ラプラス変換表
| \( f(t) \) | \( F(s) = \mathcal{L}[f(t)] \) |
|---|---|
| 1 | \(\dfrac{1}{s}\) |
| \( e^{at} \) | \( \dfrac{1}{s-a} \) |
| \(\sin a t\) | \(\dfrac{a}{s^2 + {a}^2} \) |
| \(\cos a t\) | \(\dfrac{s}{s^2 + {a}^2} \) |
| \(\sinh a t\) | \(\dfrac{a}{s^2 - {a}^2} \) |
| \(\cosh a t\) | \(\dfrac{s}{s^2 - {a}^2} \) |
| \(t\) | \(\dfrac{1}{s^2}\) |
| \(t^2\) | \(\dfrac{2}{s^3}\) |
| \(t^n\) \(n = 0, 1, 2, \cdots\) |
\(\dfrac{n!}{s^{n+1}}\) |
| \(\delta(t)\) | \(1\) |
| \(f(t-c)u(t-c)\) | \(e^{-cs} \mathcal{L}[f(t)]\) |