Laplace Transform Properties

8 flashcards · Mathematics · by Andrea

1. Af(x)

   AF(s)

2. f1(x)+f2(x)

   F1(s)+F2(s)

3. df(t)dt\frac{df(t)}{dt}dtdf(t)​

   sF(s)−f(0+)sF(s) - f(0^+)sF(s)−f(0+)

4. g(t)=∫f(t) dtg(t) = \int f(t)\ dtg(t)=∫f(t) dt

   F(s)s+g(0+)s\frac{F(s)}{s} + \frac{g(0^+)}{s}sF(s)​+sg(0+)​

5. lim⁡t→0f(t)\lim_{t \to 0} f(t)limt→0​f(t)

   lim⁡t→∞sF(s)\lim_ {t \to \infty} sF(s)limt→∞​sF(s)

6. lim⁡t→∞f(t)\lim_ {t \to \infty} f(t)limt→∞​f(t)

   lim⁡s→0sF(s)\lim_ {s \to 0} sF(s)lims→0​sF(s)

7. f(t−T)u(t−T)f(t-T)u(t-T)f(t−T)u(t−T)

   e−sTF(s)e^{-sT}F(s)e−sTF(s)

8. f(t)=f(t+T)f(t)=f(t+T)f(t)=f(t+T)

   F(s)(1−e−sT)\frac{F(s)}{(1-e^{-sT})}(1−e−sT)F(s)​ with F(s) = ∫T0f(t)e−st dt\int_{T}^{0} f(t)e^{-st} \, dt∫T0​f(t)e−stdt