Dirac delta function | Laplace transform | Differential Equations | Khan Academy

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Introduction to the Dirac Delta Function
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Differential Equations on Khan Academy: Differential equations, separable equations, exact equations, integrating factors, homogeneous equations.
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[@kaitanuba]

I really wish I was born maybe 10 years later. Because by then khanacademy would have probably covered the majority of higher college courses like Circuits and Linear Systems. I am really having a hard time understanding such courses right now due in part to the fact that my uni's lectures are nowhere as intuitive as your videos.

[@ramirosandoval41]

spoiler, they never did

[@shehneelajamil8284]

so how are you doing now ?? :P

[@mahdiamiri4336]

@@shehneelajamil8284 :))))

[@RSivaSanjayChannel]

Ahem

[@kamrynshepherd8156]

I know im asking the wrong place but does anybody know a tool to get back into an Instagram account..? I stupidly forgot my login password. I would love any help you can offer me!

[@robertschlesinger1342]

I might add a couple of credible anecdotes regarding Paul A. M. Dirac. A French physicist came to Dirac's home to discuss some cutting edge physics. The physicist was escorted into Dirac's study and he preceded for some time, trying with great difficulty to explain his work in English to Dirac. The physicist was clearly having considerable frustration with his limited spoken English. After quite some time, Dirac's sister, Betty, entered the study with some tea and biscuits, speaking fluent French, and wherein Dirac responded in fluent French. The French physicist who had spent considerable time frustrated in trying to express himself in English inquired of Dirac: Why didn't you tell me you spoke French. Dirac replied: You didn't ask. Another anecdote is from his days at Florida State University. The Physics Department held seminars which Dirac would often attend, sitting near the front row. He appeared to be dozing off throughout the presentations, but during the question & answer period, he would make brilliant comments and ask appropriate questions. He seemed asleep, but was all the while quite lucid.

[@carultch]

Is this really an event that happened to Paul Dirac, or is this a joke about how he is known for a function that represents a sudden surprise?

[@robertschlesinger1342]

@@carultch It is said to be a true account.

[@blueschewsmith]

Just wanted to let you know Sal, Dirac is pronounced with a harsh 'a' sound as in the end of 'attack'. We have a library at FSU named after him. I'm very proud to learn this subject at the university where the man who invented it taught.

[@neutral_positron]

No you are learning this subject over on youtube

[@WichitaTV]

"twice the infinity" - that`s epic!

[@domgesh392]

Yes

[@juanvolpacchio]

I used to view this videos 12 years ago while going through my chemical engineer bachelor's degree. Thank you very much for your content! I really appreciate your help at that time!

[@KSM94K]

How are you doing now sir?

[@georgepp98]

Sir, you just lighted my mind up this night and all i can do is to thank you so much!

[@mookieoftheshire]

Sal was beating dead horses for 17 minutes

[@tyomero]

Thanks! I'm trying to understand the neural response function and this was very helpful, I didn't get that the value of the integral is part of the definition. Thanks!

[@jayoberlander2954]

Kahn, will you please make some videos dealing with topology and other higher maths? You'll probably never see this, but it's worth a try.

[@xoppa09]

Sal needs college professors to get on this bandwagon, and help make this kind of video. I have seen a few good upper level undergraduate maths but they are scattered. Khan academy organizes it.

[@twokharacters]

This was an excellent refresher going to into senior mol. spectroscopy lab after having taken dif. eq. a few semesters ago.

[@diggitycat6233]

When you're OCD and Sal finishes that delta at 3:03

[@OriginalSchaffino]

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

[@johnteoss]

Thank you :) U helped me understand whats behind all the things my lecturer tought in class haha, good job!

[@uteroot]

helpful! i see your video when i taking linear algebra last semester. now i takes signals and system course and i need you too! thanks a lot a lot!!!

[@LokendraSD]

Thank You! It was very helpful introduction to Dirac delta function!

[@tonmandude]

Sometimes, I wish my professor's would explain it like this.

[@wangnick1728]

Pretty Thanks! Great presentation!

[@Ben2G]

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

[@quintinmakwe176]

Absolutely blown away! Please how can one come up with intuition like this around any topic?

[@TheGoldenHawkz]

I love this guy! Superb explanation!

[@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.

[@atogh]

i am done watching but best explanation so far

[@monira007]

It was an excellent tutorial.Really helpful.Please do a tutorial in Fourier Transform. I am struggling for it badly.Thanks

[@bosanac10109]

''[...] will never reach infinity.'' That is one hell of a true statement, my good sir.

[@BoZhaoengineering]

the best interpretation of Delta function. intuitive.

[@sil3nt9]

Excellent explanations!, thank you very much

[@bethtubechika]

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

[@mollierdiag]

Much appreciated, thank you.

[@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.

[@tristanserdyuk7438]

Fantastic. Crystal clear now.

[@ianroskow7933]

30 minutes worth of videos > 3 hours of class lecture.

[@ninabutterfly1000]

very interesting video , thank you Khan Academy.

[@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.

[@HellaPerformance]

Sal this is CRAZY TALK. CRAZY TALK I SAY.

[@patriciawulf3830]

You could make a Dr. Seuss about Dirac Delta functions: "Two tau, new tau, new tau, two tau..."😉

[@olddynamite]

This math reminds me of the integration of the normal distribution and Tchebychev's theorem taken to the limit.

[@barnettb901]

he has a good explanation of this

[@AAAAAAAAAAAAAAAAAAAAHH]

This video is way funnier than I expected it to be

[@cliffhanger625]

Beautiful, Sal. Thanks.

[@priyabajaj2224]

i have seen all the videos from 1 to 40... please elaborate that how the force can be a direc delta function that is from 16:35 to 16:58 mins ... hoping to hear u soon .

[@nathanieltalker6532]

Hey great video. But what happens when you multiply t in the dirac delta function: DDF(■t)? ThankU for the video

[@sjsawyer]

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

[@user-hs7qg5tt8t]

so so so so AMAZING omg!!!

[@elnaeemabdalla9061]

Brilliant mind ,thanks

[@grimshawr]

Brilliant!

[@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.

[@briantsedesign]

BEST Explaination !!!!

[@LEVIBAILEY5384]

Thanks so much!

[@zackm5693]

great as always

[@subhashthenua7404]

how greatly you explain very nice awesome

[@jknaresh]

Nicely explained...!

[@hlumelomkunana9070]

brilliant stuff

[@chengbinhou5432]

impressive!

[@rupikapendyala6335]

great explanation

[@gauravgill8889]

u r amazing 😃😃

[@AnuarPhysics]

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

[@whitesummer1503]

vauuuuu this was so helpful, I like your way of explaining :)

[@ghasemmanouchrhti10]

helpful, thanks

[@meafale]

remarkable

[@joegartland]

You are incredible and I love you

[@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.

[@Chroui]

yes

[@JakeDavidHarrison]

I thought he was taking tau, as the constant (2pi) initially, i was waiting for him to explain why tau was of importance.

[@Ensign_Cthulhu]

08:00 Excellent explanation of how to arrive at the delta function, but seems a little backwards. In my opinion, you would have done better to start with your tau example and then finish by defining the delta function as the limit as tau tends to zero of the integral. You might even have considered another variable (say, a) to avoid potential confusion of t and tau. In real life, of course, the magnitude of the spike is going to depend on voltage/current available and will never reach infinity.

[@michaelboateng6413]

best so far!

[@MrMackxl65]

So Lovely!

[@abdelrahmanelattar]

Thanks alot ...

[@shyamumich]

Thanks for this video

[@knowledge90s93]

If the output of a discrete system is y(k) = 2^k for an input u(k) = 3^k what is the system's impulse response g(1) given that g(0) = 2 a) 6 b)3 c) -4 d) -2

[@yaaqoubkeddaoui2970]

I just wanna know what's the tablet or kind of tool used for this demonstration

[@31428571J]

Sal, your 'writing' is becoming artistic:-)

[@pulkitmidha5710]

Hey, Sal, we have learnt in our integral calculus class that integral of ANY function from a point (say, a)to the same point 'a' is equal to zero. Isn't that contradicting to Dirac Delta Function?

[@alanchoon9040]

+Pulkit Midha I think what u are referring to is a function value that is finite. Note that the Dirac Delta Function refers to a point where the function value becomes infinitely large (or close to infinitely large). Either that comes into play or it is not really a function in a conventional sense. It is a good question and I am curious if anyone has a definite answer..

[@jiyoung719]

Omg.. Thx so muchhhhh!!!! Love it :)

[@CrispyCyclicCenk]

thank you very much

[@eddietime1811]

It makes sense that the integral is 1. You don’t need to just define it. Take this limit lim. x->0 of x * (1/x) we know that to be one, but we know that would also be the Area of something with 0 width and a height of infinity

[@prgalois]

I love you Sal, this video made Dirac Delta less counter-intuitive.

[@babitadas4887]

Good one

[@angomngamsingmeetei6434]

is there any subject that this dont know ? My mind is goin crazy,,

[@Takanayagi88]

Wait! Khan Academy has high level maths now? You are heroes :3 I'll bet someone is going to coment "this is not high level maths"

[@pianoclassico718]

this is not a high level maths , haha , but tbh , it really isn't , it's rather an introduction to ''high level'' maths

[@SilasDrewchin]

I feel like the effect of lockdowns on economic systems could be modeled using these functions. Sudden stop of everything; carry on.

[@adame1474]

but if you derive the derac delta function once it has been integrated (i.e. equals 1) then you get zero, which isn't an infinite jump at the aforementioned point. So how does that work?

[@AKUMAR281]

thanks a lot sir

[@dasfeuchteauge802]

NO I'M DEFINING IT!

[@wendyloo262]

14:24 The equation is *sum of forces*=ma This will make the equation correct and clear up the "F" notation redundancy.

[@EvanCooperful]

It's an improper integral you need to use limits, you can't just apply the normal integral rules.

[@katlee92]

what sketch tablet do you use?

[@esperanzazagal7241]

What playlist is this in?

[@Bilal_Alasha]

thank you

[@MinecraftsAssassin]

Around 8:45 , what is stopping someone from choosing a different relationship between the range and magnitude to be different than 2 ×.5? E.g. a magnitude of (1/3tau) across a range of -tau -> +tau. The result would be the same but the idea would still push the area to be 2/3 instead of 1 as the lim tau->0

[@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.

[@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!!!

[@madjourbilel1734]

You are the best

[@zakiatithi2042]

i love khan academy

[@ThaRealChuckD]

It is only 1 when the pulse occurs.

[@benjaminbrady2385]

Looks like a derivative of unit step function sub 0

[@jollyjokress3852]

I don't get why t-3 would be the area above 3? can someone explain? Thanks!

[@jollyjokress3852]

Oh I get it know (It's because the dirac delta function is "always the same" so at point 3 you have to subtract 3 from t to retain the original dirac delta function... ah okay ;))

[@spandan62]

When we say delta(x) the function tends to infinity at x=0...but its is not 0 when the function >>x nearly tends to zero..it is very small infinite small but its not zero so while taking area we take the thin strip...when we say delta (x-3) then at x=3 function tends to infinity so we integrate near it to get area...when u put limits of t or x ..it is very small limit tends to 0

[@an_orange8911]

when did he say that?

[@mohdnadeem9929]

thanku

[@Seedofwinter]

Khan, maybe you should think of running a business that shows potential teachers how to be good lecturers. There is a problem in America of people not being good lecturers

[@khongdong1096]

But it seems, at 8:00, the delta_tau function isn't continuous, hence can't have an integration, right?

[@engineerahmed7248]

Dirac delta function application is impact eg of cars, or car on a bike on sudden road bump

[@deepvision8877]

I don't think that the limit approach is a good argument to show that the integral of the Dirac delta function is 1. Consider a similar function F(t) where it's only defined between the bounds of -d and d. However, its value is 1/3d not 1/2d in this case. The area of this rectangular region would be 2/3. Now, using the same argument one can show that the limit as d goes to zero that 1/3d goes to infinity. Therefore the function F(t) approaches the same value in its limit as D_t(t) which is the Dirac delta function. Therefore using this argument one can say that the integral from -infinity to infinity of the Dirac delta function is 2/3. I could then generalize to having the function value being 1/nd were n is any integer. Then the value of the integral would be 2/n which is just another constant. Therefore all real numbers would satisfy the integral equation of the Dirac delta function. Therefore if the argument is valid, the Dirac delta function should not have a defined intergral. Meaning that the integral should not exist.