阶跃函数¶

\[ \varepsilon(t) := \lim_{n \to \infty} \gamma_n(t) = \left\{\begin{matrix} 0, &t<0 \\ 1, &t>0 \end{matrix}\right. \]

\[ \int_{-\infty}^{t}\varepsilon(\tau)\mathrm{d}\tau=t\varepsilon(t) \]

\[ \int_{-\infty}^{t}\varepsilon(\tau)\varphi(\tau)\mathrm{d}\tau=\varepsilon(t)\int_{0}^{t}\varphi(\tau)\mathrm{d}\tau \]

\[ \int_{-\infty}^{+\infty }\varepsilon(t)\varphi(t) \mathrm{d}t=\int_{0}^{+\infty }\varphi(t) \mathrm{d}t \]

\[ \varepsilon(t)=\int_{-\infty}^{t}\delta(\tau)\mathrm{d}\tau \]