Mathc initiation/a558

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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( tF, 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\n");
 
 
 printf(" Multiplication by t^n  property of the Laplace transform is :\n\n"
        "   L{t^n F(t)}  =  (-1)^n f^n(s) :                            \n\n");
 stop();

 clrscrn();
 printf("       /+oo                                            \n"
        "      |     exp(-s t) [t^n F(t)] dt = (-1)^n f^n(s) \twith s = %+.3f\n"
        "      /0                                                and  n = 1\n\n\n"
                      , s); 
        
 printf(" If     F(t) : t-> %s " 
        " Then t F(t) : t-> %s  \n\n", Feq, tFeq);     

 printf("       /+oo                              \n"
        " Then |     exp(-s t) [%s] dt = (%+.3f)  \n" 
        "      /0                             \n\n\n", tFeq, M); 
        
 printf(" And :   L{t F(t)} = -1 f'(s)           \n"
        "                   = %s                 \n"
        "                   = %s                 \n"
        "                   = (%+.3f)          \n\n", 
                                 f_seq,f2seq, f_s(s));  
        
 printf(" Mathematica Code\n\n"
        " %s \n\n", Mathematica_eq);    
 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                      


 Multiplication by t^n  property of the Laplace transform is :

   L{t^n F(t)}  =  (-1)^n f^n(s) :                            

 Press return to continue.

Exemple de sortie écran :

       /+oo                                            
      |     exp(-s t) [t^n F(t)] dt = (-1)^n f^n(s) 	with s = +0.600
      /0                                                and  n = 1


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

       /+oo                              
 Then |     exp(-s t) [t *t] dt = (+9.259)  
      /0                             


 And :   L{t F(t)} = -1 f'(s)           
                   = -1*(-2/s**3)                 
                   = 2/s**3                 
                   = (+9.259)          

 Mathematica Code

 integrate exp(-s *t) * (t *t) dt from t=0  to infinity 

 Press return to continue.