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Impulse Function

Unit Step Function

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<math>\int _{-\infty} ^{t} u(s) \, ds = \left\{

 \begin{array}{l l}

0, & \quad \mbox{if $t<0$}\\ \int _0 ^t \, ds & \quad \mbox{if $t \geq 0$}\\ \end{array} \right\} = t u(t)math>