10
votes
1answer
214 views

Contour integration with branch points inside the contour.

In my scientific research I ran into an unpleasant situation with specific type of contour integrals. Being more specific I have problems not with integrals themselves (I can use various numeric ...
2
votes
2answers
99 views

Inverse Laplace with $\ln$

How can I compute the inverse Laplace of 1) $\ln\left(\dfrac{s+1}{s-1}\right)$ 2) $\ln\left(\dfrac{s-1}{s}\right)$. Can someone please hep me to do these two problems
2
votes
0answers
57 views

inverse laplace transform of $$p^{-3/2}e^{-\sqrt{pa}}(\cos(\sqrt{ap})+\sin(\sqrt{ap}))$$

I used the Residue theorem to solve this problem. But, I could not obtain the solution given by $$\mathscr{L}^{-1}\left( { p^{-3/2}e^{-\sqrt{pa}}\over{2\sqrt{2}}} [\cos(\sqrt{ap})+\sin(\sqrt{ap})] ...
1
vote
1answer
114 views

inverse Laplace transfor by using maple or matlab

I want to use inverse Laplace transform to F function by using maple or matlab. However I cannot get any answer. I know the answer from table but I want to use one of softwares. from table: ...
1
vote
1answer
47 views

complex integral of z to the power alpha

I would like to perform an inverse laplace and at some point of the calculation I have to compute this integral $$\int_{\gamma-i\infty}^{\gamma+i\infty} z^{(1+n)\alpha-1}e^{z} \frac{dz}{2\pi i}$$ ...
1
vote
1answer
72 views

Forced wave equation question?

I'm studying for my PDEs midterm and trying to do practice problems. I'm really not sure how to do this question - I've never seen anything like it. Thanks in advance for your help. Solve the ...
4
votes
1answer
185 views

Laplace transform of and impulse sampled function using “frequency” convolution

This is a long question, but assume we have this: The book uses the frequency convolution theorem to solve this problem. To solve the integral, it uses a contour + residue theorem to solve it. The ...
1
vote
1answer
67 views

Bromwich integral of $1/s^k$ with k real (non integer) and $1<k$

Is there a simple way to compute the inverse laplace transform of $1/s^k$ with k non integer using Bromwich integral (basically without using the known laplace transform of $t^n$)?
0
votes
0answers
80 views

Contour integral (inverse Laplace transform) with arctan

I have what I think is a relatively simple contour integral involving arctan, but it is giving me difficulty. I would really appreciate any help. The integral itself is, with τ, λ, and k all real and ...
1
vote
2answers
50 views

Inverse Laplace of $\frac{s^3}{2+s^3}$

How I can find the Inverse Laplace of $\displaystyle \frac{s^3}{2+s^3}$ Thanks
2
votes
1answer
73 views

How to approach/solve this integral?

Could somebody suggest how to approach or solve this integral: $$ \int_{0}^\infty e^{-a t}{2+t-2\sqrt{1+t}\over t^2}{\rm d\,}t, $$ where $a>0$ ? It is not a homework. I tried to use residuum ...
6
votes
1answer
358 views

Inverse Laplace Transform of $\bar p_D = \frac{K_0(\sqrt[]s r_D)}{sK_0(\sqrt[]s)}$

I solved the following partial differential equation using Laplace Transform: $\LARGE \frac{1}{r_D}\frac{\partial}{\partial r_D}(r_D\frac{\partial p_D}{\partial r_D})=\frac{\partial p_D}{\partial ...
1
vote
1answer
229 views

Calculation of the Inverse Laplace Transform of $\frac{1}{p}$ by contour integration.

I am always told in my lessons of control engineering that the inverse Laplace Transform of $\frac{1}{p}$ is the Heaviside step function $\theta(t)$. But I have a problem when I calculate the inverse ...
0
votes
0answers
93 views

About evaluating $\mathcal{L}^{-1}_{s\to x}\left\{\dfrac{F(s)}{s}\right\}$ by considering contour integration with different entire functions $F(s)$

Detailedly compare the difficulties of different entire functions $F(s)$ where $F(0)\neq0$ when evaluating $\mathcal{L}^{-1}_{s\to x}\left\{\dfrac{F(s)}{s}\right\}$ by considering contour integration, ...
0
votes
0answers
196 views

About the inverse laplace transform of sinc function

How to calculate $\mathcal{L}^{-1}_{s\to x}\{\text{sinc}(s)\}$ ? Note: $\text{sinc}(s)=\dfrac{\sin s}{s}$ when $s\neq0$ . Also note that $\lim\limits_{s\to\pm\infty}\dfrac{\sin s}{s}=0$ .
3
votes
1answer
762 views

Inverse Laplace transform using contour integration

I want to show by contour integration that $\displaystyle\mathcal{L}^{-1} \{\text{arccot}(s) \}(t)= \frac{\sin t\ }{t}$. In other words, I want to evaluate $\displaystyle \frac{1}{2 \pi i} \int_{a - ...
2
votes
2answers
314 views

Inverse Laplace transform of $\frac{\log(s)}{1 + s}$

Is it possible to find the inverse laplace transform $$\mathcal{L}^{-1}\frac{\log(s)}{1 + s}$$ using the Bromwich integral formula $$\mathcal{L}^{-1} \{F(s)\}(t) = f(t) = \frac{1}{2\pi ...
1
vote
1answer
212 views

Inverse Laplace Transform by contour integration

In question 1) we get Laplace transform of $$ g(t) = t^a $$ is: $$ \hat g(t)= {1/s^{a+1}}\int_0^\infty e^{-t}x^a $$ then I was stuck at question 2) which asks me to evaluate the inverse laplace ...
5
votes
1answer
295 views

$\mathcal{B}^{-1}_{s\to x}\{e^{as^2+bs}\}$ and $\mathcal{L}^{-1}_{s\to x}\{e^{as^2+bs}\}$ , where $a\neq0$

http://en.wikipedia.org/wiki/Integral_transform#Table_of_transforms claims than the integral form of inverse bilateral Laplace transform and inverse Laplace transform are both the same. But are they ...