Dirac Delta Function

[Obamanation154]

I can't even comprehend this. My brain hurts just looking at it.

[OriginalSchaffino]

It's midnight and I have school tomorrow but this is sooooo interesting; I love math.

[DarknessUnresolved]

Nerdgasm

[BoAs3d]

you are the BEST, best than my college instructor

[89rafa]

liked, faved, and subbed. I think its enough. =P

[JAZZMUTANTDEXTER]

hi

you said (14:30) THE FORCES AND THIS AND THIS AND THIS AND THIS......MASSE

MASSE????

ALL REGARDS

[dharnisha1234]

But whats the motivation under equaling F to delta(t-2)?? please explain. your great man!! thanks

[JAZZMUTANTDEXTER]

@dharnisha1234

HI

IT s just a example of system. introduice a difference (2) for illustrate, this shifted dirac operator related to the model of 2 copies of space time close together.

[davidenelson]

mind fuck

[AnuarPhysics]

Great! How do you make your videos? Which software and hardware do you use?

Thanks.

[trese0000]

Great Video, Very Intuitive things when they are explained well.

[cliffhanger625]

Beautiful, Sal. Thanks.

[TheLiberalSoup]

Sal, doesn't this make you sort of a quantum physicist? I mean, why didn't you go into the field of mathematical physics?

[Uskebasa]

Wonderful, loved it. Thanks, I really like the way you explained it!

One note: THE CARTESIAN PLANE!

Please, don't draw it with an arrow on each ending of the axes. It's a big mistake! Really big! Arrows are pointing the sense of the axes not their infinity! Please :'(

[SemperGumby]

This is a functional, not a function.

[ultraollie]

You could always view the dirac as some sort of element in the completion of function space in some metric. Also, I like to present this as some sort of "limit" of normal density functions whose standard deviations are going to zero (half of one anyway). This leads to a natural heuristic for the Laplace transform.

[kickniko]

Delta is not a function and it is not a "generalized function". It is a functional and its definition and investigation happens in general distribution theory. Naive explanations like "infinitely high and infitely narrow" are perhaps satisfactory for constructing "understandable pictures of the world" in physics theories that (mis)use it. But mathematics is something else. In fact, even writing δ(x) for the sense of "practical usage" in physics is completely incorrect and misleading.

[Eldooodarino]

@kickniko: Volume I of IM Gelfand's 6 volume set on Generalized Functions begins by describing the dirac delta function about like this video does.

[kickniko]

@Eldooodarino

Not really "about like this video does". Finest distinctions can make up a lot of difference in the strict language of pure mathematics.

But this of course is only the quite unimportant hair-splitting that bothers nobody else than mathematicians. Real men don't need such fine distinctions. ;-)

[cwxzeng]

Thank you Sal. You are amazing

[LeconsdAnalyse]

It`s NOT a function, but a functional.

[x1x2x3ct]

@LeconsdAnalyse its a GENERALIZED function, indeed

[sjsawyer]

Wow, the quality of this video is vastly superior to that of the last vid I have seen by you!

[vonlsh]

thx you helped me understand this

however my lecturer said "anybody that calls "Dirac measure' a 'Dirac Function', should have their mouth washed out with soap"...two seconds after he called it a function XD

[sanbabsdgreat]

this has helped me understand probability fuctions,,haha,,

[bryeinsteinmc2]

Do you have a video for Dirac notation bra and ket? | > and < |

[bhigr]

You can indeed call it a function, that is mathematically correct. However, the integral definition does not correspond to the standard definition of the integral. The Riemann-Integral of this function is not defined. The Lebesgue-Integral of this function is zero. If you call it instead a "dirac-integral", then your definition is just fine. Your example function is well chosen!

[mollierdiag]

Much appreciated, thank you.

[FreemanFighter94]

Nothing is more epic than reading this in Dirac's "Principles of Quantum Mechanics".

[sil3nt9]

Excellent explanations!, thank you very much

[dalcde]

@LeconsdAnalyse When you take the limit as x approaches 0, x does NOT equal zero. For example, lim x->0 x/x is 1, although it is not defined at x = 0.

[LeconsdAnalyse]

@dalcde Yes, you are correct. I was leading up to the two formal expressions in the clip: lim dτ(t)=δ(t) as τ→0+ and, lim ∫dτ(t)·dt=1 as τ→0+. Not even Lebesgue`s dominated convergence theorem can be used to justify the interchange of `lim` and `∫`. The clip deals with the Dirac delta `function` as the physicists do.

[Uskebasa]

@dalcde But if you do the limit of x->0 of (2+x)/3 is 2/3! X EQUAL zero!

Limit define X. Except where is not defined :D

[comebackata2]

Uhm isn't the integral of (1/ T = ln T )? how did it become ( T/2T )

[thehomette]

@comebackata2 the integral is actually 1/2tau where tau is a constant, and you're integrating with respect to T, not tau. If integrating wrt tau, the solution would indeed be ln(tau)/2 but instead it's T/2tau as it's integrated wrt T.

[SpecterReflector]

Dirac Delta Hyperfunction.

[demariass]

great, what is the technology used for the vid??

[alkalait]

You could have used L'Hopital's rule (which you just happened to introduce in another video) to justify the evaluation of the indeterminate limit of the intergral of the Dirac function.

[LeconsdAnalyse]

First the definition given in the clip is meaningless, since the "delta function" is null almost everywhere, so its integral must be equal to zero. Second it is to be understood that the integral being used is the Lebesgue integral.

[MrMackxl65]

So Lovely!

[imrama]

My god- what can't this guy do!!!

[adytzuw124]

very nice.....i`m loving it!

[Th33vilthing]

great video. clear voice, interesting tone, clear descriptions = win!

[TheKotassium]

@Th33vilthing *and* it's colourful! :D

[bethtubechika]

wao, thanks to you, i finally cracked it after all these years

[diabolico5]

Control engineering and signal processing 2 of the hardest subject in EEE

[billu8660]

agree

[Kosekans]

Is "beating a dead horse" an english / american saying? I was laughing so loud :-)))

[illicitTRUTH]

There is no point to beating a dead horse.

[dev777v]

should be "flogging a dead horse" Awesome vid!!!

[LanesAccount]

@Kosekans what is funny about mutalting dead animals, and what cave have you recently crawled out of cause its a well known saying. If you had a horse and it died from a sudden heart attack and then i just came out of no where with a bat and just started beating the shit out of it, would you be laughing then??? "god bless the dead" - 2Pac

[CharacterLimit]

@LanesAccount Wow, man, take a chill pill and relax. I'm pretty sure he was laughing at the expression, not the idea.

[jknaresh]

Nicely explained...!

[tampirloko]

on 7:40 1/2.tau could go outside of the integral: 1/(2.tau) int(-tau,tau) dt. I guess is easier to see that way!

[Riverdale270]

You can also use the Dirac Delta Function for modelling options. Suppose you have a 30% probability that an option will be worthless at maturity... Pretty hard to do with a pdf function I guess, so let's use this function at return = -100%... So we'll get a 0,3δ(x+1) in the x=-1 so that if the return is -100%, the integral of your function at that point will be 30%, while the rest will be described by the pdf or something.

[FHomeBrew]

Instead of unit step functions etc I usually use something like (2^(F*x))/(1+2^(F*x)) or 2^(-F*x^2)) with high F's. it's continuous and smooth, yet has almost the same shape. and in the limit it's a good enough approximation usually. Though this vid is really interesting :-D

[norwayte]

Very, very good. Could you made a video about the relation between Dirac Delta Function and the normal distribution? You "showed" the normal distribution indirectly in this video without words.

Keep on going.

[Penksimo]

I wish to know , how can I apply this to a real life problem , ,,,,i know i am soo behind !!! but i like it ,,, keep up the god work!!!

[magikarp1319]

Maybe you could use it for spectrometry. I've seen graphs like this in orgo lab. You could have a program use this to automatically recognize particles and molecules. I am genius! These videos rule!

[cb76tube]

Very nice.

[grimshawr]

Brilliant!