# Questions tagged [laplace-transform]

Use for the Laplace integral transformation.

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### Laplace transform of triple convolution involving Heaviside function — stems from multi-state random walk

I'm a bit stuck on this problem stemming from a multi-state random walk. I have a function of the form $$C(t) = \int_0^t dt' \theta(t'-T)A(t')B(t-t')$$ and I'd like to calculate its Laplace transform....
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### Laplace transform on thermodynamics equation

I'm trying to create a simple model of a single-flash geothermal plant which consist of 3 main parts (flash-separator, turbine, and condenser). Is there any way to create a transfer function using ...
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### Why is the Laplace Transform essentially never used when dealing with problems involving resonance?

Both the Laplace Transform and the Fourier Transform can be applied to a PDE, for example the wave equation, and used to derive a solution to the equation. But I never see the Laplace Transform used ...
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### Laplace Transform Density of States & Partition function

I am currently going through Pathria's Statistical Mechanics text , and under the Canonical Ensemble description, the author stresses that the partition function of a continuous system is the Laplace ...
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### Fourier Transforms of Harmonic Functions

Suppose you are presented with the equation ($D=3$) \begin{equation} \nabla^2 A(x) = \nabla^2 B(x). \end{equation} Decompose $A$ and $B$ into their Fourier components, \begin{equation} A(x) = \int d^...
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### Why is there a sudden change in current between $t=0^{-}$ and $t=0^{+}$ when an active inductor is connected in series with a relaxed inductor?

Let us take the following question as an example: For the above question I drew the corresponding Laplace transform diagram, as follows (didn't draw the switch since it basically open circuit after \$...
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### Difference between Fourier and Laplace transforms in analyzing data

I have a set of displacement-time graphs from an experiment to convert to the frequency domain. Both the Fourier and Laplace transform seem to do this, so what's the difference between them (...
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### What is this equation, written on a wall? [closed]

I've also asked this in MathOverflow, but since the equation in question is related to acceleration and physical phenomenon, I figure this is also a good place. I was asked to ID the following, but ...
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### Question about the Radiative Transfer Equation (RTE) Phase function term

I am new to this subject. I am trying to understand what is the purpose of the phase function $$∂u/∂t=-v∘∇u-v( μ_{a}+μ_{s})u+∫vμ_s p_{s} (Ω^{'}→Ω)u(r,Ω^{'},t)ⅆΩ^{'}+q(r,Ω,t)$$ Were u= angular ...
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### Why is the impedance of a resistor the same in time and frequency domains if the Laplace transform of a constant is not the same constant?

I'm sure this is a silly question, but if the Laplace transform of a constant is not a constant, e.g. $$\mathfrak{L} = \frac{1}{s}$$ then how come the impedance of a resistor is the same in the ...