Laplace transform of dirac delta function

[Kambiz_Veshgini]

let S be the Unit Step function

for a function with a finite jump at t0 we have:

(*) L{F'(t)}=s f(s)-F(0)-[F(t0+0)-F(t0-0)]*exp(-s t0)]

so:

L{S'(t-k)}=s exp(-s k)/s-0-[1-0]*exp(-s k) = 0 & k>0

but S'(t-k)=deltadirac(t-k) and we know that L{deltadirac(t-k)}=exp(-s k)

so why do I get ZERO when using the formula (*)

 

[uart]

let S be the Unit Step function

for a function with a finite jump at t0 we have:

(*) L{F'(t)}=s f(s)-F(0)-[F(t0+0)-F(t0-0)]*exp(-s t0)]

Ok, I'm not familiar with that one, but I think you're mis-applying it.

The expression I'm familar with is just the L{F'(t)}=s f(s)-F(0) part.

My suspicion is that the [F(t0+0)-F(t0-0)]*exp(-s t0)] is just inserted to manually take care of the dirac impulse that results from the finite discontinuity and that in this case the f(s) you should be using is that of the original function without the discontinuity. Note that the unit step without the step is a pretty simple function. :)