Tagged Questions
-1
votes
1answer
30 views
Prove that L[f' ' ](s)$ = $sL[f](s)
Can anyone prove this question ?
Let $f$:$\mathbb{R}$$→$$\mathbb{C}$ be continuous function such that $f$$(0)$ $=$ $0$ and that $f'$ be a piecewise continuous function and absolutely integrable on ...
0
votes
1answer
56 views
Using Convolution Theorem to find the Laplace transform
In previous questions I have used Laplace transform to find the inverse Laplace transform.
I have worked through this work booklet ...
1
vote
1answer
65 views
Lower bounds of laplace transform of characteristic functions
I have the following integral:
\begin{equation}
f(\mu) = \int_0^\infty e^{-\mu t}\varphi_X(t)dt
\end{equation}
where $\varphi_X(t)$ is the characteristic function of some undetermined probability ...
1
vote
2answers
151 views
How to compute Inverse Laplace transform using Convolution
How do you evaluate the inverse transform below using convolution ?
$$
\mathcal{ L^{-1} } \left[ {\frac{s}{(s^2 + a^2)^2}} \right]
$$
I tried
$$\begin{align} \mathcal{ L^{-1} } \left[ ...
1
vote
1answer
97 views
Convolution Laplace transform
Find the inverse Laplace transform of the giveb function by using the
convolution theorem.
$$F(x) = \frac{s}{(s+1)(s^2+4)}$$
If I use partial fractions I get: $$\frac{s+4}{5(s^2+4)} - ...
2
votes
1answer
110 views
Laplace transform having this unusual property in convolution?
Here is the problem
Solve $y'(t) = 1 - \int_{0}^{t} y(t - v)e^{-2v}dv$
The solution sets $\mathcal{L}(y) = Y(s)$ and does the following
Notice that in step 1, they have $$Y(s)\dfrac{1}{s+2}$$
...
1
vote
1answer
353 views
a matrix inverse laplace transform problem
Let $\mathcal {L}^{-1}[\cdot]$ be an inverse Laplace transform. Let $A$ be a square matrix, and $I$ an identity matrix.
Based on the fact that $\mathcal {L} ^{-1} [{(sI-A)}^{-1}] = e ^{tA}$, how can ...
