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:

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

Integration property:

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

Laplace Transform

${ℒ}\{\delta (t-c)\}={\mathrm{e}}^{-sc}$