Mathc initiation/Fichiers h : x 68cb

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	c16b.c

/* ---------------------------------- */
/* save as c16b.c                     */
/* ---------------------------------- */
#include "x_hfile.h"
#include       "fa.h"
int main(void)
{
pt3d   P = {1,-5,1};

/* ---------------------------------- */
 clrscrn();
 
 printf("   Implicit differentiation.\n\n"
        "      ****************\n\n"
  
 "  If an equation F(x,y,z) = 0 determines,\n"
 "  implicitly, a differentiable function g of\n"
 "  two variables x and y such that z = g(x,y)\n"
 "  for every (x,y) in the domaine of g, then\n\n"

 
        "    dz      F_x(x,y,z)\n"
        "    --  = - ----------\n"
        "    dx      F_z(x,y,z)\n\n"

        "    dz      F_y(x,y,z)\n"
        "    --  = - ----------\n"
        "    dy      F_z(x,y,z)\n\n");
        
 stop();

/* ---------------------------------- */
 clrscrn();
 printf("  f   : x,y,z-> %s\n\n\n\n",feq);


 printf("  In first verify that the point p(%0.2f,%0.2f,%0.2f)\n\n", 
           P.x,P.y,P.z);
 printf("  satisfy the equation.\n\n");
 printf("  f(%0.2f,%0.2f,%0.2f) = %0.9f\n\n\n", 
           P.x,P.y,P.z,f(P.x,P.y,P.z));


 printf("  Now you can compute : Dz_y](%0.2f,%0.2f,%0.2f)\n\n\n",
           P.x,P.y,P.z);

 printf("  Dz_y](%0.2f,%0.2f,%0.2f) = %0.9f      with %s\n\n",
           P.x,P.y,P.z,-f_y(P.x,P.y,P.z)/f_z(P.x,P.y,P.z),f_yeq);
 printf("  Dz_y](%0.2f,%0.2f,%0.2f) = %0.9f      with implicitDz_y() \n\n",
           P.x,P.y,P.z,implicitDz_y(f,H,P));

 stop();

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

Exemple de sortie écran :

   Implicit differentiation.

      ****************

  If an equation F(x,y,z) = 0 determines,
  implicitly, a differentiable function g of
  two variables x and y such that z = g(x,y)
  for every (x,y) in the domaine of g, then

    dz      F_x(x,y,z)
    --  = - ----------
    dx      F_z(x,y,z)

    dz      F_y(x,y,z)
    --  = - ----------
    dy      F_z(x,y,z)

 Press return to continue.

Exemple de sortie écran :

  f   : x,y,z-> x**2*z**2+x*y**2-z**3+4*y*z-5



  In first verify that the point p(1.00,-5.00,1.00)

  satisfy the equation.

  f(1.00,-5.00,1.00) = 0.000000000


  Now you can compute : Dz_y](1.00,-5.00,1.00)


  Dz_y](1.00,-5.00,1.00) = -0.285714286      with 2*x*y+4*z

  Dz_y](1.00,-5.00,1.00) = -0.285714286      with implicitDz_y() 

 Press return to continue.