Laplace

L{f(t)} = \int_{0}^{\infty} f(t) e^{-st} dt

1/s

1

1/s^2

1/(s+a)

\frac{\omega}{s^2 + \omega^2}

\frac{s}{s^2 + \omega^2}

L\{e^{-at} f(t)\} = F(s+a)

L\{f(t-t_0)\} = e^{-st_0} F(s)

s F(s) - f(0)

L\{\int_0^t f(\tau) d\tau\} = \frac{1}{s} F(s)

\lim_{t \to \infty} f(t) = \lim_{s \to 0} s F(s)

\lim_{t \to 0} f(t) = \lim_{s \to \infty} s F(s)

L\{f * g\} = F(s) \cdot G(s)

\frac{n!}{s^{n+1}}

-\frac{d}{ds} F(s)

\frac{H}{s}(1 - e^{-sT})

(s+a)^2 + \omega^2

t \cdot e^{-at}

s^2 F(s) - s f(0) - f'(0)

L\{a f + b g\} = a F + b G

Entspricht s \to 0

s = \sigma + j\omega

Zerlegung in Grundformen

2 / s^3