Mathc initiation/003a
Installer et compiler ces fichiers dans votre répertoire de travail.
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c00f.c |
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/* --------------------------------- */
/* save as c00f.c */
/* --------------------------------- */
#include "x_afile.h"
#include "ff.h"
/* ---------------------------------- */
int main(void)
{
double f1,f2,f3;
clrscrn();
printf(" Use the divergence theorem to find,\n\n");
printf(" the FLUX of F through S.\n\n");
printf(" // /// \n");
printf(" || ||| \n");
printf(" || F.n dS = ||| div F dV \n");
printf(" || ||| \n");
printf(" // /// \n");
printf(" S Q \n\n\n");
printf(" If F = Mi + Nj + Pk \n\n\n");
printf(" /// /// \n");
printf(" ||| ||| \n");
printf(" ||| div F dV = ||| M_x + N_y + P_z dV \n");
printf(" ||| ||| \n");
printf(" /// /// \n");
printf(" Q Q \n\n\n");
stop();
clrscrn();
f1 = FLUX_dxdzdy( M,
fxyz_x,
x0, x1,LOOP,
z0, z1,LOOP,
Y0, Y1,LOOP);
printf(" /// \n");
printf(" ||| \n");
printf(" ||| M_x dV = %.3f\n",f1);
printf(" ||| \n");
printf(" /// \n");
printf(" Q \n\n");
f2 = FLUX_dxdzdy( N,
fxyz_y,
x0, x1,LOOP,
z0, z1,LOOP,
Y0, Y1,LOOP);
printf(" /// \n");
printf(" ||| \n");
printf(" ||| N_y dV = %.3f\n",f2);
printf(" ||| \n");
printf(" /// \n");
printf(" Q \n\n");
f3 = FLUX_dxdzdy( P,
fxyz_z,
x0, x1,LOOP,
z0, z1,LOOP,
Y0, Y1,LOOP);
printf(" /// \n");
printf(" ||| \n");
printf(" ||| P_z dV = %.3f\n",f3);
printf(" ||| \n");
printf(" /// \n");
printf(" Q \n\n");
stop();
clrscrn();
printf(" /// /// \n");
printf(" ||| ||| \n");
printf(" ||| div F dV = ||| M_x + N_y + P_z dV \n");
printf(" ||| ||| \n");
printf(" /// /// \n");
printf(" Q Q \n\n\n");
printf(" /// /// /// \n");
printf(" ||| ||| ||| \n");
printf(" ||| M_x dV + ||| N_y dV + ||| P_z dV = %.3f\n",f1+f2+f3);
printf(" ||| ||| ||| \n");
printf(" /// /// /// \n");
printf(" Q Q Q \n\n\n");
stop();
return 0;
}
/* --------------------------------- */
/* --------------------------------- */
Ce travail consiste à adapter l'intégrale triple au calcul du flux en 3d par le théorème de la divergence : (M_x + N_y + P_z) Ici on fait le calcul en trois étapes. L'originalité de ce travail est que l'on introduit les fonctions dérivées partielles en argument de la fonction. Vous pouvez vérifier les calculs dans la section précédente.
Exemple de sortie écran :
Use the divergence theorem to find,
the FLUX of F through S.
// ///
|| |||
|| F.n dS = ||| div F dV
|| |||
// ///
S Q
If F = Mi + Nj + Pk
/// ///
||| |||
||| div F dV = ||| M_x + N_y + P_z dV
||| |||
/// ///
Q Q
Press return to continue.
///
|||
||| M_x dV = 48.000
|||
///
Q
///
|||
||| N_y dV = 18.667
|||
///
Q
///
|||
||| P_z dV = 10.667
|||
///
Q
Press return to continue.
/// ///
||| |||
||| div F dV = ||| M_x + N_y + P_z dV
||| |||
/// ///
Q Q
/// /// ///
||| ||| |||
||| M_x dV + ||| N_y dV + ||| P_z dV = 77.333
||| ||| |||
/// /// ///
Q Q Q
Press return to continue.