Category:Laplace Transforms involving Sine Function
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This category contains examples of Laplace transforms involving the sine function.
Let $f: \R_{\ge 0} \to \mathbb F$ be a function of a real variable $t$, where $\mathbb F \in \set {\R, \C}$.
The Laplace transform of $f$, denoted $\laptrans f$ or $F$, is defined as:
- $\ds \laptrans {\map f t} = \map F s = \int_0^{\to +\infty} e^{-s t} \map f t \rd t$
whenever this improper integral converges.
If this improper integral does not converge, then $\laptrans {\map f t}$ does not exist.
Subcategories
This category has the following 3 subcategories, out of 3 total.
L
- Laplace Transform of Sine (9 P)
Pages in category "Laplace Transforms involving Sine Function"
The following 21 pages are in this category, out of 21 total.
I
- Inverse Laplace Transform of 1 over (s^2 + a^2)^3
- Inverse Laplace Transform of 1 over s^3 + a^3
- Inverse Laplace Transform of s over (s^2 + a^2)^3
- Inverse Laplace Transform of s over s^3 + a^3
- Inverse Laplace Transform of s^2 over (s^2 + a^2)^3
- Inverse Laplace Transform of s^3 over (s^2 + a^2)^3
- Inverse Laplace Transform of s^4 over (s^2 + a^2)^3
- Inverse Laplace Transform of s^5 over (s^2 + a^2)^3
L
- Laplace Transform of cosine a t - half a t sine a t
- Laplace Transform of Exponential times Sine
- Laplace Transform of Sine
- Laplace Transform of sine a t + a t cosine a t over 2 a
- Laplace Transform of sine a t - a t cosine a t over 2 a^3
- Laplace Transform of Sine of Root
- Laplace Transform of Sine of t over t
- Laplace Transform of t sine a t
- Laplace Transform of t sine a t over 2 a
- Laplace Transform of t^2 sine a t
- Laplace Transform of t^2 sine a t over 2 a
- Laplace Transform of t^3 sine a t
- Laplace Transform of t^3 sine a t over 24 a