The laplace-expansion tag has no wiki summary.
-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$$(0)$ $=$ $0$ and that $f'$ be a piecewise continuous function and absolutely integrable on ...
-4
votes
1answer
135 views
Please check this inverse this Laplace transform [closed]
I just want to check if my exercise are right:
Inverse of these Laplace transform
$$F^{-1}\left(\frac{1}{p-2}\right)= e^{2s}$$
$$F^{-1}\left(\frac{e^{-2p}}{p^2}\right)=\frac{2}{s^3(s+2)}$$
...
0
votes
1answer
45 views
Finding the determinant of a $3 \times 3$ matrix via Laplace Expansion
I have a matrix here where I need to calculate the determinant using Laplace expansion.
$$
\begin{pmatrix}
4 & 0 & 1\\19 & 1 & -3\\7 & 1 & 0
\end{pmatrix}
$$
So I did the ...
3
votes
1answer
82 views
Laplace method help
$$\int_{0}^{\infty} \frac{e^{-x \cosh t}}{\sqrt{(\sinh t)}}dt$$
I'm trying to use Laplace's method to find the leading asymptotic behavior as $x$ goes to positive infinity, but I'm having some ...
0
votes
0answers
38 views
Compute for $\epsilon$-expansion
Found this question posted on the website of Institue for Theoretische Physik.
Compute small $\epsilon$-expansion for
$ Sp (e^{\epsilon\varDelta}) $
where $\varDelta$ is the Laplace operator in ...
4
votes
1answer
107 views
Laplace integral and leading order behavior
Consider the integral:
$$
\int_0^{\pi/2}\sqrt{\sin t}e^{-x\sin^4 t} \, dt
$$
I'm trying to use Laplace's method to find its leading asymptotic behavior as $x\rightarrow\infty$, but I'm running into ...
0
votes
1answer
91 views
How do I understand the proof of Laplace's Theorem in wikipedia?
See http://en.wikipedia.org/wiki/Laplace_expansion
What does $\tau\,=(n,n-1,\ldots,i)\sigma'(j,j+1,\ldots,n)$ stand for as well as the statements follow?
"Since the two cycles can be written ...
0
votes
1answer
220 views
Help With Difficult Proof
Suppose we have the following equation 1:
$$\tag{1}
A_G(x,y,z) = \frac{A_1}{q(z)} e^{-ik \frac{x^2 + y^2}{2q(z)}}
$$
where
$$
q(z) = z+iz_0
$$
and $i$ is equal to $\sqrt{-1}$.
Suppose we have ...
1
vote
1answer
62 views
Complete expansion of Laplace integral
Let $\varphi \in C^\infty (\mathbb R^n ;\mathbb R)$ such that
1) $\varphi(0)=0$
2) $\varphi(x)>0$ on $\mathbb R^n\setminus 0$
3) $\text{Hess}_{\varphi}(0)>0 $
and let $B_1(0)$ be the ...
3
votes
1answer
177 views
Laplace expansion
This statement is from the book of Winitzki Linear Algebra via Exterior Products. (Section 3.4, page 123) Let $V$ be finite dimensional vector space, $\dim(V)=N$. The determinant of the matrix ...
