Mathc initiation/a539
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c00b.c |
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/* --------------------------------- */
/* 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( expaF, 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(" First translation property of the Laplace transform is :\n\n"
" L{exp(a t) * F(t)} = f(s-a) \n\n");
stop();
clrscrn();
printf(" /+oo \n"
" | exp(-s t) [exp(a t) F(t)] dt = f(s-a) with s = %+.3f\n"
" /0 and a = %+.3f\n\n\n",
s, aa);
printf(" If F(t) : t-> %s "
" Then exp(a*t) * F(t) : t-> %s \n\n", Feq, expaFeq);
printf(" /+oo \n"
" Then | exp(-s t) [%s] dt = (%+.3f) \n"
" /0 \n\n\n", expaFeq, M);
printf(" And : L{exp(a*t) * F(t)} = f(s-a) \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
First translation property of the Laplace transform is :
L{exp(a t) * F(t)} = f(s-a)
Press return to continue.
Exemple de sortie écran :
/+oo
| exp(-s t) [exp(a t) F(t)] dt = f(s-a) with s = +0.600
/0 and a = +0.400
If F(t) : t-> t Then exp(a*t) * F(t) : t-> exp(a*t) * t
/+oo
Then | exp(-s t) [exp(a*t) * t] dt = (+24.999998)
/0
And : L{exp(a*t) * F(t)} = f(s-a)
= 1/(s-a)^2
= 1/(s-a)^2
= (+25.000)
Mathematica Code
integrate exp(-s*t) * exp(a*t) * t dt from t=0 to infinity
Press return to continue.