MATH 308 Lecture 24

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Lecture Notes

In Boston for ICTCM Conference

Dirac Delta Function

Essentially the derivative of the Heaviside function:

$\delta (x)={\begin{cases}\infty &x=0\\0&{\text{otherwise}}\end{cases}}$

Integration property:

$\int _{-\infty }^{\infty }f(x)\,\delta (x)\,\mathrm {d} x=f(0)$ for any interval containing $x=0$

Laplace Transform

${\mathcal {L}}\left\{\delta (t-c)\right\}=\mathrm {e} ^{-s\,c}$