Mathc initiation/Fichiers c : c65cb
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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 x1 = -1.;
double y1 = 2.;
double x2 = 3;
double y2 = 1.;
double m = 0;
clrscrn();
printf(" Let F(x,y) = M(x,y) i + N(x,y) j \n\n\n");
printf(" Be continuous on an open connected region D,\n");
printf(" And let C be a piecewise-smooth curve in D\n");
printf(" With endpoints A(x1,y1) and B(x2,y2).\n\n\n");
printf(" If F(x,y) = grad f(x,y) then \n\n\n");
printf(" ( ( (x2,y2)\n");
printf(" int( M(x,y)dx + int( N(x,y)dy = [f(x,y)]\n");
printf(" (c (c (x1,y1)\n");
printf(" \n");
stop();
clrscrn();
printf(" Let F(x,y) = %si + %sj \n\n",Meq,Neq);
printf(" and has C parametrization :\n\n");
printf(" x = %s; y = %s; %.1f < t =< %.1f \n\n\n",
geq, heq, a, b);
printf(" Let f(x,y) = %s \n\n\n",feq);
printf(" Verify if F(x,y) = grad f(x,y)\n\n\n");
m =lint2d_dx(
M,
g,h,
a,b,LOOP);
m +=lint2d_dy(
N,
g,h,
a,b,LOOP);
printf(" then \n\n");
printf(" ( ( \n");
printf(" int( M(x,y)dx + int( N(x,y)dy = %+.3f\n", m);
printf(" (c (c \n\n\n");
printf(" f(x2,y2) - f(x1,y1) = %+.3f\n\n", f(x2,y2) - f(x1,y1));
stop();
return 0;
}
/* ---------------------------------- */
/* ---------------------------------- */
Nous devons commencer par vérifier manuellement que F(x,y) = grad f(x,y). Ensuite nous vérifions que le calcul de l'intégrale de F(x,y) est bien égal à f(x2,y2) - f(x1,y1).
Exemple de sortie écran :
Let F(x,y) = M(x,y)n + N(x,y)h
Be continuous on an open connected region D,
And let C be a piecewise-smooth curve in D
With endpoints A(x1,y1) and B(x2,y2).
If F(x,y) = grad f(x,y) then
( ((x2,y2) (x2,y2)
int( M(x,y)dx + N(x,y)dy = int( F.dr = [f(x,y)]
(c ((x1,y1) (x1,y1)
Press return to continue.
Exemple de sortie écran :
Let F(x,y) = (y**2 + 2*x*y)i + (x**2 + 2*x*y)j
and has C parametrization :
x = t; y = -1/4*t + 7/4; -1.0 < t =< 3.0
Let f(x,y) = (x*y**2 + x**2*y)
Verify if F(x,y) = grad f(x,y)
then
( (
int( M(x,y)dx + int( N(x,y)dy = +14.000
(c (c
f(x2,y2) - f(x1,y1) = +14.000
Press return to continue.