Question

Laplace Transform: Piecewise Function Integrability and Existence of Laplace Transform

score 197 · Answer 1 · 2026-03-27 22:03:41

197

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Laplace Transform: Piecewise Function Integrability and Existence of Laplace Transform

Published on 27 Mar 2026 - 22:03

score 68 · Answer 2 · 2019-03-21 04:39:18

68

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Laplace Transform Example: $\mathcal{L}(e^{it}) = \left[ \frac{e^{(i - s)t}}{i - s} \right]_0^\infty = \frac{1}{s - i}$?

Published on 21 Mar 2019 - 4:39

score 623 · Answer 3 · 2019-03-21 05:14:26

623

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Laplace transform of product of two functions $f(x)g(x)$ in terms of Laplace transform of $f$ and $g$.

Published on 21 Mar 2019 - 5:14

score 241 · Answer 4 · 2019-03-21 22:11:40

241

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Compute $\int_{0}^{\infty}\frac{\sin(x)}{xe^x} \ dx$.

Published on 21 Mar 2019 - 22:11

score 46 · Answer 5 · 2026-03-24 23:45:14

46

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Proof that $\frac{e^{st}}{2\pi i}$ is an orthogonal basis.

Published on 24 Mar 2026 - 23:45

score 34 · Answer 6 · 2019-03-24 13:13:11

34

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Standard way of finding a inverse Laplace transform

Published on 24 Mar 2019 - 13:13

score 257 · Answer 7 · 2019-03-24 15:20:07

257

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Proof of $\int_0^\infty f(x)g(x)\,dx = \int_0^\infty \mathcal{L}\{f(x)\}\mathcal{L}^{-1}\{g(x)\}\,ds$

Published on 24 Mar 2019 - 15:20

score 230 · Answer 8 · 2026-03-27 07:48:25

230

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What is $\int_0^\infty \log\left(\Gamma(x)\right)e^{-sx}dx$?

Published on 27 Mar 2026 - 7:48

score 31 · Answer 9 · 2019-03-26 03:35:09

31

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Computing $\mathcal{L}^{-1}\left\{\frac{s}{(s + a)^2 + b^2}\right\}$

Published on 26 Mar 2019 - 3:35

score 599 · Answer 10 · 2019-03-26 05:26:57

599

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Solving an ODE with a piecewise function

Published on 26 Mar 2019 - 5:26

score 257 · Answer 11 · 2019-03-26 23:20:53

257

Views

Evaluating $\int\limits_0^\infty \mathcal{e}^{-x}\ln^{2}x\,dx$

Published on 26 Mar 2019 - 23:20

score 692 · Answer 12 · 2019-03-27 01:12:05

692

Views

Applying dead time (pure time delay) after inverse Laplace

Published on 27 Mar 2019 - 1:12

score 184 · Answer 13 · 2019-03-27 12:55:51

184

Views

Can't solve this ODE using Laplace transforms!

Published on 27 Mar 2019 - 12:55

score 71 · Answer 14 · 2019-03-28 00:29:54

71

Views

Broken Usage of Laplace Transforms

Published on 28 Mar 2019 - 0:29

score 268 · Answer 15 · 2019-03-28 10:50:33

268

Views

Solution to this second order linear differential equation with variable coefficients

Published on 28 Mar 2019 - 10:50

List Question

Laplace Transform: Piecewise Function Integrability and Existence of Laplace Transform

Laplace Transform Example: $\mathcal{L}(e^{it}) = \left[ \frac{e^{(i - s)t}}{i - s} \right]_0^\infty = \frac{1}{s - i}$?

Laplace transform of product of two functions $f(x)g(x)$ in terms of Laplace transform of $f$ and $g$.

Compute $\int_{0}^{\infty}\frac{\sin(x)}{xe^x} \ dx$.

Proof that $\frac{e^{st}}{2\pi i}$ is an orthogonal basis.

Standard way of finding a inverse Laplace transform

Proof of $\int_0^\infty f(x)g(x)\,dx = \int_0^\infty \mathcal{L}\{f(x)\}\mathcal{L}^{-1}\{g(x)\}\,ds$

What is $\int_0^\infty \log\left(\Gamma(x)\right)e^{-sx}dx$?

Computing $\mathcal{L}^{-1}\left\{\frac{s}{(s + a)^2 + b^2}\right\}$

Solving an ODE with a piecewise function

Evaluating $\int\limits_0^\infty \mathcal{e}^{-x}\ln^{2}x\,dx$

Applying dead time (pure time delay) after inverse Laplace

Can't solve this ODE using Laplace transforms!

Broken Usage of Laplace Transforms

Solution to this second order linear differential equation with variable coefficients

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