laplace transform problem

[v9260019]

Hello all
Quesion 1 :Some books define the definition of laplace transform as :

Laplace{f(t)}=Integrate(f(t)*exp(-st)){from 0- to t}

and some books define as

Laplace{f(t)}=Integrate(f(t)*exp(-st)){from 0+ to t}

Quesion 2: Some books define the Laplace transform of differentiative as:

Let Laplace{f(t)}=F(s)

Laplace {f'(t)}=sF(s)-f(0-)

some other books define as Laplace {f'(t)}=sF(s)-f(0+)

I can't get what the difference between the two " a little " different definition of question1 and question 2

thansk a lot

 

[anomaly]

Hello all
Quesion 1 :Some books define the definition of laplace transform as :

Laplace{f(t)}=Integrate(f(t)*exp(-st)){from 0- to t}

and some books define as

Laplace{f(t)}=Integrate(f(t)*exp(-st)){from 0+ to t}

Quesion 2: Some books define the Laplace transform of differentiative as:

Let Laplace{f(t)}=F(s)

Laplace {f'(t)}=sF(s)-f(0-)

some other books define as Laplace {f'(t)}=sF(s)-f(0+)

I can't get what the difference between the two " a little " different definition of question1 and question 2

thansk a lot

I'm not really familiar with your first two. I've always heard it defined as 0 to infinity, and negative infinity to infinity.
In which case, the difference is:

"The (unilateral) Laplace transform (not to be confused with the Lie derivative, also commonly denoted ) is defined by

where is defined for (Abramowitz and Stegun 1972). The unilateral Laplace transform is almost always what is meant by "the" Laplace transform, although a bilateral Laplace transform is sometimes also defined as"
https://mathworld.wolfram.com/LaplaceTransform.html


The second is typically seen in many signals books. However, I believe I literally solved every problem in my signals class using the unilateral LaPlace transform.



As for your second part:

Let Laplace{f(t)}=F(s)

Laplace {f'(t)}=sF(s)-f(0-)

One takes in consideration of the time shift.



Hope that helps some.

 

[shivamrules]

question 1:
well this is a trivial thing ..and varies frm buk to buk..
0- or 0+ thing only changes the initial conditions..
question 2
this is easy
if the laplace is one sided or that is defined from t=0 to infinity then we have to take the second one
else if its defined from negative to positve infinty i.e. both sided then there vil be no conditions and it vil be the first one