Mathc initiation/Fichiers c : c59ca2
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c18a2.c |
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/* ---------------------------------- */
/* save as c18a2.c */
/* ---------------------------------- */
#include "x_hfile.h"
#include "fa.h"
/* ---------------------------------- */
int main(void)
{
double m = 0;
clrscrn();
printf(" Evaluate the line integral :\n\n"
" Stoke's theorem. \n\n"
" / // \n"
" | || \n"
" O F.T ds = || (curl F).n dS \n"
" | || \n"
" / C // \n"
" S \n\n\n"
" / / \n"
" | | \n"
" O F.T ds = O F dr \n"
" | | \n"
" / C / C \n\n"
" / \n"
" | \n"
" O M(x,y,z) dx + N(x,y,z) dy + P(x,y,z) dz = \n"
" | \n"
" / C \n\n");
stop();
clrscrn();
m = lint3d_dx(M,
g,h,k,
a,b,LOOP);
m += lint3d_dy(N,
g,h,k,
a,b,LOOP);
m += lint3d_dz(P,
g,h,k,
a,b,LOOP);
printf(" Let S be the part of the graph of z = %s with z >= 0. \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",Meq,Neq,Peq);
printf(" if C has the parametrization :\n\n");
printf(" x = %s; y = %s; z = %s; (z = %s) \n\n", geq, heq,keq, feq);
printf(" %.1f < t =< %.1f \n\n",a, b);
printf(" With the line integral you find :\n");
printf(" / \n");
printf(" | \n");
printf(" O (%s) dx + (%s) dy + (%s) dz = %+.3f \n", Meq, Neq, Peq,m);
printf(" | \n");
printf(" / C \n\n");
stop();
return 0;
}
/* ---------------------------------- */
/* ---------------------------------- */
Vérifions le théorème de Stoke partie 2.
Exemple de sortie écran :
Evaluate the line integral :
/ //
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O F.T ds = || (curl F).n dS
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/ C //
S
/ /
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O F.T ds = O F dr
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/ C / C
/
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O M(x,y,z) dx + N(x,y,z) dy + P(x,y,z) dz =
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/ C
Press return to continue.
Exemple de sortie écran :
Let S be the part of the graph of z = 9-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) = + 3*zi + 4*xj + 2*yk
if C has the parametrization :
x = 3*cos(t); y = 3*sin(t); z = 0; (z = 9-x**2-y**2)
0.0 < t =< 6.3
With the line integral you find :
/
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O (+ 3*z) dx + (+ 4*x) dy + ( + 2*y) dz = +113.097
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/ C
Press return to continue.