Mathc initiation/a550

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	c00b.c

/* --------------------------------- */
/* save as c00b.c                    */
/* --------------------------------- */
#include "x_afile.h"
#include      "fb.h"                 /* Try fb.h, fc.h ... fj.h */
/* --------------------------------- */
int main(void)
{
double  M = LT_dt( F_mns_a, a,b, LOOP, s);

 clrscrn();  
 
 printf(" The Laplace transform of F(t) is f(s) \n\n" 
        "            / oo                         \n" 
        "           |                             \n" 
        " L{F(t)} = |    exp(-s t) F(t) dt = f(s) \n" 
        "           |                             \n" 
        "           /  0                        \n\n");
 
 
 printf(" Second translation  property of the Laplace transform is :\n\n"
        "   L{F(t-a)} = exp(-a s) f(s)  : if t > a  : 0  if t < a   \n\n");
 stop();

 clrscrn();
 printf("  /+oo                                                       \n"
        " |  exp(-s t) [F(t-a)] dt = exp(-a s) f(s)  with  s = %+.3f  \n"
        " /a                                          and  a = %+.3f\n\n", 
                                s, aa); 
        
 printf(" If   F(t) : t-> %s  Then F(t-a) : t-> %s  \n\n", 
          Feq, F_mns_aeq);     

 printf("       /+oo                              \n"
        " Then |     exp(-s t) [%s] dt = (%+.3f)  \n" 
        "      /a                               \n\n", F_mns_aeq, M); 
        
 printf(" And :          L{F(t-a)} = exp(-a s) f(s) \n"
        "                          = %s            \n"
        "                          = %s            \n"
        "                          = (%+.3f)     \n\n", 
                                 f_seq,f2seq, f_s(s));  
        
 printf(" Mathematica Code\n\n"
        " %s   \n"
        " %s \n\n", Mathematica_eq_1, Mathematica_eq_2);  
           
 stop(); 
 
 return 0;
}
/* --------------------------------- */
/* --------------------------------- */

Exemple de sortie écran :

 The Laplace transform of F(t) is f(s) 

            / oo                         
           |                             
 L{F(t)} = |    exp(-s t) F(t) dt = f(s) 
           |                             
           /  0                        

 Second translation  property of the Laplace transform is :

   L{F(t-a)} = exp(-a s) f(s)  : if t > a  : 0  if t < a   

 Press return to continue.

Exemple de sortie écran :

  /+oo                                                       
 |  exp(-s t) [F(t-a)] dt = exp(-a s) f(s)  with  s = +0.600  
 /a                                          and  a = +0.300

 If   F(t) : t-> t  Then F(t-a) : t-> t-a  

       /+oo                              
 Then |     exp(-s t) [t-a] dt = (+2.320)  
      /a                               

 And :          L{F(t-a)} = exp(-a s) f(s) 
                          = exp(-a s) (1/s^2)            
                          = exp(-a s)/s^2            
                          = (+2.320)     

 Mathematica Code

 integrate exp(-s *t) * (t- a) dt from t=a  to infinity   
 integrate exp(-.6*t) * (t-.3) dt from t=.3 to 300 

 Press return to continue.