Laplace関数の変換表 - Internet Explorer 2.0

Laplace関数の変換表

Diracのデルタ関数$ \delta(t): $ \mathcal{L} \left\lbrack \delta(t) \right\rbrack = 1

単位ユニット関数$ u_s(t): $ \mathcal{L} \left\lbrack u_s \right\rbrack = \frac{1}{s}

$ t^n: $ \mathcal{L} \left\lbrack t^n \right\rbrack = \frac{n!}{s^{n+1}}

特に

$ 1: $ \mathcal{L}\lbrack 1 \rbrack = \frac{1}{s}

$ t: $ \mathcal{L} \left\lbrack t \right\rbrack = \frac{1}{s^2}

$ e^{-at}t^n: $ \mathcal{L} \left\lbrack e^{-at}t^n \right\rbrack = \frac{n!}{(s+a)^{n+1}}

特に

$ e^{-at}: $ \mathcal{L} \left\lbrack e^{-at} \right\rbrack = \frac{1}{s+a}

$ e^{-at} \sin \omega t: $ \mathcal{L} \left\lbrack e^{-at} \sin \omega t \right\rbrack = \frac{\omega}{(s+a)^2+\omega^2}

$ \sin \omega t: $ \mathcal{L} \left\lbrack \sin \omega t \right\rbrack = \frac{\omega}{s^2+\omega^2}

$ e^{-at} \cos \omega t: $ \mathcal{L} \left\lbrack e^{-at} \cos \omega t \right\rbrack = \frac{s+a}{(s+a)^2+\omega^2}

$ \cos \omega t: $ \mathcal{L} \left\lbrack \cos \omega t \right\rbrack = \frac{s}{s^2+\omega^2}

$ f'(t): $ \mathcal{L} \left\lbrack f'(t) \right\rbrack = sF(s) - f(0)