]> $$\underset{-\infty }{\overset{\infty }{\int }}\delta \left(t\right)dt=1$$ $$\underset{-\infty }{\overset{\infty }{\int }}\delta \left(t-\tau \right)dt=1$$ $$x\left(\tau \right)=\underset{-\infty }{\overset{\infty }{\int }}x\left(t\right)\delta \left(t-\tau \right)dt$$ $$\delta \left(-t\right)=\delta \left(t\right)$$ $$\delta \left(at\right)=\frac{1}{\left|a\right|}\delta \left(t\right)$$ $$\delta \left(t\right)=\frac{du\left(t\right)}{dt}$$ $$$$ $$f\left(t\right)\delta \left(t\right)=f\left(0\right)\delta \left(t\right)$$ $$f\left(t\right)\delta \left(\tau -t\right)=f\left(\tau \right)\delta \left(\tau -t\right)$$ $$f\left(\tau \right)\delta \left(t-\tau \right)=f\left(t\right)\delta \left(t-\tau \right)$$ $$$$ $$c_1\left(t\right)\ast c_2\left(t\right)=\underset{-\infty }{\overset{\infty }{\int }}{c}_1\left(\tau \right)c_2\left(t-\tau \right)d\tau =\underset{-\infty }{\overset{\infty }{\int }}{c}_1\left(t-\tau \right)c_2\left(\tau \right)d\tau$$ $$c_1\left(t\right)\ast c_2\left(t\right)=c_3\left(t\right)$$ $$c_1\left(t-{\tau }_1\right)\ast c_2\left(t\right)=c_3\left(t-{\tau }_1\right)$$ $$c_1\left(t-{\tau }_1\right)\ast c_2\left(t-{\tau }_2\right)=c_3\left(t-{\tau }_1-{\tau }_2\right)$$ $$f\left(t\right)\ast \delta \left(t\right)=f\left(t\right)$$