- #1

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**Dirac function :(**

Hello everyone...

I have some triple with my PDEs course especially with the Dirac function.

How can I prove it is discontinuous function?

I do not know where can I start...

Could somebody help me, please.

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- Thread starter Aroma2010
- Start date

- #1

- 1

- 0

Hello everyone...

I have some triple with my PDEs course especially with the Dirac function.

How can I prove it is discontinuous function?

I do not know where can I start...

Could somebody help me, please.

- #2

- 116

- 0

Well, for a start, the Dirac "function" is not even considered a function. It doesn't qualify for it. There are two approaches two define it. You can considere it as a limit of several continuous sequences of functions, for example:

[tex]\delta_{n}=\frac{1}{n\sqrt{\pi}} e^{-x^{2}/n^{2}} , n\rightarrow 0 [/tex]

is one such sequence. The limit, however, is not defined as a function. The right name is

- #3

- 12,122

- 160

(Moderator's note: thread moved from "Differential Equations")

Start with the definition of a continuous function. At least one of the conditions is not satisfied, at at least one value ofHello everyone...

I have some triple with my PDEs course especially with the Dirac function.

How can I prove it is discontinuous function?

I do not know where can I start...

Could somebody help me, please.

- #4

- 160

- 0

Aroma2010 said:I have some triple with my PDEs course especially with the Dirac function.

How can I prove it is discontinuous function?

I do not know where can I start...

Could somebody help me, please.

It's pretty simple really. Just prove that the left and right limits at 0 are 0 (pretty easy), so in order to be continuous, f(0) must be 0, but it isn't, QED.

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