Calculus with the Dirac Delta Function

In this video I take a closer look at properties of the Dirac Delta Function involving integrals and derivatives.

For more videos in this series visit:

[baqerghezi]

I have just found a treasure, your channel is great. Thank you.

[nitroman]

Hi This great video, I have a question in the part where you integrated f(x)delta(x) using integration by parts. How did the f(x)delta(x) go to zero when you integrated from - infinity to +infinity. In the previous video, you said that when we integrate the delta function, the value is one…

[civl]

at 6:11, if f(x)=x, can we still say f(x）*delta（x) = 0 at +/-infinity for the first term from integration by parts？coz its like infinity times zero

[vaooch]

(to define the primitive of the delta functino/distribution or the heavyside function) In my textbook it says this as well but how is x included in the interval when x>0 but not when x < 0, the delta function is infinite at x = 0, so it would seem logical to me that the heavyside is 0 for both occassions. It's by definition symmetrical as well so I don't understand this.

[TefJLives]

Any problem with writing \delta^{(n)}(x) = (-1)^n \delta(x) (d/dx)^n ?

[dominicellis]

So why is there so much in math that’s not well defined because the true nature of reality is infinite all we perceive is the imaginary and real components but we can’t perceive the other dimensions like we see the world quaternionaclly but in truth it’s an octonion system