Week of 10/29

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Revision as of 15:14, 31 October 2007

A few examples of the importance of Gaussian distributions

It turns out that the FWHM is nontrivial: this link shows how to compute it

the answer turns out to be $2 \sqrt{2 \ln 2} \sigma \approx 2.3548 \sigma$

The fundamental property of the delta function: you must remember this

$\int _ a ^ b \delta (t - t_0) f(t) dt = f(t_0)$ if Failed to parse (Cannot write to or create math temp directory): t_0 \element [a,b] \,

$\int _ a ^ b \delta (t - t_0) f(t) dt = 0$ if Failed to parse (Cannot write to or create math temp directory): t_0 \notelement [a,b] \,

Two nice links on Sinc functions: from Mathworld and Wikipedia

The following two figures are from Barbara Romanowicz, a seismologist at the University of California, Berkeley.

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+The fundamental property of the delta function: you must remember this
+<math>\int _ a ^ b \delta (t - t_0) f(t) dt = f(t_0)</math> if <math>t_0 \element [a,b] \,</math>
+<math>\int _ a ^ b \delta (t - t_0) f(t) dt = 0</math> if <math>t_0 \notelement [a,b] \,</math>
 [http://www-history.mcs.st-and.ac.uk/history/Biographies/Dirac.html Paul Dirac's bio]