The Dirac Delta 'Function': How to model an impulse or infinite spike
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- Опубліковано 19 жов 2024
- In this introduction to the Dirac Delta Function we'll see how we can deal with something happening instantaneously like a hammer hit. We will model this impulse with a 'function' that is infinite at one point and zero everywhere else. But such a thing isn't really a function! Sometimes we called it a functional or a generalized function. Regardless, it is defined by its pleasing properties such as what happens when you integrate the dirac delta function multiplied by another function. It can also be thought of as the derivative of the step function. In our next video we will study the Laplace Transform of the Dirac Delta Function and see how we can use it when studying differential equations.
Watch the rest of the Laplace Transform series in my Differential Equations playlist here: • Laplace Transforms and...
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It's not even about distribution theory, but I found here a right place to learn about distribution theory. You're awesome in your job.
if you're doing quantum mechanics and you want a |psi|^2 function for a perfect point particle, the dirac delta function is 100% (probability joke) about distribution theory
Wow! You explained it really well. I've been trying to understand this Dirac Delta Function for about an hour now, and couldn't find any resources that explains it visually. Your explanation is just what I needed. Thank you.
I can' thank you enough for this video. We were doing generalized functions rigorously, and I was so lost. This explanation just made so much sense. Please consider making some rigorous advanced math videos! We need you!
I'm Doing My MS in Chemical Science at Indian Association for Cultivation of Science , We have a course on Mathematical and Computational Chemistry , this video really helped me a lot.
I’m doing blow at penn state
@@trexbattle lolll
Thank You, Dr!!!! A wonderful and clear explanation
Came here to hear the pronunciation of 'Dirac', forgot about it middway, ended up watching the whole video. Then realised No utterance of 'Dirac' but still, very bounding explanation.
dirac delta is one of those things like the unit circle or pi that just keeps appearing like whack a mole
your vector calculus helped me too much, very very grateful to you
Exceptional performance❤❤
Nyc comment 👍
Thank you Sir for explaining these concepts 🌻
The neatest explanation one can find on youtube ! Thanks
I didn't even know there is a mean value theorem for integrals. Thank you so much!
Excellent little explanation.
The Dirac distribution is the Fourier transform of unity and a special case of convolution, where A*f=g, g(x)=d(x-y). f(y)dy , if we imagine the gravitational interaction as a function of g(x) and the electromagnetic interaction as a function of f(y), then these forces (i.e. the lines of force) only interact when x is equal to y ( the Dirac impulse).
thats so cool
Thank you so much for that clear explanation.
I watched your linear algebra.It help me a lot. Thanks!
cool video. i remember first encountering this function in the context of point charges in EM theory.
Thank you. Once again, your videos are getting me through engineering school.
You are actually a legend
Thank you!
Thanks! Your content has helped me with conceptualizing many ideas presented in my EE courses.
so underrated...
Hi Trefor, I think you could be a great teacher but unfortunately I can't tolerate this thing that seems fashionable at the moment (especially among UK news reporters) of speeding up and slowing down speech for no apparent reason.
Amazing lecture and figures!
Great video and explanation! 👌
Great video as always! Could you elaborate on why the delta function isn't considered a function? At about 2:24 you mention that it's because the value at x=a isn't a number, but neither is x=0 for the function 1/x, so what's the difference between the two? Thanks!
Late reply but when defining 1/x you exclude 0 from the domain
Thanks a lot sir 🔥🔥🔥
Good explanation
Outstanding!!
The delta is in fact a function if you use the hyperreals. One model of it is a gaussian. It cannot be given as a real function because both its domain and range are not standard (infinitesimal and unlimited)
Thank you
the math God!
Do you have any good videos where a deeper dive is taken, not exactly mathy proofs but still deeper than this? I'm taking a theoretical methods class (physics based, math for physics.... so we're covering geometrical vectors, special functions, odes, pdes, matrices, bases, and more in 1 semester. The expectation isn't really "prove this for all cases" but still much more abstract than merely execution of a Laplace.
An example hw was to derive a generalized laplacian operator for a non-orthogonal coordinate system which was defined in Cartesian and then use it on that generalized system... so videos at the oddly specified level?
Sir That was some Good stufff
thank you :)
2:00 then a miracle happens as epsillon goes to zero, delta goes to infinity, but the integral stays = 1.
At 2:39, What if I want to dive deeper into the meaning of delta function ? Any recommendation for resources.
Nailed it
yessss, awesome video !
I don't understand why did someone decide that the area of a delta function is one? The same way one could take a rectangle with an area of 2 or above and shrink it to almost zero, the amplitude would jump also to infinity right? so why 1 and not 2 or any other number???
It’s just a convention, but a decent one as it means when you integrate you aren’t stretching other things by a number, just multiplying by 1
This is just like the unit circle has a radius with 1, that is simply a convention. Besides, the Dirac function has a lot to do with quantum physics
great video :)
Doesn't the Mean Value Theorem only apply to continuous functions?
On an continous interval
Sir I have a humble request please make a video on tensor calculus and vector calculus of curves and vector calculus of vector field. I have a question in your video of difference between single and multivariate calculus you told us about rectangular prisms using two integral signs one with respect to x and the other with respect to y means integrating the function with respect to x and y at the same time. Here can we do the reverse means derivative of a multivariate function both with respect to x and y at the same time which we call mixed second order partial derivative? Why dont we call this total or complete derivative as you called the multivariate integral the total or complete integral and not second order complete integral? What is total or complete derivative? What does dz/dxdy tells us it surely doesn't tells us about the tangent plane. Then what is this and why it is not in practical use? One example is z= 2x²y +4xy then dz/dxdy or dz/dxy = 2x+4 ..
Are dz/dxdy and dz/dxy same?
If not then which one of this is total derivative and which is complete derivative and in which direction it is pointed? I have heard somewhere that it tells about the torsion of geodetic . This sounds very unintuitive. Sir please make a detailed video on this about this misconception. Please sir, you are the best.
"Step-function... what are you doing back there..!" 😲😲😈😈
🤩
am not doing any math related study and have never done one. i'm a social worker. how did i get here and my brain hurts.
Ah the UA-cam algorithm at its finest
My brains cheers for such amazing content
So it's the derivative of functions that don't have a derivative.
You are like saying that the ice creams expired and so they don't exist.......
For an function to be differentiable it must be continuous, a flat line have no change in time........
Gbage. What was the doctorate for???
Your description of Delta function is not correct. The integral of Delta function is Zero, not 1 by Lebesgue integral theory, because Delta function takes infinity at t=a, and takes Zero except t=a on the board. You do not understand the elementary rule in mathematics, that is, the change of the operation "limit epsilon-->Zero" and "taking integral" is not permitted. I guess that you do not know Distribution theory and Lebesgue integral theory.
666 likes!