Mathc initiation/Fichiers c : c63cb
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c18b.c |
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/* ---------------------------------- */
/* save as c18b.c */
/* --------------------------------- */
#include "x_hfile.h"
#include "fb.h"
/* ---------------------------------- */
int main(void)
{
double ay = 0;
double by = 2.;
int ny = 2*50;
int nx = 2*50;
int nz = 2*50;
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_dzdxdy(
M,
fxyz_x,
ay,by,ny,
s,t,nx,
u,v,nz,
H);
printf(" /// \n");
printf(" ||| \n");
printf(" ||| M_x dV = %.3f\n",f1);
printf(" ||| \n");
printf(" /// \n");
printf(" Q \n\n");
f2 = flux_dzdxdy(N,
fxyz_y,
ay,by,ny,
s,t,nx,
u,v,nz,
H);
printf(" /// \n");
printf(" ||| \n");
printf(" ||| M_y dV = %.3f\n",f2);
printf(" ||| \n");
printf(" /// \n");
printf(" Q \n\n");
f3 = flux_dzdxdy(P,
fxyz_z,
ay,by,ny,
s,t,nx,
u,v,nz,
H);
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'orginalité de ce travail est que l'on introduit les fonctions dérivées partielles en arguement de la fonction.
Exemple de sortie écran :
/// ///
||| |||
||| div F dV = ||| M_x + N_y + P_z dV
||| |||
/// ///
Q Q
/// /// ///
||| ||| |||
||| M_x dV + ||| N_y dV + ||| P_z dV = 24.000
||| ||| |||
/// /// ///
Q Q Q
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