I'm not entirely sure. I do realize that there should be a negative inside the phi test function but I omitted it because it's zero anyway and I would have had to account for it if the delta function was something like (x-a), but here I didn't. However, when I do the substitution I have to deal with a negative u differential which makes the whole function negative in my mind.BvU said:Wouldn't that yield ##\phi(-0)## instead of ##-\phi(0)## ?
The delta function, denoted as δ(x), is a mathematical concept in calculus that represents a function that is zero everywhere except at x = 0, where it is infinite. It is also known as the Dirac delta function, named after physicist Paul Dirac.
The delta function is commonly used in science to model point sources, such as the mass or charge of a particle concentrated at a single point. It is also used in solving differential equations and in Fourier analysis to represent a single frequency component in a signal.
The delta function has several important properties, including: it is zero everywhere except at x = 0, its integral over all real numbers is equal to 1, and it is infinitely tall and infinitely narrow. It also follows the sifting property, where it can "sift out" a specific value from an integral.
No, the delta function cannot be graphed in the traditional sense as it is infinitely tall and infinitely narrow. However, it can be represented as a spike at x = 0 on a graph with the y-axis representing its value.
The delta function and the Kronecker delta are closely related, but they are not the same thing. The Kronecker delta, denoted as δij, is a discrete version of the delta function and is equal to 1 when i = j and 0 otherwise. It is commonly used in linear algebra and discrete mathematics.