Mathc initiation/Fichiers c : c62cb
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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 ax = -1;
double bx = 1.;
int nx = 2*100;
int ny = 2*100;
double m = 0;
/* ---------------------------------- */
clrscrn();
printf(" Let S be the part of the graph of z = %s with z >= 0. \n\n", feq);
printf(" If F(x,y,z) = %si %sj %sk, find the flux of F through S\n\n\n",
Meq,Neq,Peq);
printf(" Consider g(x,y,z) = z - (%s)\n\n",feq);
printf(" n = grad(g(x,y,z)) / ||grad(g(x,y,z))||\n\n\n");
m = flux_dydx( M,N,P,
f, u,v,ny,
ax,bx,nx,
H);
printf(" The flux of F through S is \n\n");
printf(" // \n");
printf(" || \n");
printf(" || F.n dS = %.3f\n",m);
printf(" || \n");
printf(" // \n");
printf(" S \n\n\n");
stop();
/* ---------------------------------- */
clrscrn();
printf(" / b / v(x)\n");
printf(" | | \n");
printf(" | | F.(-f_xi-f_yj+k) [f_x^2+f_y^2+1]^1/2 dy dx = %.3f\n",m);
printf(" | | ----------- \n");
printf(" | | [f_x^2+f_y^2+1]^1/2\n");
printf(" | | \n");
printf(" / a / u(x)\n\n\n");
printf(" With.\n\n\n");
printf(" F : (x,y,z)-> %si %sj %sk \n\n",Meq,Neq,Peq);
printf(" f : (x,y)-> %s \n\n", feq);
printf(" u : (x)-> %s \n", ueq);
printf(" v : (x)-> %s \n\n", veq);
printf(" a = %+.1f b = %+.1f \n",ax,bx);
stop();
/* ---------------------------------- */
clrscrn();
printf(" / b / v(x)\n");
printf(" | | \n");
printf(" | | F.(-f_xi-f_yj+k) dy dx = %.3f\n",m);
printf(" | | \n");
printf(" / a / u(x)\n\n\n");
printf(" With.\n\n\n");
printf(" F : (x,y,z)-> %si %sj %sk \n\n",Meq,Neq,Peq);
printf(" f : (x,y)-> %s \n\n", feq);
printf(" u : (x)-> %s \n", ueq);
printf(" v : (x)-> %s \n\n", veq);
printf(" a = %+.1f b = %+.1f \n",ax,bx);
stop();
return 0;
}
/* ---------------------------------- */
/* ---------------------------------- */
L'algorithme consiste à adapter la fonction qui calcule les intégrales doubles au calcul des flux.
Remarque :
Dans cette version nous utilisons cet algorithme simplifié pour l'intégrale.
/ b / v(y)
| |
| | F.(-f_xi-f_yj+k) dx dy =
| |
/ a / u(y)
Dans la précédente version nous avons utilisé cet algorithme.
/ b / v(y)
| |
| | F.(-f_xi-f_yj+k) [f_x^2+f_y^2+1]^1/2 dx dy =
| | -----------
| | [f_x^2+f_y^2+1]^1/2
| |
/ a / u(y)
Exemple de sortie écran :
Let S be the part of the graph of z = 1-x**2-y**2 with z >= 0.
If F(x,y,z) = xi yj zk, find the flux of F through S
Consider g(x,y,z) = z - (1-x**2-y**2)
n = grad(g(x,y,z)) / ||grad(g(x,y,z))||
The flux of F through S is
//
||
|| F.n dS = 4.711
||
//
S
Press return to continue.
Exemple de sortie écran :
/ b / v(x)
| |
| | F.(-f_xi-f_yj+k) dy dx = 4.711
| |
/ a / u(x)
With.
F : (x,y,z)-> xi yj zk
f : (x,y)-> 1-x**2-y**2
u : (x)-> -sqrt(1-x**2)
v : (x)-> +sqrt(1-x**2)
a = -1.0 b = +1.0
Press return to continue.