Mathc initiation/Fichiers h : c72a3


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c01c.c
/* --------------------------------- */
/* save as c01c.c                    */
/* --------------------------------- */
#include "x_hfile.h"
#include      "fc.h"
/* --------------------------------- */
int main(void)
{
CTRL_splot p;

p.xmin  = -1,   p.xmax    =  1;
p.ymin  = -1,   p.ymax    =  1;
p.zmin  = -1,   p.zmax    =  1;
p.rot_x = 56,   p.rot_z   = 16;
p.scale =  1,   p.scale_z =  1;

pt2d     Q = i_pt2d(0.,0.);

 clrscrn();
 
 printf(" Let f be a function of two variables        \n\n");
 printf(" that has continuous second partial derivatives\n");
 printf(" throughout an open disk R containing (a,b). \n\n");
 printf(" If f_x(a,b) = f_y(a,b) = 0 and             \n\n");
 printf("      D(a,b) < 0,                            \n\n");
 printf(" Then p(a,b,f(a,b)) is a saddle point on the   \n");
 printf(" graph of f \n\n\n");
 
 stop();

 clrscrn();
 
 printf(" Verify if f_x(a,b) = f_y(a,b) = 0.\n\n\n");
 printf(" f   : x,y-> %s\n\n\n",   feq  );
 printf(" f_x(%0.2f,%0.2f) = %0.9f    \n\n",Q.x,Q.y, fxy_x(f,H,Q));
 printf(" f_y(%0.2f,%0.2f) = %0.9f  \n\n\n",Q.x,Q.y, fxy_y(f,H,Q));
 
 stop();

 clrscrn();
 
 printf(" Verify if D(a,b) < 0\n\n\n");
 printf(" f   : x,y-> %s\n\n\n",feq);
 printf(" D(%0.2f,%0.2f) = %0.9f    \n\n",Q.x,Q.y,D_fxy(f,f_xy,H,Q) );
 printf(" Then p(%0.2f,%0.2f,%0.2f,) is a saddle point on the\n",
           Q.x,Q.y, f(Q.x,Q.y));
 printf(" graph of f\n\n\n");
 
 stop();

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

     G_3d_p(    p,
                feq,f,
                Q);

 printf(" Open the file ... load \"a_main.plt\" ... with gnuplot.\n\n");
 
 stop();
 
 return 0;
}
/* --------------------------------- */
/* --------------------------------- */


Exemple de sortie écran :

 Let f be a function of two variables        

 that has continuous second partial derivatives
 throughout an open disk R containing (a,b). 

 If f_x(a,b) = f_y(a,b) = 0 and             

      D(a,b) < 0,                            

 Then p(a,b,f(a,b)) is a saddle point on the   
 graph of f 


 Press return to continue.


Exemple de sortie écran :

 Verify if f_x(a,b) = f_y(a,b) = 0.


 f   : x,y-> x**3 + 3*x*y - y**3


 f_x(0.00,0.00) = 0.000000010    

 f_y(0.00,0.00) = -0.000000010  


 Press return to continue.



Exemple de sortie écran :

 Verify if D(a,b) < 0


 f   : x,y-> x**3 + 3*x*y - y**3


 D(0.00,0.00) = -9.000000000    

 Then p(0.00,0.00,0.00,) is a saddle point on the
 graph of f


 Press return to continue.


Exemple de sortie écran :

 f : (x,y)-> x**3 + 3*x*y - y**3


 Open the file ... load "a_main.plt" ... with gnuplot.

 Press return to continue.