Laplace transform of the unit step function | Laplace transform | Khan Academy

[@ranXXX7]

To the author of this video, Man! For the first time I actually actually appreciate the luxury of KZbin, but it is particularly because of your life saving effort that I shall one day be able to boast that I know math. Not because I learnt it in school, but because I watched your videos. I thank you from the bottom of my heart!!!

[@SH7DShahad]

It's been 10 years, what are you in life now?

[@B0TZ]

@@SH7DShahad its been 8 months , how is your life now from before?

[@ayazmughal4058]

@@B0TZ its been 3 months now, how has your life been changed since you commented?

[@joshmather7879]

@@ayazmughal4058 its been one month, how has your life been since you commented?

[@karabovictor2007]

​​@@joshmather7879its been 10 months, how has your life been since you commented?

[@asemnafiz]

Which genius came up with this stuff! Sometimes when I go through something like this I can't help but to wonder how the first mathematician came up with it in the first place!

[@TheWoolyWolf]

oliver heaviside

[@VFXCommander]

+asemnafiz Me!

[@djataberk1]

Wish they did not ?? :(

[@AK-fn7ro]

can anyone tell me why all scientist and inventers are mostly from britain and germany

[@Fluvance]

@@AK-fn7ro cause america's stoopid

[@khanacademy]

The quality is only bad the first few minutes after the video is uploaded (while it is being processed). Re-watch it again in a few minutes.

[@mathalysisworld]

ok

[@hans_____]

It's like you actually WANT us to understand!! None of my other "teachers" ever seem to feel that way....... Thank you sir for your excellence and your love for your fellow man.

[@Sk-pg7uv]

Its amazing how you and my professor teach the same exact thing but with you it just magically makes SO MUCH SENSE!

[@rajngla77vol2]

who ever did this thank you very much, learned LaPlace and step functions couple years ago and this is great material to refresh your memory!!

[@AymanRSaleh]

You are my hero sir. I watched your videos last year in my ode and pde class, and thought I'd never need this stuff again. This is the second time you've made me actually understand laplace.

[@SimeonHanks]

I swear you've got an amazing talent. I can't pin it down, but you are so easy to learn from. Thank you Sal.

[@fuahuahuatime5196]

Good explanation, but I feel that 23:00 is just a little bit misleading. The reason why is because the laplace of the shifted function isn't simply the laplace of the unshifted function. *There's an extra step* where you have to find the unshifted function by using manipulations such that you get the original function again.

[@4fatcats]

ikr, I was so confused by that since f(x) is not f(t) so why should L[fx] == L[ft]??

[@biller545]

Somebody give this champion an award or something!

[@alexwhb122]

you are a teaching god. Thank you so much for this video. It was so helpful.

[@xXguzman98Xx]

Why is the laplace transform L{u(t)f(t-c)} equal to e^(-cs)*L{f(t)} where f(t) is the unshifted function and not equal to e^(-cs)*L{f(t-c)} where f(t-c) is the shifted function? When you worked out the integral with the variable x, you got as an answer that L{u(t)f(t-c)}=e^(-cs)*L{f(x)} and since x=t-c, shouldn't L{u(t)f(t-c)}, when you substitute (t-c) back for x, be equal to e^(-cs)*L{f(t-c)} instead of e^(-cs)*L{f(t)}?

[@aliakbarbaldiwala3673]

yes

[@mcjezus6799]

I came here looking for this comment

[@bosskababy]

me 2

[@Mr.Blue07]

I feel you, bro.

[@ItsFilthyInHere]

I believe it should be that L{u_c(t)f(t-c)}=e^(-sc)*L{f(t-c)}

[@Mirmida00]

Man, i just wanna say a big thank you from brazil! i really dont go to class cause the teacher kinda sucks, and i started studying 4 days before my calculus 4 exam. i was rageing like hell cause i couldn't understanding a lot of stuff by myself, but then i found your videos... you sir, made me get a 8.5 in 10! and i atudy at one of the hardest universities of the country. thank you so much!

[@adios04]

what university?

[@icwhatudont]

grandfather use to say, "don't bore others with the details, just show them the baby"

[@JustinDiazJokes]

ive been watching his videos for years now, and i am just starting to notice. JUST SHOW ME THE MONEY SAL!

[@drakemuk]

Luis Valdivia You have tons of Laplace tables in Google Images. That shoud do...

[@quadrinhosmonica2735]

At 21:30 why didn't Sal back substitute x = (t-c)? He just ignored it, went along and used a "t" inside the laplace transform symbol

[@peanutbutterjelly2188]

i think it should be written as f(t-c) instead of f(t).

[@zlatanbrekke6538]

I think the argument he made was Kind of weird. You could substitute back, But there is no point. The point is that it doesn’t matter What you call the integrering variable, since it will go away when you integrate. Its still a Laplace-Transform if its x you are integrating instead of t, its still a function og s. Kinda like ∫₀² ax³ dx = ∫₀² as³ ds = 4a its still the same, even tho we use different variables to integrate

[@aidskeys]

11:40 - Finally someone who acknowledges that using mindless variable names such as ones from the latin alphabet sucks. 'Mon the x! Thanks khan.

[@demovseverybody]

When i am a dad, I'll name my 1st Male kid "Sal" cause you are a legend to all, i am honored to have learn t all that i know from you?!!

[@putin_navsegda6487]

I love your old math videos ! Best explanation ever ! It's pity you don't record it anymore.

[@funkmaster322]

Good job man your videos are really helping me out for the FE exam review. You have a good balance of practice and theory going on. Keep it up!

[@Blasphemykat]

Amine Aboufirass So did this end up being on the FE exam?

[@funkmaster322]

***** I took the Civil Engineering one (structural)... I did not see any laplace transforms.... Im guessing they only have it there for other engr majors which heavily rely on this kind of concept....

[@Blasphemykat]

Thanks for replying, I appreciate it :)

[@funkmaster322]

***** NP. Good luck

[@badwolf69420]

Can anyone explain the missing step of how f(t-c) = f(t) ??? I was following this course with no problems up until this point. It clearly confused a lot of other people too.

[@TheCriticalGouge]

Very nice presentation. I go fullscreen on my 25 inch monitor and it's awesome.

[@happyfishjj]

thx! I finally understand that why the unit step function disappears after subsituting 0 to c ! thx a lot!

[@MehanathanNackeeran]

This is amazing!!!!, This is what our future is all about.(Actually present as well). Thank you. Thank you very much who ever you are sir!!!. PS.: You Just Made Me Love Laplace all over again.

[@albaquerkie]

I don't know why I go to class anymore... This 25 minute video made way more sense than my hour and a half lecture.

[@MuhammadSalman-gv6mx]

Awsummm Workkkk Sir, U know What Our Instructor Was Doing these things, Like things Are moving In air , But u Did, Insert those Concepts For What I was Thinking Thnx Again

[@wrongloop]

I would suggest watching the mit differential equations and then watch this videos, you would get a way better understanding with two or three different points.

[@VivianTTZ]

Thank u so much. This makes so much more sense!

[@sarvagyabhatnagar7806]

I didn't understand how you went from f(x) to f(t) from 19:00 to L(f(t)) at 21:33. The Laplace of f(x) should be L(f(x)) where x = t-c, however, the final answer includes the Laplace of f(t). Shouldn't it be Laplace of (t-c)? Greatly appreciate any help.

[@kalyansekhar1664]

A super Duper help to me , thank you from the bottom of my heart :)

[@weezilla]

Thanks a lot. I was never formally introduced to step functions and my diffeq book gave a very poor introduction to them. I got it figured out now, thanks =)

[@Niceown20]

This was so helpful

[@0097122]

great Video and a great instructor ...i got it all now !

[@somebody5498]

high quality ! surprized

[@ueiwqoak]

Why is the laplace of f(x) = laplace f(t) when x = t-c ? Why does that seem wrong to me?

[@dray1480]

bro you make it so simple i learned nothing for being in class lol

[@evilgeniuzify]

man!!! thank you thank you for saving my over priced education

[@AnoushehT]

he explained before that at the end the answer would be as the same to take the laplace transofrm of the unshifted function (in this case sin t) instead of the shifted function, check a few mins back before this sin t example, u will find out

[@jonathanmeulman3931]

ah. The smooth voice of revision

[@allenytw]

thanks a lot, i need more about this coz i study sth about engeering, math, thankyou

[@binibakos1342]

Sir, You are a lifesaver. I salute you, Bro.

[@chor1962]

Hi Sal Thanks for the videos, could you please explain how did you assume F(X) is equal to F(t) in the end of the video because earlier you said x = t-c ? Thanks again.

[@guangzheyu5539]

Rajesh Chandnani there is in F(t), only F(s).

[@delballer]

very helpful ....i have a test on this 2morow thank u :d

[@ctodtubular]

Awesomely helpful. Thank you.

[@aah134-K]

at the end, why did you take the laplace transform of sin of t instead if sin of t - pi. Very helpful btw, I was totally lost until I ended up here

[@harsh.thakkar]

This helped more than a gruelling hour long lecture in college

[@npopson]

Thanks for these videos. Such great explanations!

[@cantorbernoulli4407]

Thanks mate keep going even if you upload it when i was just learning multiplication

[@nikan4now]

Thanks. This was very helpful.

[@yash1152]

* Thanks a lot, for introducing this new -- (shifted) "unit step function" * shifted is my own annotation, as i think _μ_zero_ or just *μ* is a more fundamental function, with the general _μ_c_ being shifted to right by +c i.e. the *μ( t - c )* Anyways: * this step fxn eases alot the task of defining functions which are stepped at only a few (say 1-3) points like the fxns for absolute, or signum, or other such * eases a lot - or at least provides a new way to think about ... * other than that, i don't think it helps much for other *periodically partwise functions* like floor, ceiling, fractional-part, modulus, remainder, etc.

[@sophiecarlberg]

KHAANNNNN!!!!!!!

[@ickeera]

great explanation,Thank you so much

[@pubggamers2973]

very well explained !

[@rahulp1495]

great video you saved me ....thnx a lot

[@FaizanZahidNustian]

indeed the unit step function was looking crazy before this video :D

[@OptimusSubPr1me]

forget million dollar debts for education, you are the one stop shop!

[@flashreality8222]

I'm stuck Step Function 😬😬🤭

[@albert275]

holy shit, this video was magical...

[@weiyangli9619]

Thank you Khan.

[@bluestacks2986]

Wasn't 24:15 supposed to be the Laplace transform of the shifted function? Why did x = t-c just magically become t?

[@CharacterLimit]

@sikory I believe the Laplace transform finds the moments of a function.

[@luisvirgilio2722]

Aulas muito boas. Uso legenda. I'm Brazilian.

[@DannyzReviews]

*Great*

[@AbinamiLivingJamala]

Sal has a cold... thumb up to wish Sal well. and... Sal for President!!! Yes He khan!!!!

[@asif7240]

Thank you!

[@nishanthmohan3157]

I DONT UNDERSTAND How you said L(x) is same as L(t) when you substituted x=t - c

[@sweeseen9577]

great ~ i finally got what it means

[@tptera9961]

Mr Sal I love your work, in this video I kinda disagree with how u simplified Laplace of the step function, u replaced x=t at the end but we know that X=t+c please help me out here

[@danielyeh]

just wondering what kind of program you are using. i also have a tablet pc and it looks pretty nice to write on.

[@gorillawarfare7523]

I'm pretty sure that should be t - pie

[@ITFCBlue10]

pi*

[@klikkolee]

when you adjust the limits of integration, doesn't that assume that c>0?

[@mahsa5482]

Thanks a lot.

[@alicegeorge8757]

Thank you 😃

[@_s_l]

this is an absolutely amazing explanation!!....but why do we shift the function to the right and multiply it by unit step function, what is the purpose of that?

[@naifalkhunaizi4372]

YOU ARE AMAZING

[@keyvanfardi419]

It's like you taught Laplace how to use his Transform !!!!!!!!!!!!!

[@TheLexiJess]

My DE's textbook, (Trench) uses these fucken insane latin alphabets with laplace and it pisses me off. This is much better, thank you :)

[@reapingshadow2866]

Why do I have to watch these videos to complete my homework? Where is my school's lectures???

[@MCSGproject]

I want to to take the laplace transform of a heaviside function, how come i have to be lectured for 24 min? This is a 5 min tops video.

[@RainbowPaint]

I love you Khan

[@norwayte]

You are right.

[@benjaminbrady2385]

9:35 that sure does look a lot like convulsion

[@aeroscience9834]

14:00 isn't what your doing only valid if c is positive (or zero)? Is this still valid for negative values of c?

[@fenrikfedme]

c can't have negative values since t >= 0 and c >= t

[@HonsHon]

Jesus this was explained 34217923489231749872384293741982373982x better than how my DE professor explained it.

[@mindfreakrk]

at got a suggestion for u if u dnt mind...at 4:46 u say it's here quite often i saw in ur videos u say here and there it's not always helpful to relate whr u are talking abt....so cud u pls luk into dis mattr snd try 2 brng out a solnt for it thnk u guys

[@shaswatkumar4078]

did u mean that unit step function is used to obtain equation for change in wave form?

[@theodorheinrich]

Good stuff, just one tiny remark: You're trying to avoid greek letters, not latin ones (which you use all the time ;) )

[@shahzeb-khan]

I don't know wether you know it or not but it can be solved by using graph in under a minute

[@TheAllboutwin]

Just don't go to lectures, learn from course notes and youtube!!

[@CharacterLimit]

@sinspawn1024 Then I assume you simply integrate from t=0, since u(t)=1 if t>0 under your conditions. So, you'd have to find L{f(t-c)}.

[@jasonl.5973]

from 22:26 i dont understand whats going on, others quite nice

[@TheGhazali93]

I'm naming my son after you Sal

[@cacags]

Eline ağzına saglık hocam güzel olmus

[@1357911d]

great job bro i dont know what inspired u to do this but instead of paying thousands of dollars for tuition its just better to watch ur videos and understand what the hell is going on

[@falco2469]

There is an error at 9:30. It should be u_c(t-c)*f(t-c)

[@chaebme]

Good

[@ryeofoatmeal]

what if i have both are unit step function instead of f of t... i thought i almost done but then my question slightly different

[@petrestok2704]

wow, now iťs... simple :D

[@wrongloop]

point of view

[@perditiond2x]

What if the unit step function is given as U(x-pi)?

[@dalalalsamhan8922]

my hero