Slovník originálov a ich Laplaceových obrazov
|
| $f(t)$ - Originál |
$F(s)$ - Obraz |
| $$\delta (t)$$ |
$$1$$ |
| $$1 (t)$$ |
$${1}\over{s}$$ |
| $$A \cdot 1 (t)$$ |
$${A}\over{s}$$ |
| $$e^{-at} \cdot 1(t)$$ |
$${1}\over{s+a}$$ |
| $$e^{at} \cdot 1(t)$$ |
$${1}\over{s-a}$$ |
| $$A t \cdot 1 (t)$$ |
$${A}\over{s^2}$$ |
| $$A {{1} \over {(n-1)!}} t^{n-1} \cdot 1 (t), n>1$$ |
$${A}\over{s^n}$$ |
| $$t e^{-at} \cdot 1 (t)$$ |
$${1}\over{(s+a)^2}$$ |
| $${{1} \over {(n-1)!}} t^{n-1} \cdot 1 (t), n \geq 1$$ |
$${1}\over{(s+a)^n}$$ |
| $$\sin (\omega t ) \cdot 1(t)$$ |
$${\omega}\over{s^2 + \omega^2}$$ |
| $$\cos (\omega t ) \cdot 1(t)$$ |
$${s}\over{s^2 + \omega^2}$$ |
| $$ e^{-at}\sin (\omega t ) \cdot 1(t)$$ |
$${\omega}\over{(s+a)^2 + \omega^2}$$ |
| $$e^{-at} \cos (\omega t ) \cdot 1(t)$$ |
$${s+a}\over{(s+a)^2 + \omega^2}$$ |
| $$A \cdot f(t)$$ |
$$A \cdot F(s)$$ |
| $$A_1 \cdot f_1 (t) + A_2 \cdot f_2 (t)$$ |
$$A_1 \cdot F_1 (s) + A_2 \cdot F_2 (s)$$ |
| $$f'(t)$$ |
$$sF(s)-f(0)$$ |
| $$f^{(n)}(t)$$ |
$$s^n F(s) - s^{n-1} f(0) - s^{n-2} f'(0) -\\ \dots - f^{(n-1)}(0) $$ |
| $$\int_{0}^{t} f(\tau) d\tau$$ |
$${F(s)}\over{s}$$ |
| $$\text{lim}_{t\rightarrow \infty} f(t)$$ |
$$\text{lim}_{s\rightarrow 0} [sF(s)]$$ |
| $$\text{lim}_{t\rightarrow 0} f(t)$$ |
$$\text{lim}_{s\rightarrow \infty} [sF(s)]$$ |
| $$\text{lim}_{t\rightarrow \infty} f'(t)$$ |
$$\text{lim}_{s\rightarrow 0} [s^2 F(s)]$$ |
| $$\text{lim}_{t\rightarrow 0} f'(t)$$ |
$$\text{lim}_{s\rightarrow \infty} [s^2 F(s)]$$ |
