# Tagged Questions

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### 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 ...
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### 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
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I used the Residue theorem to solve this problem. But, I could not obtain the solution given by $$\mathscr{L}^{-1}\left( { p^{-3/2}e^{-\sqrt{pa}}\over{2\sqrt{2}}} [\cos(\sqrt{ap})+\sin(\sqrt{ap})] ... 1answer 114 views ### inverse Laplace transfor by using maple or matlab I want to use inverse Laplace transform to F function by using maple or matlab. However I cannot get any answer. I know the answer from table but I want to use one of softwares. from table: ... 1answer 47 views ### complex integral of z to the power alpha I would like to perform an inverse laplace and at some point of the calculation I have to compute this integral$$\int_{\gamma-i\infty}^{\gamma+i\infty} z^{(1+n)\alpha-1}e^{z} \frac{dz}{2\pi i}$$... 1answer 72 views ### Forced wave equation question? I'm studying for my PDEs midterm and trying to do practice problems. I'm really not sure how to do this question - I've never seen anything like it. Thanks in advance for your help. Solve the ... 1answer 185 views ### Laplace transform of and impulse sampled function using “frequency” convolution This is a long question, but assume we have this: The book uses the frequency convolution theorem to solve this problem. To solve the integral, it uses a contour + residue theorem to solve it. The ... 1answer 67 views ### Bromwich integral of 1/s^k with k real (non integer) and 1<k Is there a simple way to compute the inverse laplace transform of 1/s^k with k non integer using Bromwich integral (basically without using the known laplace transform of t^n)? 0answers 80 views ### Contour integral (inverse Laplace transform) with arctan I have what I think is a relatively simple contour integral involving arctan, but it is giving me difficulty. I would really appreciate any help. The integral itself is, with τ, λ, and k all real and ... 2answers 50 views ### Inverse Laplace of \frac{s^3}{2+s^3} How I can find the Inverse Laplace of \displaystyle \frac{s^3}{2+s^3} Thanks 1answer 73 views ### How to approach/solve this integral? Could somebody suggest how to approach or solve this integral:$$ \int_{0}^\infty e^{-a t}{2+t-2\sqrt{1+t}\over t^2}{\rm d\,}t, $$where a>0 ? It is not a homework. I tried to use residuum ... 1answer 358 views ### Inverse Laplace Transform of \bar p_D = \frac{K_0(\sqrt[]s r_D)}{sK_0(\sqrt[]s)} I solved the following partial differential equation using Laplace Transform: \LARGE \frac{1}{r_D}\frac{\partial}{\partial r_D}(r_D\frac{\partial p_D}{\partial r_D})=\frac{\partial p_D}{\partial ... 1answer 229 views ### Calculation of the Inverse Laplace Transform of \frac{1}{p} by contour integration. I am always told in my lessons of control engineering that the inverse Laplace Transform of \frac{1}{p} is the Heaviside step function \theta(t). But I have a problem when I calculate the inverse ... 0answers 93 views ### About evaluating \mathcal{L}^{-1}_{s\to x}\left\{\dfrac{F(s)}{s}\right\} by considering contour integration with different entire functions F(s) Detailedly compare the difficulties of different entire functions F(s) where F(0)\neq0 when evaluating \mathcal{L}^{-1}_{s\to x}\left\{\dfrac{F(s)}{s}\right\} by considering contour integration, ... 0answers 196 views ### About the inverse laplace transform of sinc function How to calculate \mathcal{L}^{-1}_{s\to x}\{\text{sinc}(s)\} ? Note: \text{sinc}(s)=\dfrac{\sin s}{s} when s\neq0 . Also note that \lim\limits_{s\to\pm\infty}\dfrac{\sin s}{s}=0 . 1answer 762 views ### Inverse Laplace transform using contour integration I want to show by contour integration that \displaystyle\mathcal{L}^{-1} \{\text{arccot}(s) \}(t)= \frac{\sin t\ }{t}. In other words, I want to evaluate \displaystyle \frac{1}{2 \pi i} \int_{a - ... 2answers 314 views ### Inverse Laplace transform of \frac{\log(s)}{1 + s} Is it possible to find the inverse laplace transform$$\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 ...
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 ...