# Book to study Dirac delta function from a physics point of view [duplicate]

I am a beginning physics graduate student. I am often bewildered by the strange properties of the Dirac delta function such as:

1. $\delta (a x)= \frac{1}{a} \delta (x)$

2. The derivative of $\delta (x)$

etc etc.

Such strange properties of $\delta (x)$ are mentioned in the first chapter of Arfken-Weber (7th ed.) without proof. Please suggest me a book from which I can learn the minimum essential mathematics of $\delta (x)$ function that is required to study physics. I am not looking for an advanced mathematical treatment but the book should have the proofs of the theorems stated.

• For starters, $\delta(x)$ is considered to be a distribution as opposed to a function, if you're a mathematician that is. I've best understood the 'thing' as a the limit of a sequence of ever narrowing Gaussian distributions. Apr 4, 2016 at 19:16
• See e.g. this question. Apr 4, 2016 at 19:17
• $\int F(x)\delta(x-a)dx=F(a)$ is the only other property I ever needed to know beyond the two listed. Apr 4, 2016 at 19:27
• Possible duplicates: physics.stackexchange.com/q/127376/2451 Apr 4, 2016 at 19:28