Mathc initiation/Fichiers c : c54cb

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	c18byx.c

/* --------------------------------- */
/* save as c18byx.c                  */
/* --------------------------------- */
#include  "x_hfile.h"
#include       "fb.h"
/* --------------------------------- */
int main(void)
{
 clrscrn(); 
 printf(" The Green's theorem :   \n\n");
 
 printf("    (                            (b   (v(x)              \n" 
        " int( M(x,y) dx + N(x,y) dy = int( int( (N_x - M_y) dy dx\n"
        "    (c                           (a   (u(x)      \n\n\n\n\n");
 
 printf(" Use the Green's theorem to evaluate :   \n\n");  
 
 printf("    (                                (%.3f   (%s     \n",bx,veq);
 printf(" int( %s dx + %s dy = int(     int( %s dy dx\n",
                          Meq, Neq, N_x_mns_M_y_eq);
 printf("    (c                               (%.3f   (%s \n\n\n",ax,ueq);         
 stop(); 
 
 
 clrscrn();     
 printf(" M(x,y) = %s \n",   Meq);
 printf(" N(x,y) = %s \n\n", Neq);

 printf(" N_x_mns_M_y(x,y) = %s  \n\n", N_x_mns_M_y_eq);
 
 printf(" v(x) = %s   \n", veq); 
 printf(" u(x) = %s \n\n", ueq);

 printf(" With simpson_dydx().\n\n");
 printf("    (%.1f     (%s                \n", bx, veq);
 printf(" int(    int( %s  dy dx = %.5f\n", N_x_mns_M_y_eq, 
             simpson_dydx(N_x_mns_M_y, u,v,LOOP, ax,bx,LOOP) );
 printf("    (%.1f     (%s           \n\n\n", ax, ueq);
 
 printf(" With green_dydx().\n\n");
 printf("    (%.1f     (%s                         \n", bx, veq);
 printf(" int(    int( (N_x - M_y)  dy dx = %.5f\n", 
             green_dydx(M,N, u,v,LOOP, ax,bx,LOOP) );
 printf("    (%.1f     (%s                     \n\n\n", ax, ueq);

 stop();

 return 0;
}
/* --------------------------------- */
/* --------------------------------- */

Nous avons une fonction pour calculer directement l'intégrale double de Green. Elle calcule elle même les dérivées partielles nécessaires.

Exemple de sortie écran :

 The Green's theorem :   

    (                            (b   (v(x)              
 int( M(x,y) dx + N(x,y) dy = int( int( (N_x - M_y) dy dx
    (c                           (a   (u(x)      




 Use the Green's theorem to evaluate :   

    (                                (1.000   (x**2     
 int( (x+y**2) dx + (1+x**2) dy = int(     int( (2*x)-(2*y) dy dx
    (c                               (0.000   (x**3 


 Press return to continue.

Exemple de sortie écran :

 M(x,y) = (x+y**2) 
 N(x,y) = (1+x**2) 

 N_x_mns_M_y(x,y) = (2*x)-(2*y)  

 v(x) = x**2   
 u(x) = x**3 

 With simpson_dydx().

    (1.0     (x**2                
 int(    int( (2*x)-(2*y)  dy dx = 0.04286
    (0.0     (x**3           


 With green_dydx().

    (1.0     (x**2                         
 int(    int( (N_x - M_y)  dy dx = 0.04286
    (0.0     (x**3                     


 Press return to continue.