUYsNiVRJWF2ZWNGJ0YvRjJGYnEtRiw2JVEiZUYnRi9GMkZlcUZdcC1GLDYlUSZldmFsZkYnRi9GMi1GNjYkLUYjNictRiw2JVEiJUYnRi9GMi1GIzYmLUZLNi1RKCZtaW51cztGJ0ZDRk5GUUZTRlVGV0ZZRmVuRmlwL0Zbb0ZqcC1GLDYlUSRleHBGJy9GMEZQRkMtRjY2JEY9RkNGQ0Zlby1GQDYkUSM0MEYnRkNGQ0ZDLUYsNiNRIUYnLyUrZXhlY3V0YWJsZUdGUEZD

Observez la diff\303\251rence (commande inerte et commande ex\303\251cutive)...

Quelques sommes classiques :

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

<Text-field style="Heading 1" layout="Heading 1">2. \303\211quations</Text-field>

On r\303\251sout formellement une \303\251quation :

On peut calculer des valeurs approch\303\251es des solutions :

LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2I1EhRictRiM2J0YrLUYjNictRiw2JVEmZXZhbGZGJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRictSSNtb0dGJDYtUTAmQXBwbHlGdW5jdGlvbjtGJy9GOlEnbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRkQvJSlzdHJldGNoeUdGRC8lKnN5bW1ldHJpY0dGRC8lKGxhcmdlb3BHRkQvJS5tb3ZhYmxlbGltaXRzR0ZELyUnYWNjZW50R0ZELyUnbHNwYWNlR1EmMC4wZW1GJy8lJ3JzcGFjZUdGUy1JKG1mZW5jZWRHRiQ2JC1GIzYlLUYsNiVRIiVGJ0Y2RjkvJStleGVjdXRhYmxlR0ZERkBGQEZobkZARitGaG5GQEYrRmhuRkA=

On r\303\251sout num\303\251riquement une \303\251quation :

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

... puis un syst\303\250me d\342\200\231\303\251quations :

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

On a affaire \303\240 une s\303\251quence d'expressions... R\303\251cup\303\251rons par exemple la deuxi\303\250me solution :

LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2JVEkc29sRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkobWZlbmNlZEdGJDYmLUYjNiUtSSNtbkdGJDYkUSIxRicvRjNRJ25vcm1hbEYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRidGPkY+LyUlb3BlbkdRIltGJy8lJmNsb3NlR1EiXUYnRkBGPg==

R\303\251cup\303\251rons enfin les valeurs du couple solution :

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

<Text-field style="Heading 1" layout="Heading 1">3. Expressions et fonctions</Text-field>

On d\303\251finit une expression LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYoLUkjbWlHRiQ2I1EhRictRiM2KEYrLUYjNiYtRiw2JlEiZkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnRjkvJTBmb250X3N0eWxlX25hbWVHUSkyRH5JbnB1dEYnL0Y9USdub3JtYWxGJ0YrRjlGP0ZCRitGOUY/RkI= de la variable LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYoLUkjbWlHRiQ2I1EhRictRiM2KEYrLUYjNihGKy1GIzYmLUYsNiZRInRGJy8lJ2l0YWxpY0dRJXRydWVGJy8lK2V4ZWN1dGFibGVHUSZmYWxzZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJ0Y7LyUwZm9udF9zdHlsZV9uYW1lR1EpMkR+SW5wdXRGJy9GP1Enbm9ybWFsRidGK0Y7RkFGREYrRjtGQUZERitGO0ZBRkQ= :

LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYsLUkjbWlHRiQ2JVEocmVzdGFydEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi1RIjtGJy9GM1Enbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRjEvJSlzdHJldGNoeUdGPS8lKnN5bW1ldHJpY0dGPS8lKGxhcmdlb3BHRj0vJS5tb3ZhYmxlbGltaXRzR0Y9LyUnYWNjZW50R0Y9LyUnbHNwYWNlR1EmMC4wZW1GJy8lJ3JzcGFjZUdRLDAuMjc3Nzc3OGVtRictRiw2JVEiZkYnRi9GMi1GNjYtUSomY29sb25lcTtGJ0Y5RjsvRj9GPUZARkJGREZGRkgvRktGT0ZNLUYsNiVRJHNpbkYnL0YwRj1GOS1JKG1mZW5jZWRHRiQ2JC1GIzYlLUYsNiVRInRGJ0YvRjIvJStleGVjdXRhYmxlR0Y9RjlGOS1GNjYtUSgmbWludXM7RidGOUY7RlZGQEZCRkRGRkZIL0ZLUSwwLjIyMjIyMjJlbUYnL0ZORmRvRltvRl5vRjk=

et une fonction de la variable LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYoLUkjbWlHRiQ2I1EhRictRiM2KEYrLUYjNihGKy1GIzYmLUYsNiZRInRGJy8lJ2l0YWxpY0dRJXRydWVGJy8lK2V4ZWN1dGFibGVHUSZmYWxzZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJ0Y7LyUwZm9udF9zdHlsZV9uYW1lR1EpMkR+SW5wdXRGJy9GP1Enbm9ybWFsRidGK0Y7RkFGREYrRjtGQUZERitGO0ZBRkQ= :

LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2I1EhRictRiM2J0YrLUYjNigtRiw2JVEiZ0YnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi1RIzo9RicvRjpRJ25vcm1hbEYnLyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR0ZELyUpc3RyZXRjaHlHRkQvJSpzeW1tZXRyaWNHRkQvJShsYXJnZW9wR0ZELyUubW92YWJsZWxpbWl0c0dGRC8lJ2FjY2VudEdGRC8lJ2xzcGFjZUdRLDAuMjc3Nzc3OGVtRicvJSdyc3BhY2VHRlMtRiM2KC1GLDYlUSJ0RidGNkY5LUY9Ni1RKCYjODU5NDtGJ0ZARkJGRUZHRklGS0ZNRk8vRlJRJjAuMGVtRicvRlVGaW4tRiM2KkYrLUYjNictRiw2JVEkY29zRicvRjdGREZALUY9Ni1RMCZBcHBseUZ1bmN0aW9uO0YnRkBGQkZFRkdGSUZLRk1GT0ZobkZqbi1JKG1mZW5jZWRHRiQ2JC1GIzYlRlgvJStleGVjdXRhYmxlR0ZERkBGQEZbcEZALUY9Ni1RKCZtaW51cztGJ0ZARkJGRUZHRklGS0ZNRk8vRlJRLDAuMjIyMjIyMmVtRicvRlVGYXAtSSNtbkdGJDYkUSIxRidGQC1GPTYtUSIrRidGQEZCRkVGR0ZJRktGTUZPRmBwRmJwLUkmbWZyYWNHRiQ2KC1GIzYlLUklbXN1cEdGJDYlRlgtRmRwNiRRIjJGJ0ZALyUxc3VwZXJzY3JpcHRzaGlmdEdRIjBGJ0ZbcEZALUYjNiVGYnFGW3BGQC8lLmxpbmV0aGlja25lc3NHRmZwLyUrZGVub21hbGlnbkdRJ2NlbnRlckYnLyUpbnVtYWxpZ25HRl5yLyUpYmV2ZWxsZWRHRkRGW3BGQEYrRltwRkBGK0ZbcEZARitGW3BGQEYrRltwRkA=

On peut calculer l'image d'un r\303\251el :

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LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2I1EhRictRiM2JS1GLDYlUSJmRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvRjhRJ25vcm1hbEYnLUkjbW9HRiQ2LVEiO0YnRj0vJSZmZW5jZUdGPC8lKnNlcGFyYXRvckdGNi8lKXN0cmV0Y2h5R0Y8LyUqc3ltbWV0cmljR0Y8LyUobGFyZ2VvcEdGPC8lLm1vdmFibGVsaW1pdHNHRjwvJSdhY2NlbnRHRjwvJSdsc3BhY2VHUSYwLjBlbUYnLyUncnNwYWNlR1EsMC4yNzc3Nzc4ZW1GJ0Y6Rj0=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

On a affect\303\251 \303\240 LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JlEidEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0Yn la valeur 1, mais pas 2.

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

On peut les d\303\251river :

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

On peut les d\303\251river plusieurs fois :

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

On calcule une primitive :

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

ou une int\303\251grale :

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

On peut aussi calculer des limites :

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

On peut calculer les d\303\251riv\303\251es partielles d'une fonction de 3 variables :

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

... puis son laplacien. Le laplacien est l'op\303\251rateur d\303\251fini par 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

Simplifions le r\303\251sultat :

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

LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2I1EhRictRiM2Ji1GLDYlUSlzaW1wbGlmeUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi1RMCZBcHBseUZ1bmN0aW9uO0YnL0Y4USdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGQi8lKXN0cmV0Y2h5R0ZCLyUqc3ltbWV0cmljR0ZCLyUobGFyZ2VvcEdGQi8lLm1vdmFibGVsaW1pdHNHRkIvJSdhY2NlbnRHRkIvJSdsc3BhY2VHUSYwLjBlbUYnLyUncnNwYWNlR0ZRLUkobWZlbmNlZEdGJDYkLUYjNiQtRiw2JVEiJUYnRjRGN0Y+Rj5GPkYrLyUrZXhlY3V0YWJsZUdGQkY+

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 est une fonction harmonique (laplacien nul)...

<Text-field style="Heading 1" layout="Heading 1">4. Graphiques</Text-field>

Maple peut tracer de jolies courbes et surfaces en tout genre...

On d\303\251finit une expression LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYoLUkjbWlHRiQ2I1EhRictRiM2KEYrLUYjNiYtRiw2JlEiZkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnRjkvJTBmb250X3N0eWxlX25hbWVHUSkyRH5JbnB1dEYnL0Y9USdub3JtYWxGJ0YrRjlGP0ZCRitGOUY/RkI= de la variable LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2JlEieEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnRjIvJTBmb250X3N0eWxlX25hbWVHUSkyRH5JbnB1dEYnL0Y2USdub3JtYWxGJw== que l'on fait tracer :

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

et une fonction LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JlEiZ0YnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnRjIvRjZRJ25vcm1hbEYn de la variable LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYoLUkjbWlHRiQ2I1EhRictRiM2Ji1GLDYmUSJ4RicvJSdpdGFsaWNHUSV0cnVlRicvJStleGVjdXRhYmxlR1EmZmFsc2VGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRidGNy8lMGZvbnRfc3R5bGVfbmFtZUdRKTJEfklucHV0RicvRjtRJ25vcm1hbEYnRitGN0Y9RkA= que l'on fait \303\251galement tracer :

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

On peut repr\303\251senter graphiquement les deux fonctions sur le m\303\252me graphique :

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

Ondes sinuso\303\257dales

On peut afficher plusieurs courbes d\303\251finies s\303\251par\303\251ment sur un m\303\252me dessin en chargeant la librairie "plots" .

Superposons deux ondes sinuso\303\257dales de m\303\252me fr\303\251quence en quadrature :

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

On a 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 avec 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

On peut tracer simultan\303\251ment un plus grand nombre de courbes (avec une s\303\251quence) :

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

On peut faire des animations en chargeant la librairie "plots" :

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

On a superpos\303\251 plusieurs ondes sinuso\303\257dales avec des fr\303\251quences multiples d'une fr\303\251quence initiale.

Fonctions puissances, polynomiales

Tra\303\247ons la famille des fonctions puissances :

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

Quelques fonctions polynomiales :

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

Un polyn\303\264me de degr\303\251 5 peut avoir 1,2,3,4 ou 5 racines r\303\251elles...

Du c\303\264t\303\251 des fonctions hyperboliques...

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Translations, homoth\303\251ties

D\303\251formations horizontales et verticales d'un graphe :

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Courbes param\303\251tr\303\251es

On peut tracer des courbes param\303\251tr\303\251es. Attention, il faut bien placer les crochets...

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On a l'impression de voir un cercle... En fait c'est une ellipse :

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Avec les fonctions hyperboliques, on peut tracer... des hyperboles !

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

Une courbe param\303\251tr\303\251e int\303\251ressante :

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

Version dynamique :

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

Il s'agit d'une courbe de Lissajous observ\303\251e sur un oscilloscope (\303\251tude conjointe de deux ondes sinuso\303\257dales).

Une autre courbe param\303\251tr\303\251e int\303\251ressante :

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

Porte coulissant le long de deux glissi\303\250res perpendiculaires (porte de garage) :

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Touche pas \303\240 mon coffre 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On lin\303\251arise 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et LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2JlEiWUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkobWZlbmNlZEdGJDYlLUYjNiYtRiw2JlEidEYnRi9GMkY1RjIvJTBmb250X3N0eWxlX25hbWVHUSkyRH5JbnB1dEYnL0Y2USdub3JtYWxGJ0YyRkNGMkZD :

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

Et l'on d\303\251couvre une hypocyclo\303\257de importante : l'astro\303\257de ! (trajectoire d'un point situ\303\251 sur un cercle roulant \303\240 l'int\303\251rieur d'un cercle quatre fois plus grand sans glissement)

LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzZKLUkjbWlHRiQ2JVEjeHhGJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRictSSNtb0dGJDYtUSomY29sb25lcTtGJy9GM1Enbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRj0vJSlzdHJldGNoeUdGPS8lKnN5bW1ldHJpY0dGPS8lKGxhcmdlb3BHRj0vJS5tb3ZhYmxlbGltaXRzR0Y9LyUnYWNjZW50R0Y9LyUnbHNwYWNlR1EsMC4yNzc3Nzc4ZW1GJy8lJ3JzcGFjZUdGTC1JKG1mZW5jZWRHRiQ2JC1GIzYmLUYsNiVRInNGJ0YvRjItRjY2LVEiLEYnRjlGOy9GP0YxRkBGQkZERkZGSC9GS1EmMC4wZW1GJy9GTlEsMC4zMzMzMzMzZW1GJy1GLDYlUSJ0RidGL0YyRjlGOS1GNjYtUSgmc3JhcnI7RidGOUY7Rj5GQEZCRkRGRkZIRmVuL0ZORmZuLUkjbW5HRiQ2JFEiM0YnRjktRjY2LVEnJnNkb3Q7RidGOUY7Rj5GQEZCRkRGRkZIRmVuRl9vLUY2Ni1RIn5GJ0Y5RjtGPkZARkJGREZGRkhGZW5GX28tRiw2JVEkY29zRicvRjBGPUY5LUZQNiQtRiM2JEZpbkY5RjktRjY2LVEqJnVtaW51czA7RidGOUY7Rj5GQEZCRkRGRkZIL0ZLUSwwLjIyMjIyMjJlbUYnL0ZORmZwRmpvLUZQNiQtRiM2JEZURjlGOS1GNjYtUSI6RidGOUY7Rj5GQEZCRkRGRkZIRkpGTS1GLDYlUSN5eUYnRi9GMkY1Rk9GXG9GYG9GZG8tRiw2JVEkc2luRidGXXBGOUZecEZicEZicUZocEZccUZnb0Znb0Znby1GNjYtUSIjRidGOUY7Rj5GQEZCRkRGRkZIRmVuRl9vLUYsNiVRL35jZXJjbGV+bW9iaWxlRidGL0YyLUknbXNwYWNlR0YkNiYvJSdoZWlnaHRHUSYwLjBleEYnLyUmd2lkdGhHRmZuLyUmZGVwdGhHRmByLyUqbGluZWJyZWFrR1EobmV3bGluZUYnLUZccjYmRl5yRmFyRmNyL0ZmclElYXV0b0YnLUYsNiVRKGRpc3BsYXlGJ0YvRjItRlA2JC1GIzY2LUYsNiVRKGFuaW1hdGVGJ0YvRjItRlA2JC1GIzYwLUYsNiVRJXBsb3RGJ0YvRjJGVy1GUDYmLUYjNiwtRlA2Ji1GIzYxRistRlA2JC1GIzYqRlRGVy1GLDYlUSUmcGk7RidGXXBGOUZkb0Zpbi1GNjYtUSIvRidGOUY7Rj4vRkFGMUZCRkRGRkZIL0ZLUSwwLjE2NjY2NjdlbUYnL0ZORmF1LUZhbzYkUSI4RidGOUY5RjlGV0ZfcUZldEZXRlQtRjY2LVEiPUYnRjlGO0Y+RkBGQkZERkZGSEZKRk0tRmFvNiRRIjBGJ0Y5LUY2Ni1RIy4uRidGOUY7Rj5GQEZCRkRGRkZIRmVwRl9vLUZhbzYkUSIyRidGOUZkb0Znb0ZpdEY5RjkvJSVvcGVuR1EiW0YnLyUmY2xvc2VHUSJdRidGVy1GLDYlUSZjb2xvckYnRi9GMkZmdS1GLDYlUSVibHVlRidGL0YyRlctRiw2JVEqdGhpY2tuZXNzRidGL0YyRmZ1LUZhbzYkUSI1RidGOUY5RjlGYnZGZXZGV0ZpbkZmdUZpdUZcdi1GYW82JFEjMTZGJ0Y5RlctRiw2JVEnZnJhbWVzRidGL0YyRmZ1LUZhbzYkUSMxN0YnRjlGOUY5RldGZ29GZ29GZXFGaHFGW3JGY3MtRlA2JC1GIzYwRmpzRlctRlA2Ji1GIzYsLUZQNiYtRiM2Ly1GLDYlUSJ4RidGL0YyLUZQNiQtRiM2KC1GLDYlUScmIzk2MDtGJ0ZdcEY5RmRvRlRGXHVGY3VGOUY5RlctRiw2JVEieUYnRi9GMkZceUZXRlRGZnVGYnAtRmFvNiRRJC4wMUYnRjlGXHZGaW5GOUY5RmJ2RmV2RldGaHZGZnUtRiw2JVEkcmVkRidGL0YyRldGXndGZnVGYXdGOUY5RmJ2RmV2RldGaW5GZnVGaXVGXHZGZHdGV0Znd0ZmdUZqd0Y5RjlGV0Znb0Znb0Znb0ZlcS1GLDYlUS9+YXN0cm8mIzIzOTtkZUYnRi9GMkZbckZqcy1GUDYkLUYjNjAtRlA2Ji1GIzY1LUZhbzYkUSI0RidGOUZkb0Zqb0ZecEZXRmd6RmRvRmJxRl5wRldGaW5GZnVGaXVGXHZGX3ZGZG9GZ29GaXRGOUY5RmJ2RmV2RlctRiw2JVEoc2NhbGluZ0YnRi9GMkZmdS1GLDYlUSxjb25zdHJhaW5lZEYnRi9GMkZXRmh2RmZ1LUYsNiVRJmJyb3duRidGL0YyRldGXndGZnVGYXdGOUY5RjlGOUZnb0Znb0ZlcS1GLDYlUS1+Y2VyY2xlfmZpeGVGJ0YvRjIvJStleGVjdXRhYmxlR0Y9Rjk=

Courbes polaires

Une courbe en coordonn\303\251es polaires 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 s'\303\251tudie par le biais d'une courbe param\303\251tr\303\251e 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.

Quelques spirales :

LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYpLUkjbWlHRiQ2JVEocmVzdGFydEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi1RIjtGJy9GM1Enbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRjEvJSlzdHJldGNoeUdGPS8lKnN5bW1ldHJpY0dGPS8lKGxhcmdlb3BHRj0vJS5tb3ZhYmxlbGltaXRzR0Y9LyUnYWNjZW50R0Y9LyUnbHNwYWNlR1EmMC4wZW1GJy8lJ3JzcGFjZUdRLDAuMjc3Nzc3OGVtRictRiw2JVElcGxvdEYnRi9GMi1JKG1mZW5jZWRHRiQ2JC1GIzYoLUZUNiYtRiM2LS1GLDYlUSJ0RidGL0YyLUY2Ni1RIixGJ0Y5RjtGPkZARkJGREZGRkhGSi9GTlEsMC4zMzMzMzMzZW1GJ0ZmbkZpbkZmbi1GNjYtUSI9RidGOUY7L0Y/Rj1GQEZCRkRGRkZIL0ZLRk9GTS1GNjYtUSomdW1pbnVzMDtGJ0Y5RjtGYW9GQEZCRkRGRkZIL0ZLUSwwLjIyMjIyMjJlbUYnL0ZORmdvLUkmbWZyYWNHRiQ2KC1GIzYmLUkjbW5HRiQ2JFEiNUYnRjktRjY2LVEnJnNkb3Q7RidGOUY7RmFvRkBGQkZERkZGSEZKL0ZORkwtRiw2JVEnJiM5NjA7RicvRjBGPUY5RjktRiM2JS1GX3A2JFEiMkYnRjlGL0YyLyUubGluZXRoaWNrbmVzc0dRIjFGJy8lK2Rlbm9tYWxpZ25HUSdjZW50ZXJGJy8lKW51bWFsaWduR0ZkcS8lKWJldmVsbGVkR0Y9LUY2Ni1RIy4uRidGOUY7RmFvRkBGQkZERkZGSEZmb0ZlcC1Gam82KC1GIzYnLUZfcDYkUSMxMUYnRjlGYnAtRjY2LVEifkYnRjlGO0Zhb0ZARkJGREZGRkhGSkZlcEZmcEY5RmpwRl9xRmJxRmVxRmdxRjlGOS8lJW9wZW5HUSJbRicvJSZjbG9zZUdRIl1GJ0Zpbi1GLDYlUSdjb29yZHNGJ0YvRjJGXm8tRiw2JVEmcG9sYXJGJ0ZpcEY5RjlGOUY1LyUrZXhlY3V0YWJsZUdGPUY5

C'est la spirale d'Archim\303\250de.

LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2I1EhRictRiM2JkYrLUYsNiVRJXBsb3RGJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRictSShtZmVuY2VkR0YkNiQtRiM2LC1GOzYmLUYjNjEtRiw2JVEjbG5GJy9GNVEmZmFsc2VGJy9GOFEnbm9ybWFsRictRjs2JC1GIzYkLUYsNiVRInRGJ0Y0RjdGSEZILUkjbW9HRiQ2LVEiLEYnRkgvJSZmZW5jZUdGRy8lKnNlcGFyYXRvckdGNi8lKXN0cmV0Y2h5R0ZHLyUqc3ltbWV0cmljR0ZHLyUobGFyZ2VvcEdGRy8lLm1vdmFibGVsaW1pdHNHRkcvJSdhY2NlbnRHRkcvJSdsc3BhY2VHUSYwLjBlbUYnLyUncnNwYWNlR1EsMC4zMzMzMzMzZW1GJ0ZORlFGTi1GUjYtUSI9RidGSEZVL0ZYRkdGWUZlbkZnbkZpbkZbby9GXm9RLDAuMjc3Nzc3OGVtRicvRmFvRmhvLUZSNi1RKiZ1bWludXMwO0YnRkhGVUZmb0ZZRmVuRmduRmluRltvL0Zeb1EsMC4yMjIyMjIyZW1GJy9GYW9GXnAtSSNtbkdGJDYkUSIwRidGSC1GUjYtUSMuLkYnRkhGVUZmb0ZZRmVuRmduRmluRltvRl1wL0Zhb0Zfby1GYXA2JFEjMTBGJ0ZILUZSNi1RJyZzZG90O0YnRkhGVUZmb0ZZRmVuRmduRmluRltvRl1vRmdwLUZSNi1RIn5GJ0ZIRlVGZm9GWUZlbkZnbkZpbkZbb0Zdb0ZncC1GLDYlUScmIzk2MDtGJ0ZGRkhGSEZILyUlb3BlbkdRIltGJy8lJmNsb3NlR1EiXUYnRlEtRiw2JVEnY29vcmRzRidGNEY3RmNvLUYsNiVRJnBvbGFyRidGRkZIRlEtRiw2JVEoc2NhbGluZ0YnRjRGN0Zjby1GLDYlUSxjb25zdHJhaW5lZEYnRjRGN0ZIRkhGSEYrLyUrZXhlY3V0YWJsZUdGR0ZI

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

Quelques rosaces :

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

Courbes implicites

Une ellipse :

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

Une hyperbole :

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

Le folium de Descartes :

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

... et la lemniscate de Bernoulli :

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

Quelques surfaces : gaussienne, quadriques...

Maple peut aussi faire de tr\303\250s beaux dessins en 3D... On peut tracer des surfaces.

La gaussienne standard :

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

Un parabolo\303\257de elliptique :

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

... et un parabolo\303\257de hyperbolique :

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

Un ellipso\303\257de de r\303\251volution :

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

... et un hyperbolo\303\257de \303\240 une nappe :

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

Compl\303\251ments plus sophistiqu\303\251s

<Text-field style="Heading 1" layout="Heading 1">5. Proc\303\251dures</Text-field>

Cordes vibrantes et s\303\251ries de Fourier

\303\211quation des ondes : 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(Membranes vibrantes : 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)

La quantit\303\251 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 repr\303\251sente la forme de la corde \303\240 l'instant LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JlEidEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnRjIvRjZRJ25vcm1hbEYn, \303\240 la position LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JlEieEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnRjIvRjZRJ25vcm1hbEYn.

On peut \303\251crire une proc\303\251dure pour illustrer le mouvement de la corde \303\240 l'aide d'animations.

Corde vibrante pinc\303\251e (e.g. d'une guitare) :

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

La corde a \303\251t\303\251 pinc\303\251e avec un m\303\251diator. En la pin\303\247ant sans m\303\251diator exactement au milieu :

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

Corde vibrante frapp\303\251e (e.g. d'un piano) :

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

Ensembles de Julia

Pour chaque 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, on d\303\251finit l'ensemble des points LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYpLUklbXN1YkdGJDYlLUkjbWlHRiQ2JlEieEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUYjNiYtSSNtbkdGJDYlUSIwRidGNS9GOVEnbm9ybWFsRidGMkY1RjgvJS9zdWJzY3JpcHRzaGlmdEdGQC1JI21vR0YkNi5RIitGJ0Y1RkEvJSZmZW5jZUdGNy8lKnNlcGFyYXRvckdGNy8lKXN0cmV0Y2h5R0Y3LyUqc3ltbWV0cmljR0Y3LyUobGFyZ2VvcEdGNy8lLm1vdmFibGVsaW1pdHNHRjcvJSdhY2NlbnRHRjcvJSdsc3BhY2VHUSwwLjIyMjIyMjJlbUYnLyUncnNwYWNlR0ZZLUYvNiZRImlGJ0YyRjVGOC1GRjYuUScmc2RvdDtGJ0Y1RkFGSUZLRk1GT0ZRRlNGVS9GWFEmMC4wZW1GJy9GZW5GXW8tRiw2JS1GLzYmUSJ5RidGMkY1RjhGO0ZDRjVGQQ== tels que la suite de points d\303\251marrant de 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 et v\303\251rifiant 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 soit born\303\251e (et lorsque c'est le cas, elle est born\303\251e en module par 2) :

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

\303\200 chaque point (a,b) de la grille 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, on associe un niveau de couleur correspondant au nombre d'it\303\251rations <N telles que la suite soit born\303\251e.

Une valeur de LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JlEiY0YnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0Yn et quelques valeurs de LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JlEiTkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0Yn :

LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzZoby1JI21pR0YkNiVRImNGJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRictSSNtb0dGJDYtUSJ+RicvRjNRJ25vcm1hbEYnLyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR0Y9LyUpc3RyZXRjaHlHRj0vJSpzeW1tZXRyaWNHRj0vJShsYXJnZW9wR0Y9LyUubW92YWJsZWxpbWl0c0dGPS8lJ2FjY2VudEdGPS8lJ2xzcGFjZUdRJjAuMGVtRicvJSdyc3BhY2VHRkwtRjY2LVEqJmNvbG9uZXE7RidGOUY7Rj5GQEZCRkRGRkZIL0ZLUSwwLjI3Nzc3NzhlbUYnL0ZORlMtSSNtbkdGJDYkUSYwLjI4NEYnRjktRjY2LVEoJm1pbnVzO0YnRjlGO0Y+RkBGQkZERkZGSC9GS1EsMC4yMjIyMjIyZW1GJy9GTkZnbi1GVjYkUScwLjAxMjJGJ0Y5LUY2Ni1RJyZzZG90O0YnRjlGO0Y+RkBGQkZERkZGSEZKRk0tRiw2JVEiSUYnRi9GMi1GNjYtUSI7RidGOUY7L0Y/RjFGQEZCRkRGRkZIRkpGVEY1LUYsNiVRIk5GJ0YvRjJGNUZPRjUtRlY2JFEjMzBGJ0Y5RmJvLUknbXNwYWNlR0YkNiYvJSdoZWlnaHRHUSYwLjBleEYnLyUmd2lkdGhHRkwvJSZkZXB0aEdGYXAvJSpsaW5lYnJlYWtHUShuZXdsaW5lRictRiw2JlEncGxvdDNkRidGLy8lK2V4ZWN1dGFibGVHRj1GMi1JKG1mZW5jZWRHRiQ2JS1GIzZpbi1GVjYlUSIwRidGXHFGOS1GNjYuUSIsRidGXHFGOUY7RmVvRkBGQkZERkZGSEZKL0ZOUSwwLjMzMzMzMzNlbUYnLUY2Ni5GOEZccUY5RjtGPkZARkJGREZGRkhGSkZNLUY2Ni5RKiZ1bWludXMwO0YnRlxxRjlGO0Y+RkBGQkZERkZGSEZmbkZobi1GVjYlUSQxLjVGJ0ZccUY5RltyLUY2Ni5RIy4uRidGXHFGOUY7Rj5GQEZCRkRGRkZIRmZuRk1GW3JGYHJGZnFGW3JGXXJGYHJGW3JGY3JGW3JGYHJGZnFGW3ItRiw2JlEsb3JpZW50YXRpb25GJ0YvRlxxRjJGW3ItRjY2LlEiPUYnRlxxRjlGO0Y+RkBGQkZERkZGSEZSRlRGW3ItRl9xNictRiM2KUZdci1GVjYlUSM5MEYnRlxxRjlGZnFGW3JGY3FGXHFGOUZccUY5LyUlb3BlbkdRIltGJy8lJmNsb3NlR1EiXUYnRmZxRltyLUYsNiZRJWdyaWRGJ0YvRlxxRjJGW3JGaXJGW3ItRl9xNictRiM2KC1GVjYlUSQyMDBGJ0ZccUY5RmZxRltyRmB0RlxxRjlGXHFGOUZjc0Zmc0ZmcUZccC1GLDYmUSZzdHlsZUYnRi9GXHFGMkZbckZpckZbci1GLDYmUSxwYXRjaG5vZ3JpZEYnRi9GXHFGMkZmcUZbci1GLDYmUShzY2FsaW5nRidGL0ZccUYyRltyRmlyRltyLUYsNiZRLGNvbnN0cmFpbmVkRidGL0ZccUYyRmZxRltyLUYsNiZRJWF4ZXNGJ0YvRlxxRjJGW3JGaXJGW3ItRiw2JlEnZnJhbWVkRidGL0ZccUYyRmZxRltyLUYsNiZRJmNvbG9yRidGL0ZccUYyRltyRmlyRltyLUYsNiZRLWNvdWxldXJqdWxpYUYnRi9GXHFGMkZccUY5RlxxRjktRjY2LkZkb0ZccUY5RjtGZW9GQEZCRkRGRkZIRkpGVEZbckZccEZbckZccEZbci1GLDYmRi5GL0ZccUYyRltyLUY2Ni5GUUZccUY5RjtGPkZARkJGREZGRkhGUkZURltyLUZWNiVGWEZccUY5LUY2Ni5GZW5GXHFGOUY7Rj5GQEZCRkRGRkZIRmZuRmhuLUZWNiVGW29GXHFGOS1GNjYuRl5vRlxxRjlGO0Y+RkBGQkZERkZGSEZKRk0tRiw2JkZhb0YvRlxxRjJGW3ZGW3ItRiw2JkZob0YvRlxxRjJGW3JGX3ZGW3ItRlY2JVEkMTAwRidGXHFGOUZbdkZccEZpcEZecUZbdkZccEZccEZbckZccEZddkZbckZfdkZbckZhdkZjdkZldkZndkZpdkZbdkZbckZbd0ZbckZfdkZbci1GVjYlUSQzMDBGJ0ZccUY5Rlt2RlxwRmlwRl5xLUYsNiNRIUYnRlxwLUZdcDYmRl9wRmJwRmRwL0ZncFElYXV0b0YnRmN3RlxxRjk=

D'autres valeurs de LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYoLUkjbWlHRiQ2JlEiY0YnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkjbW9HRiQ2LlEifkYnRjIvRjZRJ25vcm1hbEYnLyUmZmVuY2VHRjQvJSpzZXBhcmF0b3JHRjQvJSlzdHJldGNoeUdGNC8lKnN5bW1ldHJpY0dGNC8lKGxhcmdlb3BHRjQvJS5tb3ZhYmxlbGltaXRzR0Y0LyUnYWNjZW50R0Y0LyUnbHNwYWNlR1EmMC4wZW1GJy8lJ3JzcGFjZUdGTi1GOTYuUSI6RidGMkY8Rj5GQEZCRkRGRkZIRkovRk1RLDAuMjc3Nzc3OGVtRicvRlBGVUYvRjJGNQ==

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

Ensemble de Mandelbrot

C'est l'ensemble des points LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JlEiY0YnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnRjIvRjZRJ25vcm1hbEYn tels que la suite de points d\303\251marrant de LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUklbXN1YkdGJDYlLUkjbWlHRiQ2JlEiekYnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUYjNiYtSSNtbkdGJDYlUSIwRidGNS9GOVEnbm9ybWFsRidGMkY1RjgvJS9zdWJzY3JpcHRzaGlmdEdGQC1JI21vR0YkNi5RIj1GJ0Y1RkEvJSZmZW5jZUdGNy8lKnNlcGFyYXRvckdGNy8lKXN0cmV0Y2h5R0Y3LyUqc3ltbWV0cmljR0Y3LyUobGFyZ2VvcEdGNy8lLm1vdmFibGVsaW1pdHNHRjcvJSdhY2NlbnRHRjcvJSdsc3BhY2VHUSwwLjI3Nzc3NzhlbUYnLyUncnNwYWNlR0ZZRj1GNUZB et v\303\251rifiant 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 soit born\303\251e :

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