The convolution and the laplace transform | Laplace transform | Khan Academy

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Understanding how the product of the Transforms of two functions relates to their convolution.
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Differential Equations on Khan Academy: Differential equations, separable equations, exact equations, integrating factors, homogeneous equations.
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[@kashish8960]

this video makes me think why I am spending tons of money in collage when I get all I want from Internet for free. Thanks a lot sir you are true Savior of engineering students

[@ozzyfromspace]

I dropped out of college two semesters ago. Now all I do is mathematics (no money but I'm as free as a bird). Get that degree though lol

[@dymo7607]

@@ozzyfromspace F

[@AlloyedFrequencies]

@@ozzyfromspace lol

[@philcooper279]

That's the magic of the internet.

[@loadinginnovation]

@@ozzyfromspace good 4 you bro

[@daviddashti9227]

"Let me just do this in yellow" *commences to draw in pink* 30 seconds later "I couldn't resist switching colors" *commences to draw in blue*

[@vorpalinferno9711]

At this level the books are so confusing and dont explain anything. This is explained in a way how a human being can follow the procedure. Good stuff.

[@lily-lilie]

How did people graduate before Khan Academy? infinite thanks

[@DutchKid121]

Cs get degrees lol

[@delalias5754]

BOOKS

[@thijslenssen192]

@chris rogers You saying this made my almost non exsisting motivation even worse.

[@Sundoren]

you are truly amazng even your voice :D you make the table colorfull just for us. just to increase our mood while tryng to understand the lesson. thank you a million times.

[@AkshayPatil-qf5eh]

maths is fun when you understand...... thank u for this....

[@Bearkiller777]

Thanks Sal for the videos I am doing / reviewing convolution as part of my Digital Systems/Engineering class i think the quiz is today on Convolution. this really helps me a lot thanks.

[@jengativ]

great teaching, thank you very much. worth 10x more than my book and class put together

[@AnujAgrawal08]

Can you make a video demonstrating why the laplace transform converts the convolution into a simple multiplication in the s domain? I mean, via this video, you did verify the fact that it works correctly but it would be great if we could learn WHY it works or the mathematical proof behind it. Thanks.

[@alxjones]

You could also just do (2s/(s^2+1)^2)=(-1)d/dx(1/(s^2+1), so the inverse Laplace is just tL^-1{1/(s^2+1)} which is tsin(t)

[@anishdeshpande395]

Your videos are really good. you teach nice and slow to make a better understanding. Its really very helpful. I even recomended your videos to some of my friends who are facing difficulty in this subject. Thank you very mmuch

[@JPMediaProductions]

Life saver!! You explained this way better than my professor and made it interesting. Also subbed you.

[@salemmola80]

Thank you so much.....I just wish you were my teacher!!!!!

[@Eudaimonia239]

this is good , wish to know if you have fourier series and transform in here , cause i have a test of that next week, you are trully really helpfull

[@EmmanuelAyeni]

THanks this is a well taught and detailed lecture

[@davidwahba179]

Thanks Sal, this helped a lot

[@jaouadrahouani4975]

This guy is a HERO, he should be nominated for president or give him a golden medal at least!

[@__donez__]

@champignones I second that! Can you please post some videos on Fourier Series and Transform? Thanks for all of your help!

[@MrSparkyEE]

Please do a video on Fourier Series and Fourier Transform!

[@moejoe987654321]

Man laplace transforms are easy. You just have to capitalize the function. L[f] -> F Just press shift.

[@issacquantum]

Man, THANK YOU!!

[@Eudaimonia239]

thanks a lot for everything, i love science and engineering, but more for all, i love learning and what better way than via internet, this is for all those people who say internet is full of garbage, well is full of usefull information too. i just wanna make a question do you have Z-transform?, cause i like that subject in particular.

[@adibasdas]

i feel so stupid when im study to these things while justin bieber or nicki minaj are making tons of money.

[@SoloPro]

+adibasdas LOGIC!

[@DutchKid121]

I like how that sounds, is that a famous theory?

[@Craftman368]

That's the most pretentious and flowery thinking I've heard in a while. I don't like pop music at all but just because you don't enjoy something doesn't make it degenerate. Wtf is "civilization in your mind"? Just because someone may listen to generic, admittedly uninspired music doesn't mean they get dumber. If you're gunna make huge claims like that you need to provide sources.

[@Craftman368]

There does seem to be a correlation there, but correlation is not causation. Rather than concluding that music makes people dumber, I would suggest that the correlation is more likely a result of the cultures of different demographics. For example, lower income groups who don't have access to a decent education may have a culture which favors Lil Wayne music (apparently listeners of Lil Wayne score very low on SAT). There are a lot of factors at play, concluding that listening to certain types of music effects your IQ is a leap.

[@Craftman368]

Feel free to judge the majority of pop music or rap music in a negative light, I'm even guilty of that. I was just stating my doubt that listening to that sort of music effects your intelligence. I would say that it's much more likely that certain types of music attract less smart people, rather then that certain types of music actually make people less smart.

[@Novak2611]

You can simply do L(sin t)=1/(1+s^2) and take the derivative of that. In one hand (1/(1+s^2))'= -2s/(1+s^2)^2. In the other hand L'(sin t)=-t sin t. So the inverse Laplace of 2s/(1+s^2)^2 equals to t sin t.

[@kibukamusoke]

Thanks so much!!!

[@alfredosarmento9081]

You are great sir. TXs

[@AnujAgrawal08]

I find your videos great for developing an intuition for the subject. However most times I have to watch your videos at 1.5x speed to save some time! I guess you can skip the very minor details and leave it upto the audience to figure it out and instead include some more valuable stuff in your videos. Cheers!

[@bahiraborhan7068]

thank a lot for videos

[@fabricioazevedo87]

@eglxiang You should watch the first's videos in the playlist of DE's, then this must become more clear for you.

[@peterjuma34]

well explained,,,

[@dilashamanchanayake5203]

Thanks a lot...

[@bodyguard7229]

u are the man i ent gonna lie

[@user-fg1wx7zn8g]

thank you

[@asif7240]

Thanks

[@chilly_29sl68]

brilliant

[@Theboss10332]

Pls do a vid on Fourier transform sal

[@sisip123]

I agree, fourier would have been great! and something on the erfc and erf.

[@johncgibson4720]

So, in the end, you got a flight control output signal that makes the drone oscillate up and down more and more violent over time until the drone disintegrates mid-air. That is what t.sin(t) means.

[@lydiafbaby]

@eglxiang by the definition of the Laplace transform, that's what they're equal to.

[@somchaiaimpoe907]

ขอบคุณครัล

[@mwm48]

...how come i can rarely get ANY of your videos to display more than blank screen, this seems to happen more often than not. does anyone have any info on how to resolve this problem? :( btw, the videos that decided to work were very informative, especially since my professor's English is kinda rough, thanks for the vids!

[@eglxiang]

Sorry that I am still confused with some parts? Could anyone help me to answer it a little bit? Why L( sin t ) = 1 / (S^2 + 1) ? And why L( cos t ) = s/ (S^2 + 1) ? What is the defination of Laplace function L( )? And what is the relationship between t and S ?

[@matthewkeu1992]

@champignones ya power series pls.. expeciallyfrobenius

[@fhutturtle7808]

Came in clutch

[@coal2710]

I don't know why, but those neon colors are making me happy. Maybe because they remind me of mdma pills.

[@ejercicioparatodos1886]

I was expecting the demostration

[@jkalka2844]

Which video does he evaluate the integral in?

[@Danhec95]

j kalka /watch?v=IW4Reburjpc

[@ruleofwrist20]

I am the social media officer of my math club at TX State and wanted to link to your webpage and youtube page and wondered if you had any protocol for doing so....we reap no benefit other than helping students with valuable tools to understand math and other topics as well....let me know....thank

[@OswaldChisala]

Computing an integral is one thing, but I find that Sal neglected to support the concept with a convincing proof or even intuition. The value of a problem is less in understanding how to solve it, and more in understanding why you can solve it. I hope to see some insight into the motivations for the convolution integral. No disrespect intended, thanks.

[@OswaldChisala]

Hello "Samurai Jack", All I'm saying is that an intuition of any idea can go a long way, and putting that into his videos would be a nice touch. Crunching numbers is one thing (we have Wolfram, Mathematica, and MATLAB for that) but we also need to understand how to effectively apply what we learn. Seeing the value of an idea gives it purpose, and in my minds eye, this extends quite naturally to the provocation of the Convolution Theorem. At this point, I have built up an intuition for these transformations, and am better equipped to consider how I can solve specific types of engineering MISO design problems. And finally, there's a difference between being spoon-fed answers and being enlightened about the foundational ideas of a given subject, or derivative thereof. Need I go on? Without implying disrespect, I think not. Best wishes "Samurai Jack". Regards, Oswald.

[@PrinceFX]

@champignones +1 vote for Fourier Transform!

[@philcooper279]

Waffled a bit, but still a good video.

[@karthikraavi5934]

While evaluating the convolution integral why didnt you take the limits from minus infinity to plus infinity ??

[@emmanuelrakhutsi2807]

it is a theorem sir

[@norwayte]

Intuition?! Convolution gives a third function. One interpretation of convolution is weighting a function (f-τ) depending on time with another function (g). The function value of the function (g) in τ says how strong the value less than τ of the weighted function - means (f-τ) - goes into the result function (third function) in point of time t. It has similarity with moving average. More intuition for this would be great, Sal. Good video.

[@gerrit-jan]

so just separate and multiply

[@ihgffed]

MATLAB code?... help please

[@OletramX]

A bit slow, Id say, but good.

[@prateekdebadarsiroul5466]

If it can be done by partial function easily..why we need this..as it z lengthy????

[@HaliPuppeh]

You might not always be able to do it with partial fractions.

[@flawflaw1]

ferovac ;)

[@abdelrahmanmagdy2636]

this integral can be solved just by applying sin (a)*cos(b)= sin(a+b)+sin(a-b) so sin(t-taw)*cos(taw)=sin(t)+sin(t-2taw) easy integral !!

[@redougulas]

why are we doing this!??? what have our lives been reduced to!!!???

[@aureliotambiga1049]

daldal mo!!

[@--8251]

Yeah that's right man

[@michaelanderson3693]

thumbs up if you now eat convolutions for breakfast

[@Aheitchoo]

'0 dislikes'

[@woo216]

fourier series pl0x originalcommentblox

[@zed.6128]

I will pay from Rs. 50 - Rs. 68 per question . Kindly let me know can anyone solve mathematics problem starting from 11th upto engineering , mostly questions will be from engineering mathematics like matrices, laplace, differential equations solution etc .

[@acoustic0740]

Do U Know sure! Ping me

[@samuelukah1376]

pm me

[@ashwinimohan6467]

should've been a bit faster

[@kazemvafaeian4980]

too much talk, many jumps. preferred more organized, repetitions is ok for complicated concepts not simple ones.

[@DelphianSociety]

Great videos Sal, but I really think you underestimate your viewership too much. I think most of us were kind of bored throughout this video because you seem to think every minute detail needs attention. I commend you for making these videos, but perhaps make it somewhat more concise, or better yet, you could include more material in the same video? p.s. - I agree with the people asking for Fourier transform.

[@michaelpurtell4741]

these videos are great but at times especially this one is a painful statement of the obious and I never had heard of the convolution before

[@jontopham2742]

You bored me by repeating the same thing too many times

[@aureliotambiga1049]

daldal mo!!

[@--8251]

Yeah that's right man