]> $$\mathit{f}\left(\mathit{t}\right)$$ $$\mathit{F}\left(\mathit{s}\right)$$ $$f\prime \left(t\right)$$ $$sF\left(s\right)-f\left(0\right)$$ $$f″\left(t\right)$$ $$s^{2}F\left(s\right)-sf\left(0\right)-f\prime \left(0\right)$$ $$\frac{{\mathit{d}}^{\mathit{n}}\mathit{f}\left(\mathit{t}\right)}{\mathit{d}{\mathit{t}}^{\mathit{n}}}$$ $$s^{n}F\left(s\right)-\sum _{i=0}^{n-1}{s}^{n-1-i}{f}^{\left(i\right)}\left(0\right)$$ $$f\left(t-t_0\right)u\left(t-t_0\right)$$ $$F\left(s\right)e^{-s{t}_0}$$ $$\underset{0}{\overset{t}{\int }}f\left(\tau \right)d\tau$$ $$\frac{1}{s}F\left(s\right)$$ $$f\left(t-\tau \right)$$ $$e^{-s\tau }F\left(s\right)$$ $$e^{-at}f\left(t\right)$$ $$F\left(s+a\right)$$ $$f\left(0\right)=\underset{t\to 0}{\lim }f\left(t\right)=\underset{s\to \infty }{\lim }sF\left(s\right)$$ $$f\left(\infty \right)=\underset{t\to \infty }{\lim }f\left(t\right)=\underset{s\to 0}{\lim }sF\left(s\right)$$ $$-t·f\left(t\right)$$ $$\frac{d}{ds}F\left(s\right)$$ $$\delta \left(t\right)$$ $$1$$ $${\delta }_{-1}\left(t\right)\text{or}1$$ $$\frac{1}{s}$$ $$e^{-at}$$ $$\frac{1}{s+a}$$ $$t$$ $$\frac{1}{s^2}$$ $$\sin \left(at\right)$$ $$\frac{a}{s^2+a^2}$$ $$\cos \left(at\right)$$ $$\frac{s}{s^2+a^2}$$