All Questions
4
questions
2
votes
1
answer
107
views
How do we know $\lim_{t\rightarrow \infty }e^{-st + 4t} = 0 ? $
I'm trying to evaluate an integral, and the final step is to evaluate $e^{-st + 4t}$ at infinity minus $e^{-st + 4t}$ at $10$. (The limits of integration were $\infty$ and $10$.)
To evaluate the ...
- 2,331
1
vote
1
answer
124
views
How to solve this DE involving a convolution $\int_0^t ds \ e^{-\kappa s} \cos(\omega s) f(t-s)$?
I've got a DE of the form
$$
\frac{df}{dt} = A - B f(t) - C \int_0^t ds\ e^{-\kappa s} \cos(\omega s) f(t-s)
$$
which I want to solve given an initial condition $f(0^{+})=f_0 \in \mathbb{R}$. All the ...
- 2,767
2
votes
2
answers
56
views
yet another simple Laplace transform
what is $ℒ(t^2e^{3t})$
I have got this far so far:
$=\int_{0}^\infty (t^2e^{t(3-s)})$
Integration by parts using:
$u = t^2$ and $du = 2t$
$v = \frac{e^{t(3-2)}}{3-s}$ and $dv = e^{t(3-s)}$
Which ...
- 121
2
votes
1
answer
4k
views
Fundamental matrix and exponential of matrix using Laplace Transform
I'm trying to work out how to find $$\exp(At)$$ for a system of linear differential equations $$x'=Ax.$$
I know that the solution is a fundamental matrix of the system such that $$\exp(At)=I$$
at ...
- 1,146