Mathc initiation/Fichiers c : c59cb1
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c18b1.c |
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/* ---------------------------------- */
/* save as c18b1.c */
/* ---------------------------------- */
#include "x_hfile.h"
#include "fb.h"
/* ---------------------------------- */
int main(void)
{
double ay = -2.;
double by = 2.;
int ny = 2*100;
int nx = 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(" Let C be the trace of S on the x-y-plane. \n\n");
printf(" Verify Stokes's theorem for the vector field, \n\n");
printf(" F(x,y,z) = %si %sj %sk\n\n\n\n\n",Meq,Neq,Peq);
printf(" Stoke's theorem.\n\n");
printf(" / // \n");
printf(" | || \n");
printf(" O F.T ds = || (curl F).n dS \n");
printf(" | || \n");
printf(" / C // \n");
printf(" S \n\n\n");
stop();
/* ---------------------------------- */
clrscrn();
printf(" // \n");
printf(" || \n");
printf(" || (curl F).n dS = \n");
printf(" || \n");
printf(" // \n");
printf(" S \n\n\n");
printf(" with F = Mi + Nj + Pk \n\n");
printf(" (curl F) = [(P_y-N_z)i + (M_y-P_z)j + (N_X-M_Y)k]\n\n\n\n");
printf(" (-f_xi-f_yj+k) \n");
printf(" n = ------------ \n");
printf(" [(f_x)^2+(f_y)^2+1]^1/2 \n\n\n\n");
printf(" dS = [(f_x)^2+(f_y)^2+1]^1/2 dA dA = dxdy\n\n");
stop();
/* ---------------------------------- */
clrscrn();
printf(" With the Stokes's theorem you find :\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 : (y)-> %s \n", ueq);
printf(" v : (y)-> %s \n\n", veq);
printf(" a = %+.1f b = %+.1f\n\n",ay,by);
m = stokes_dxdy(M,N,P,
f,
H,
ay,by,ny,
u, v,nx);
printf(" / b / v(y)\n");
printf(" | | \n");
printf(" | | (curl F).n [(f_x)^2+(f_y)^2+1]^1/2 dx dy = %.3f\n",m);
printf(" | | \n");
printf(" / a / u(y)\n\n\n");
stop();
return 0;
}
/* ---------------------------------- */
/* ---------------------------------- */
Vérifions le théorème de Stoke partie 1.
Exemple de sortie écran :
Let S be the part of the graph of z = 4-x**2-y**2 with z >= 0.
Let C be the trace of S on the x-y-plane.
Verify Stokes's theorem for the vector field,
F(x,y,z) = + 2*yi + exp(z)j - atan(x)k
Stoke's theorem.
/ //
| ||
O F.T ds = || (curl F).n dS
| ||
/ C //
S
Press return to continue.
Exemple de sortie écran :
//
||
|| (curl F).n dS =
||
//
S
with F = Mi + Nj + Pk
(curl F) = [(P_y-N_z)i + (M_y-P_z)j + (N_X-M_Y)k]
(-f_xi-f_yj+k)
n = ------------
[(f_x)^2+(f_y)^2+1]^1/2
dS = [(f_x)^2+(f_y)^2+1]^1/2 dA dA = dxdy
Press return to continue.
Exemple de sortie écran :
With the Stokes's theorem you find :
F : (x,y,z)-> + 2*yi + exp(z)j - atan(x)k
f : (x,y)-> 4-x**2-y**2
u : (y)-> -sqrt(4-y**2)
v : (y)-> +sqrt(4-y**2)
a = -2.0 b = +2.0
/ b / v(y)
| |
| | (curl F).n [(f_x)^2+(f_y)^2+1]^1/2 dx dy = -25.129
| |
/ a / u(y)
Press return to continue.