https://www.physicsforums.com/showthread.php?t=73447(adsbygoogle = window.adsbygoogle || []).push({});

I saw the above tutorial by arildno and looked at how he defined the Dirac Delta "function" as a functional. But isn't there a more easier way to do this. I have seen the following definition in a lot of textbooks.

[tex]\delta(t) \triangleq \lim_{\epsilon \to 0} \frac{1}{\epsilon} \Pi\Big(\frac{t}{\epsilon}\Big)[/tex]

where [tex]\Pi(t)[/tex] is the gate function and is defined as

[tex]

\Pi (t) :=

\begin{cases}

0 & \mbox{ for } |x| > \frac{1}{2} \\

\frac{1}{2} & \mbox{ for } |x| = \frac{1}{2} \\

1 & \mbox{ for } |x| < \frac{1}{2},

\end{cases}

[/tex]

What's wrong by defining the delta function in this way?

**Physics Forums - The Fusion of Science and Community**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Defining Dirac Delta Function

Loading...

Similar Threads - Defining Dirac Delta | Date |
---|---|

I Convergence of a recursively defined sequence | Mar 7, 2018 |

I Second derivative of a curve defined by parametric equations | Mar 1, 2017 |

A Inverse Laplace transform of a piecewise defined function | Feb 17, 2017 |

A Taylor/Maclaurin series for piecewise defined function | Feb 17, 2017 |

Use of Dirac delta to define an inverse | Dec 14, 2011 |

**Physics Forums - The Fusion of Science and Community**