The Laplace Transform: A Generalized Fourier Transform

This video is about the Laplace Transform, a powerful generalization of the Fourier transform. It is one of the most important transformations in all of science and engineering.
@eigensteve on Twitter
Brunton Website: eigensteve.com
Book Website: databookuw.com
Book PDF: databookuw.com/databook.pdf
Error: @10:20, should be e^{-st}
This video was produced at the University of Washington

[@Eigensteve]

Error: @10:20, should be e^{-st}

[@SRIMANTASANTRA]

But, this typo is understandable. Anyway, thank you, Prof. Steve.

[@gaelc13]

the H(t) definition should rather be 0 for t=0, isn't it ?

[@TURALOWEN]

Gael C. That is exactly how it is defined in the lecture.

[@gaelc13]

@@TURALOWEN Exact, my error : the space is so crowded that I missed the fact that the system as it is written at @7:30 refers to F(t)

[@nidhigoyal8893]

Sir is there any upcoming webinars or workshop of yours so that we could a bit more out of it ?

[@user-lk9kr6ry9d]

I'm Korean. I do a study of Laplace transform in high school. I also studied Fourier transform but couldn't find their common points, but your help is wonderful. Thank you for your detailed lecture!!

[@JHS-gu4lw]

캬 한쿡인 여기서 보네요

[@hashirroshinvaliyaparambil70]

Your 16 minutes video on Laplace transform gave me a deep understanding in this domain thane my 4 years bachelor's degree. You are priceless Mr Steve Brunton

[@Eigensteve]

Thanks!

[@tsalVlog]

I don't know why, but I laughed really hard at "I think of it as a political Fourier transform".

[@Eigensteve]

Nice

[@Aziqfajar]

I can see why. Nice one

[@tractatusviii7465]

yeah, that's a great gimmick. useful too

[@jamesduff2647]

So did I..😂😂😂

[@jonathanuis]

I'm doing my masters in control, I never really understood how Laplace works, Thanks a lot Steve, you make the concepts very understandable. regards from Germany

[@Eigensteve]

Happy to help!

[@vimostan269]

Agree! My ODE text book starts with the usage directly. I didn't even notice those badly behaved functions.

[@Physicsandmathswithpraveen]

In books and school they teach laplace before fourier and we never get a chance to sit back and relate them yes 🙂

[@Amine-gz7gq]

laplace transform scans for sinusoidals and exponentials in your transfer function so you can locate poles (region where you have resonance between your TF denominator and the e^-st function) and zeroes.

[@adityatandon2994]

This is probably the best explanation of the Laplace Transform that I've come across on the internet. 20 minutes did what 4 years of my bachelors degree failed to do - solidify my engineering math concepts.

[@jamen1993]

I thought that I grasped an intuitive understanding of the laplace transform once I recognised that it is essentially the correlation of a function with a decaying exponential oscillation, yet your presentation gave me additional insights.

[@spitimalamati]

I made a T-shirt in the ‘70s with the Laplace Transform on it. In grad school, I loved using the Heaviside Theorem in digital process control. ChemE here.

[@volkerblock]

Excellent representation. Almost 60 years ago I learned the Laplace transformation, now I finally (hopefully) understand it. So, never give up, enlightenment will come at some point. ​

[@jurepustoslemsek7882]

holy sh*t! I've been trying to figure out what Laplace transform actually does and you've finally explained it in a way that I understand. thank you so much!

[@Eigensteve]

You're very welcome!

[@justin.booth.]

This is the best lighting I have EVER seen in a math lecture video. Sheer perfection!

[@naveensd101]

I wish my math prof had this good handwriting.

[@paxdriver]

This is the best video on KZbin. On the entire internet, this is the best one made. Thank you and kudos for being such a rad teacher

[@Eigensteve]

Wow, thank you!

[@dashjinn]

You having only 186K subscribers with so many really interesting and impactful videos just says about the direction of our society so much. I wish I had your videos during my bachelors... my love for math would have remained.. Thanks.

[@douglasvalerio8880]

I`ve been first introduced to the Laplace Transform and only later to the Fourier Transform, and never before seen this approach, this generalization makes so much more sense Thanks for sharing this knowledge

[@rene0]

Only after watching you write an i with a serif facing the 'wrong' way i was sure you were writing mirror script. Well done.

[@mikefredd3390]

I thought to myself, “self”, how can an Integral that looks the same as the FT but has a reduce integration range be a more general function? But lo and behold in the most straight forward and simplified presentation you explained it! Most productive use of my time in quite awhile. Thanks and I’ll watch some more videos.

[@ivanmazzalay7736]

This is great... I studied and always forget it, but you gave some elements of the definitions that are the keys to remember the process! Thank you so much!

[@TKR911]

Dear professor, you do a really good job with these explanations ! Thank you

[@Eigensteve]

You are welcome!

[@MojoMonkeyMan67]

Brilliant, absolutely brilliant. Im speechless at how amazing this explanation is. Thank you Mr. Brunton

[@AJ-et3vf]

Awesome teaching! Very insightful! I've watched tons of others videos about Laplace transform, but even in this I felt like I learned something new or gained a new perspective on Laplace. Thank you very much.

[@mrmister3507]

Im starting my master in Robotics in a few months and Im binging all of your videos. You're such a great teacher and you help me to get a true understanding of the theory. Thank you for posting all of these videos. Your students are extremely lucky to have a someone who understands the theory so thoroughly and is also excellent at teaching. That's a combination most professors can only dream of!

[@krinkovakwarfare]

Not only did you broach the topic in a concise yet comprehensive way, you have written all this mirrored for our sake Impressive 💪

[@abhaykela]

Thank you for sharing this lecture video. I find it as one of the best explanations on Laplace and Fourier transformation.

[@zwww_ee5235]

This is the video i came back to through my eng degree for laplace transform refresh, so concise and well explained, thank you Steve!

[@1243576891]

Awesome videos! I followed this series from the first one to here. Glad to learn the connection between Fourier Transform, Wavelet Transform and Laplace Transform!

[@rajeshviky]

Steve Brunton has never failed me even once :) Yet, an another impressive video. Thank you!

[@volkerblock]

Hervorragende Darstellung. Vor fast 60 Jahren lernte ich die Laplace Transformation, nun endlich habe ich sie (hoffentlich) verstanden. Also, nie aufgeben, irgendwann kommt die Erleuchtung.

[@MaksymCzech]

Once again, thank you for your lectures!

[@Eigensteve]

Glad you like them!

[@danilomartins1901]

It’s just so hard o to find an intuitive video on what the Laplace transform actually is, other than just a random integral. You’re a genius! Key takeaway: Laplace is a weighted, one sided Fourier transform.

[@lucasbarroca8919]

Amazing, the Laplace transform was presented to me as magic wand, I've never been told how it works or why it works. This video clarified a lot for me. Thanks

[@_notch]

This is a bit above my level, yet i managed to understand most of it! Great summaries of what just happened.

[@Eigensteve]

Thanks!

[@plamenyankov2182]

I am a Data Science student and I thank KZbin's algorithm for suggesting your channel to me! For what I've seen because it's mind-blowing and I plan to watch all of your content and learn it by heart! Thank you Professor, you are doing amazing and very important job!

[@Eigensteve]

Cool, thanks!

[@ailtonteixeira4730]

I'm glad to find this lecture, now i saw the meaning and beauty.

[@ElMalikHydaspes]

really a well done explanation of bringing the two concepts together ... 🎉

[@koninja1986]

This was randomly suggested to me by youtube. I don't know why, I never got past calc 2 and don't watch math vids much on youtube anymore. If I was still climbing the calc ladder I'd want Steve as a prof though. The enthusiasm is quite engaging.

[@underlecht]

Best explaination. Thank you. I'll check your other videos.

[@trip_on_earth]

Thanks a lot for explaining this so clearly. Regards from India

[@mortezakhoshbin]

you teach differently than others, and i learn new things about the subjects that im sure im so knowlegble on them! you say the basics so beauty

[@nishapawar3368]

there r so many videos about laplace transform but I loved this one.....#mustwatch

[@chimetimepaprika]

Nice. I understood FT from this explanation in a way I never have previously.

[@alexanderbeliaev5244]

Finally, the misery resolved! now I see the logic behind s variable. Highly insightful channel, I wish I had these videos 10 years ago...

[@peepeefrog_]

Amazing! A million times better than what I had in university in my days

[@preetymala3189]

Teaching way and writting technique both are outstanding. It help me a lot. Thank you 😊 SIR

[@meetghelani5222]

Thanks a lot for making this video, highly appreciate your efforts.

[@timurpryadilin8830]

What a wonderful explanation. Thank you!

[@shameer339]

Never seen such a great explanation for Laplace transform 🤩🤩🤩

[@noouch]

Love your minimalist setup, always nicer to have a teacher draw and gesticulate.

[@MysuruBharath]

Wow!, great intuition Prof. Steve. Thanks.

[@mitchjust6688]

Really efficient way for video lecturing. Looks nice, I assume it's cheap(er) in time and processing power (for making them) and most importantly, does the job.

[@divyaprakashbiswas8781]

You are a magician!! Thanks a lot for your lectures.

[@Ajaykumaraita]

Dear professor you are such a great orator with visualisation.. Thank you. Please keep posting videos for this Laplace series.,

[@Eigensteve]

So nice of you!

[@lunakid12]

Very nice visuals and lovely structure, great performance, drawing skills, handwriting, even the colors! :) One minor advice, if I may: the act of chopping off of the < 0 half could be better communicated (before the "reveal" at ~10:45) by not talking (only; and perhaps a little too lovingly :) ) about the technicalities of H(t), but a) simply stating that we're just going to ignore everything < 0, and b) why that's both necessary and OK to do. Using H for that is trivial, use the time for explaining the rationale (of why the - half is treated differently from the +) instead, so that following it up in the math could feel natural and straightforward.

[@branarch3878]

As a person who’s starting a control systems engineering / control theory course next semester - thank you so much!!!

[@Eigensteve]

Awesome, glad it helped!

[@gabrielh5105]

Thank you professor Brunton

[@electricdreamer]

For those of you who wonder how he writes "backwards". He's not. The trick is, he writes normally onto a piece of glass in front of a mirror, if you point the camera from the same side towards the mirror through the glass, this is what you get.

[@edison8309]

Better explaination ever! Big thanks prof!

[@felipegabriel9220]

That lecture was undoubtedly perfect, 100/10!

[@moustholmes]

Then why are you giving it 100/3628800? That's not a very high score

[@felipegabriel9220]

@@moustholmes i forgot some parenthesis

[@Amb3rjack]

A fascinating video which I found utterly compelling. I actually almost sort of understood a tiny part of some of it . . . . .

[@hupa1a]

Wow! This series is gold!

[@Eigensteve]

Awesome!

[@philosoraptor3]

Pretty excellent overview, though it bugs me a bit to call the Laplace transform as a generalized Fourier, as it's more a restriction of the domain of the Fourier transform so that you can enlarge the space of allowed functions. But you were clear enough about this in your actual exposition!

[@Eigensteve]

Thanks, and I appreciate the note.

[@jamen1993]

Thank you for this very insightful explanation.

[@Eigensteve]

You're very welcome!

[@robertbillette4671]

Wow Steve! Such a good teacher. Wish I had you in my undergrad as a teacher

[@bassboosted9708]

Now I finally understand solipsism with that formula. The math behind it opened my eyes.

[@subhadeepreaditassubhodeep6161]

Excellent video Steve!

[@6Oko6Demona6]

Steve, you're left-handed, you write on the glass so it's readable from your side and then you mirror the whole video. Your handwriting character is unexplainable otherwise.

[@DanaWebb2017]

He knows his stuff backward and forwards.

[@Eigensteve]

I love it!

[@ClarkHathaway3238]

I just noticed that too lol. You can confirm it by looking at his wedding ring

[@philippemichelvidori7248]

he writes well for a teacher ( left handed )

[@lawrencedoliveiro9104]

Leonardo da Vinci, I think it was, taught himself to write backwards and used that as a form of encryption for his diaries.

[@thedarkknight579]

Thank you very much for the lecture Steve.

[@Eigensteve]

You are very welcome

[@maneki9neko]

Steve, you're wonderful.

[@pratapbhanusolanki6613]

Professor Burton, Thank you for the insightful video. I am wondering what happens to the heavy side function H(t) in the inverse Laplace derivation? Can we reconstruct the f(t) for negative t?

[@muhammedyusufsener1622]

Great explanation sir, many thanks!

[@ivarangquist9184]

0:45 "I'm gonna walk you through how to derive the Fourier transform from the Fourier transform"

[@Eigensteve]

Whoops!

[@AshishPatel-yq4xc]

I realized it was just a slip but for a moment I was thinking , this is getting recursive :)

[@federicogottardo4869]

great explanation, very clear and intuitive

[@Eigensteve]

Glad you think so!

[@AJ-et3vf]

Awesome video! Thank you!

[@thomasrad6296]

This is amazing content. Thank you for this.

[@artificiallychallenged]

Great lecture. I really enjoy your style of teaching.

[@Eigensteve]

Glad to hear that!

[@olivioarmandocordeirojunio8280]

Thanks a lot sir. You help to make the world better.

[@IamGilgamesh666]

Excellent presentation, excellent explanation. Excellent work! :-)

[@dr.alikhudhair9414]

Wonderful explanation .. Thanks a lot professor

[@SRIMANTASANTRA]

Hi Professor Steve Brunton, Thank you so much.

[@Eigensteve]

You are very welcome

[@SRIMANTASANTRA]

Hi Professor Steve, My pleasure

[@syedun42]

Very nice and wonderful lecture

[@JoaoVitorBRgomes]

Regards from Brazil! Thx

[@alfcnz]

WHO ARE YOU??? 😍😍😍 Just subscribed! Loved absolutely everything!

[@prandtlmayer]

TOP QUALITY and really enjoyable!

[@Eigensteve]

Glad you enjoyed it!

[@motbus3]

ode ordinary differential equations must say, first video i watched in this channel. kept my attention trying to figure out how he writes mirrored

[@el_witcher]

He writes just like we do. There's a camera in front of him which does the reversal.

[@AntoineDennison]

@@el_witcher Really? He's righting from right to left... But he's writing with such ease, I guessed there must be some tech employed.

[@huankunwang3867]

Very good explaination, thank you so mcuh for all your works.

[@Eigensteve]

You're very welcome!

[@davidwilkie9551]

It's like mathematical Chocolate Cake, only the best ingredients. Very well done. And I once knew what it was about as a rool for Electronic Engineering, so the basic connection between Pi related sine waves, and e exponential "transformation", should now be the obvious QM-TIMESPACE Temporal vector coordination of e-Pi-i partial differentiates in Superspin Superposition-point interference of hyper-hypo modulating Conformal fields/interference positioning. (If you know what I mean)

[@alinematheus3644]

Nice explanation! Thank you, professor!

[@Eigensteve]

Glad you liked it!

[@hansweichselbaum2534]

You really make math exciting! Thanks for sharing.

[@emilywong4601]

Fourier and Laplace transforms are used in electronic music for converting sound to and from digital to analog signals.

[@emilywong4601]

Electronic music uses sin waves for sound.

[@sridharc92]

"One-sided, Weighted Fourier transform, or a political Fourier transform". Pure Gold! :-D

[@Eigensteve]

:)

[@damirshodiev673]

You are incredible, man ! thanks

[@mecrajib]

Thanks. you are a great teacher.

[@guillermovasquez1370]

Steve, your information its very useful. Regards from Colombia.

[@Eigensteve]

Glad it was helpful!

[@HerChip]

Really nice studio (video/lights etc) setup!

[@Eigensteve]

Thanks!

[@Laowu1898]

Great explanation

[@mingcui7931]

"I think its a political Fourier transform", made my day!

[@agihtiassalam8628]

Very impressive lecture Prof, I enjoyed it ! Anyway, if you think numerical laplace inversion is useful in order to inverted back to real domain, please make a video about it. I use laplace transform to transfrom the fluid flow equation (Pde) then I use gaver-stefhest numerical laplace inversion to transform it back to time domain. I think there are couple of methods to numerically inverted the equation in laplace space but I only know one, the gaver stefhest. Thank you for the great lecture.

[@shubhamdeshmukh1900]

Only if they could teach so articulately in college 🙌 I have become your fan!🙌🙌🙌

[@stuartloynes2390]

Great explanation, thanks.

[@Eigensteve]

Thanks for watching!

[@isobelwhetstone1525]

really love this video, u are an amazing teacher