do you know what are delta function?

Question

delta function in physics, can you tell me a refrence book for such functions ?

Answer 1

As sciencewiz suggests, delta is a symbol representing change, but there is such thing as a delta function.

The delta "function" is best thought of as an impulse signal, or a blip that happens at a given point in time (we usually call this time t = 0).

It is not a function in a strict mathematical analysis sense, as the graph of a fuction cannot be a vertical line, while the graph of the delta "function" is a vertical line, of infinite length, at t = 0, and zero elsewhere. For this reason, it is sometimes also referred by engineers as the impulse symbol. Mathematical analysts would actually call it a distribution.

It has important applications in electrical engineering, as well as in physics.

The technical definition of the delta function has two parts:


Delta (x) = 0, when x is not euql to zero.

Integral [-infinity to infinity] Delta(x) dx = 1.

The delta function turns out, in a manner of speaking, to be the derivative of the unit step function H, where:

H(x) = 1 if x>0
= 0 if x<0.

I say "in a manner of speaking" because the derivative of H is not really defined at x = 0, so we have to look at the limit of a sequence of derivatives as x approaches 0 from each side.

I learned the Delta function in a graduate course in Fourier Analysis. The text I used there is the one I would recommend, even though it is not a physics book (unfortunately, it is not an inexpensive book):

The Fourier Transform and Its Applications
Ronald N. Bracewell
McGraw-Hill, 2000

Chapter 5

Also, see this web site for more background
http://en.wikipedia.org/wiki/Dirac_delta_function

Answer 2

Delta just indicates change...such as a change in temperature (delta T), change in time (delta t), change in pressure (delta p), etc.