Mathc initiation/Fichiers c : c54ca

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	c18ayx.c

/* ---------------------------------- */
/* save as c18ayx.c                   */
/* --------------------------------- */
#include  "x_hfile.h"
#include       "fa.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 :   

    (                                   (1.571    (2*x/Pi     
 int( (y-sin(x)) dx + (cos(x)) dy = int(     int( (-sin(x))-(1) dy dx
    (c                                  (0.000    (0 


 Press return to continue.

Exemple de sortie écran :

 M(x,y) = (y-sin(x)) 
 N(x,y) = (cos(x)) 

 N_x_mns_M_y(x,y) = (-sin(x))-(1)  

 v(x) = 2*x/Pi   
 u(x) = 0 

 With simpson_dydx().

    (1.6    (2*x/Pi                
 int(    int( (-sin(x))-(1)  dy dx = -1.42202
    (0.0    (0           


 With green_dydx().

    (1.6    (2*x/Pi                         
 int(    int( (N_x - M_y)  dy dx = -1.42202
    (0.0    (0                     


 Press return to continue.