1. ## Delta Function

I just hate this function with a love.

Can somebody possibly explain to me how possibly it makes sense?

1)d(x) = 0 almost everywhere, then INT (-inf,inf)d(x)=0.
That is a theorem.

2)If L(f(x)) = L(g(x)) where L is Laplace transform then f(x)=g(x). Yet d(x) contradicts uniqueness.

Is the rule that mathemations just avoid this "function" and engineers just use it without and problems?

2. Originally Posted by ThePerfectHacker
I just hate this function with a love.

Can somebody possibly explain to me how possibly it makes sense?

1)d(x) = 0 almost everywhere, then INT (-inf,inf)d(x)=0.
That is a theorem.

2)If L(f(x)) = L(g(x)) where L is Laplace transform then f(x)=g(x). Yet d(x) contradicts uniqueness.

Is the rule that mathemations just avoid this "function" and engineers just use it without and problems?
No its that we don't bother to tell engineers about generalised functions, the
theory of which justifies most of the antics of engineers and physicist with
the delta function and its relations (like the derivative of the delta function!).

There are a number of theories of generalised functions is that of Schwartz
Distributions. You can start here though its does not look as comprehensive
as I would like its a good place to start.

RonL

3. Originally Posted by ThePerfectHacker
I just hate this function with a love.

Can somebody possibly explain to me how possibly it makes sense?
Perhaps your problem is that it is not a function but a distribution.

-Dan

4. Originally Posted by topsquark
Perhaps your problem is that it is not a function but a distribution.

-Dan
What do you mean by that? Probability distribtion?
I barely know any probability theory.

5. Originally Posted by ThePerfectHacker
What do you mean by that? Probability distribtion?
I barely know any probability theory.
Follow the link in my post and you will find that "distribution" is one of the
names for at least one model of generalised function.

RonL

6. Originally Posted by ThePerfectHacker
What do you mean by that? Probability distribtion?
I barely know any probability theory.
Although it is often named "delta function", it is actually not a function
Accordingly, you should be careful when trying to apply theorems proven for functions.