Mathc initiation/a527

Sommaire

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	c00b.c

/* --------------------------------- */
/* save as c00b.c                    */
/* --------------------------------- */
#include "x_afile.h"
#include      "fg.h"                 /* Try fb.h, fc.h ... fj.h */
/* --------------------------------- */
int main(void)
{
double  M = LT_dt( dF, 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(" A property of the Laplace transform is : \n\n"
        "   L{F'(t)}  = s * f(s) - F(0)            \n\n");
 stop();

 clrscrn();
 printf("       /+oo                                        \n"
        "      |     exp(-s t) [F'(t)] dt = s * f(s) - F(0) \twith  s = (%+.3f)\n"
        "      /0                                       \n\n\n", s); 
        
 printf(" If   F(t)  : t-> %s " 
        " Then F'(t) : t-> %s  \n\n", Feq, dFeq);     

 printf("       /+oo                              \n"
        " Then |     exp(-s t) [%s] dt = (%+.3f)  \n" 
        "      /0                             \n\n\n", dFeq, M); 
        
 printf(" And :    L{F'(t)} = s * f(s) - F(0)    \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                      


 A property of the Laplace transform is : 

   L{F'(t)} = s * f(s) - F(0)             

 Press return to continue.

Exemple de sortie écran :

       /+oo                                        
      |     exp(-s t) [F'(t)] dt = s * f(s) - F(0) 	with  s = (+0.200)
      /0                                       


 If   F(t)  : t-> cos(t)  Then F'(t) : t-> -sin(t)  

       /+oo                              
 Then |     exp(-s t) [-sin(t)] dt = (-0.962)  
      /0                             


 And :    L{F'(t)} = s * f(s) - F(0)    
                   = s * (s/(s^2+1) - cos(0))                 
                   = s**2/(s^2+1) - 1                 
                   = (-0.962)          

 Mathematica Code

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

 Press return to continue.