Mathc initiation/Fichiers c : c66ca

Sommaire

Installer et compiler ces fichiers dans votre répertoire de travail.

	c18a.c

/* ---------------------------------- */
/* save as c18a.c                     */
/* ---------------------------------- */
#include "x_hfile.h"
#include      "fa.h"
/* ---------------------------------- */
int main(void)
{
double   x1 = 1.;
double   y1 = 0.;
double   z1 = 2.;

double   x2 = -2;
double   y2 = 1.;
double   z2 = 3.;

double   m = 0;

 clrscrn();
 printf(" Let  F(x,y,z) = M(x,y,z) i + N(x,y,z) j + P(x,y,z) k\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,z1) and B(x2,y2,z2).\n\n");
 
 printf(" If F(x,y,z) = grad f(x,y,z) then \n\n");
 
 printf("    (                 (                (                    (x2,y2,z2)\n");
 printf(" int( M(x,y,z)dx + int( N(x,y,z)dy+ int( P(x,y,z)dz = [f(x,y)]\n");
 printf("    (c                (c               (c                   (x1,y1,z1)\n\n\n");

 stop();

 clrscrn();
 printf(" Let  F(x,y,z) = %si + %sj + %sk       \n\n",Meq,Neq,Peq);
 printf(" and has  C parametrization :\n\n");
 printf(" x = %s;     y = %s;    z = %s;    %.1f < t =< %.1f \n\n\n",
          geq, heq, keq, a, b);
 printf(" Let  f(x,y,z) = %s              \n\n",feq);
 printf(" (Check manually) if F(x,y,z) = grad f(x,y,z)\n\n");

 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("  then \n\n");
 
 printf("    (                 (                (                     \n");
 printf(" int( M(x,y,z)dx + int( N(x,y,z)dy + int( P(x,y,z)dz =  %+.3f\n",m);
 printf("    (c                (c               (c                \n\n\n");

 printf("  f(x2,y2,z2) - f(x1,y1,z1) = %+.3f\n\n", f(x2,y2,z2) - f(x1,y1,z1));

 stop();

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

Vérifions manuellement que F(x,y) = grad f(x,y). 

             f(x,y,z) = 3*x**2*y**3 + 2*x*z**2 + z

                 f_x =  6*x*y**3 + 2*z**2
                 f_y = 9*x**2*y**2
                 f_z =  4*x*z+1
                  
                          f_x                    f_y              f_z
              F(x,y,z) = (6*x*y**3 + 2*z**2)i + (9*x**2*y**2)j + (4*x*z+1)k

Vérifions par le calcul que :

       (                 (                (                    (x2,y2,z2)
    int( M(x,y,z)dx + int( N(x,y,z)dy+ int( P(x,y,z)dz = [f(x,y)]
       (c                (c               (c                   (x1,y1,z1)

Exemple de sortie écran :

 Let  F(x,y,z) = M(x,y,z) i + N(x,y,z) j + P(x,y,z) k

 Be continuous on an open connected region D,
 And let C be a piecewise-smooth curve  in D
 With endpoints A(x1,y1,z1) and B(x2,y2,z2).

 If F(x,y,z) = grad f(x,y,z) then 

    (                 (                (                    (x2,y2,z2)
 int( M(x,y,z)dx + int( N(x,y,z)dy+ int( P(x,y,z)dz = [f(x,y)]
    (c                (c               (c                   (x1,y1,z1)


 Press return to continue. 


 Let  F(x,y,z) = (6*x*y**3 + 2*z**2)i + (9*x**2*y**2)j + (4*x*z+1)k       

 and has  C parametrization :

 x = (-3*t+1);     y = t;    z = t+2;    0.0 < t =< 1.0 


 Let  f(x,y,z) = 3*x**2*y**3 + 2*x*z**2 + z              

 (Check manually) if F(x,y,z) = grad f(x,y,z)

  then 

    (                 (                (                     
 int( M(x,y,z)dx + int( N(x,y,z)dy + int( P(x,y,z)dz =  -31.000
    (c                (c               (c                


  f(x2,y2,z2) - f(x1,y1,z1) = -31.000

 Press return to continue.