The Laplace Transform - A Graphical Approach

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11 жыл бұрын

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A lot of books cover how to perform a Laplace Transform to solve differential equations. This video tries to show graphically what the Laplace Transform is doing and why figuring out the poles and zeros of a system help us to reconstruct the time domain impulse response (which is the solution to a diffy Q.)
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If you have any questions on it leave them in the comment section below or on Twitter and I'll try my best to answer them.
I will be loading a new video each week and welcome suggestions for new topics. Please leave a comment or question below and I will do my best to address it. Thanks for watching!

Пікірлер: 406

@fatihersoy7559 4 жыл бұрын

You're a "teacher". My 'professors' at uni, they're "tellers". Nice lecture, from a nice lecturer. Thank you!

@ad2181 3 жыл бұрын

My Controls Teacher at U of Florida was Dr. Bullock a walking incompetent idiot. I hope you get this message! I'm relearning controls.

@vaughnmonkey 2 жыл бұрын

That is the best and most accurate way I have ever heard this explained. You are absolutely right and its amazing that Brain can be such an amazing teacher without even having feedback from us. while our "professors" can't when we are sitting in front of them begging them to teach us.

@MikoPellas 2 жыл бұрын

Exactly. IMO teacher holds a higher status than professor. Teachers actually "teach", while professors merely "profess"

@georgeclooney6208 4 ай бұрын

@@vaughnmonkeynot begging fakin paying for them to teach us

@MugiwaraSuponji 7 жыл бұрын

imma be real, this video blew my fuckin mind. the part where you went from the 3D s-plane plot to the poles and zeros? holy shit. it's like i just found the secrets to the universe.

@SeraphisQ 7 жыл бұрын

It's hard to put into words how good these videos actually are. What an amazing piece of work. I'll make sure to watch and like every one of them.

@fzigunov 8 жыл бұрын

Man, after so many classes and so many videos I finally understood it! Thanks for the "real world" approach! I was struggling just with correlating with reality! Awesome work, keep up!

@marialey7658 8 жыл бұрын

THANKS A LOT ! first time someone explains it in a way that I can actually grasp the idea behind the Laplace transform

@BrianBDouglas 11 жыл бұрын

You can go between the time domain (differential equations) and the S-domain (transfer functions) just by solving the integral for the LT or reverse LT and you don't really have to concern yourself with the whole process I explain. I hope that helps you and doesn't add more confusion!

@pratibharacheljohn3814 3 жыл бұрын

I have been following your lectures since 6 months now and I can't thank you enough. I wish I had seen these way earlier. Awesome way of explaining even the most confusing concepts!!

@BrianBDouglas 11 жыл бұрын

I'm working on the root locus videos now! The first in the series will be out next week.

@BrianBDouglas 11 жыл бұрын

By LR did you mean Laplace Transform? The simple explanation is that FT breaks time signals into just sinusoids (or their frequency content). You can't use the FT to solve differential equations because it doesn't cover the exponential part. But you can use them FT for all sorts of frequency related problems like noise, sound, filters, and so on. LT breaks time signals into sinusoids and exponentials (just like the solution to Diffy Q's) so that's the motivation.

@kamilbudagov9335 2 жыл бұрын

is it possible to know exact value of magnitude and phase for arbitrary frequency from continuous frequency spectrum?

@bboysil 6 жыл бұрын

JUST PERFECT! I came back to this after many years and I have to say there are a LOT of insights this video. Perfect for remembering or if you're trying to understand the intuition of what the Laplace transform does.

@shishirsks 8 жыл бұрын

Awesome! THis video will help thousands to understand laplace transform.

@Ropsch 11 жыл бұрын

Brian, I love the way your videos are built up and edited. You have really put a lot of thought in it. Brilliant!

@DanT2990 11 жыл бұрын

Finally an interesting, intuitive and colourful series on control systems! I'm in my final year in my aerospace engineering program and I'm using your videos as a refresher for control systems. I'm actually learning new perspectives I never thought about and they are helping me to understand topics I didn't quite get. My final year design project is purely based on control systems so this is going to help me immensely. Thank you!

@ThatGuy-mf9ye 2 жыл бұрын

Studying for my FE exam after I've taken all my signals classes and control electives; this really helps bring home some of the intuition that they miss. Thanks!

@poppyblop484 5 жыл бұрын

The clarity and detail into each topic is amazing, it is so clear and easy to understand. Thank you so much!

@90ben09 11 жыл бұрын

I just wanted to say thank you so much for this video it has really helped me to understand laplace transforms in a way that I never did before. Also thank you for making these available to us all, I really appreciate what you do.

@rileystewart9165 7 жыл бұрын

I must say you have excellent hand writing. Makes following much easier.

@apoorvvyas52 8 жыл бұрын

understood the whole point of doing Laplace transforms and finding poles and zeroes for the first time. Great work. Thank you very much for posting this videos

@Chadwikj 10 жыл бұрын

High quality visuals keeping pace with your lecture was fantastic. Excellent job with this.

@MarkNewmanEducation 6 жыл бұрын

Thanks for the visual approach. At last someone who will draw a few pictures and not just fill a blackboard with greek letters!! I wish people would explain things more this way.

@BrianBDouglas 11 жыл бұрын

Hi Shouvik, great suggestion! I've just filled out the form to get my channel reviewed by KZfaq to see if it meets the criteria for their education filter. I don't know how long it'll take but hopefully it'll be available soon. Thanks for the comment.

@alanly3780 7 жыл бұрын

VERY well explained! Thank you, the contour map of the laplace transform plane was really helpful to visualize whats actually going on.

@speedbump0619 11 жыл бұрын

I took differential equations in 1994, and never understood what the s-plane was (honestly, I don't think my professor understood it either). I cannot thank you enough for finally providing a sensible explanation of what in the world the Laplace transform is actually doing. Now I've got to go back and re-read every control theory book I've ever bought, since I can probably make sense of them now.

@jamesheadrick7206 7 жыл бұрын

As a controls 2 student, reviewing your videos from Fourier transforms too classical controls theory I am very impressed with your videos! Keep it up!

@faifai4 7 жыл бұрын

This video is insanely good.

@allenkkwong 10 жыл бұрын

Direct and clear in explanation! Great lecture.

@dericc8611 8 жыл бұрын

Kinda blew my mind at the end :D Thanks so much for this video!

@achimbuchweisel2736 8 жыл бұрын

Great visualization of the Laplace Transformation! Made my day.

@Beudd 6 жыл бұрын

Absolutely clear. Brilliant. I like this kind of video because it shows that we can explain some abstracts concepts with precise words and illustrations.

@RexGalilae 8 жыл бұрын

It's a great idea you came up with instead of simply writing while talking, wasting time in the process. Good work!

@closingtheloop2593 7 жыл бұрын

Always a good refresher. Thanks!

@funcionamaldito 8 жыл бұрын

I thought that "solution to differential equations must be either ..." was misleading. He's specifically talking about linear differential equations with constant coefficients.

@SuHAibLOL 7 жыл бұрын

yeah exact differential equations wouldn't behave that way for example

@SuHAibLOL 7 жыл бұрын

Athul Prakash no you can find non sinusoidal and non exponential from simply some separable equations

@grandlotus1 7 жыл бұрын

You go, girl! (I'm at a loss to say anything probative.) Is math a conspiracy of smart people over the rest of us? I mean, i'm not dumb (stop sniggering), but this could be total baloney and I have no way to discern. For example the quote "...just below infinity..." I don't believe in shaming myself, but, huh?

@TheDavidlloydjones 6 жыл бұрын

Hugo, No, you're not shaming yourself. This guy is a wonderful example of David Hilbert's wise remark "You get all sorts of nonsenses when you bring in infinity." What he says about the declining case of a sinusoidal signal being "unfathomably large but not infinite," for instance, is a hoot. How be you try "limitless," baby?

@technoguyx 4 жыл бұрын

You can even get terms of type t*exp(at), t^2*exp(at), ..., t^k*exp(at) if the characteristic polynomial of the linear diff. eq. has a root of multiplicity larger than one. These terms arise from taking the exponential of the Jordan form of the associated linear system.

@Centuries_of_Nope 8 жыл бұрын

In computer engineering. Started this class and is the hardest part of the whole degree. Watching this, it took until you drew the circuit until things started to click. Thank you.

@GonzaloBelascuen 9 жыл бұрын

Amazing Video, thank you!!

@ricojia7322 7 жыл бұрын

Your video is unique. It answers my questions perfectly.Thank you so much Brian, I regret so much that I pay a ton to university, hoping to learn things step by step, but the only things I get are complications.

@shekharyadav380 6 жыл бұрын

The 3d plot explanation was amazing.....cleared a lot of things......thanks a loooottttt !!!

@maksoff Жыл бұрын

First video on youtube, where one "thumbs up" is not enough. Amazing video, after so many years it is not magic for me anymore!

@ludwigrasmijn8218 6 жыл бұрын

AMAZING! best part was the 3d part going to 2d to show the poles and zero, best explanation ever

@rajatjadhav1061 2 жыл бұрын

This was really good for actual understanding and imaginative approach. Now we can really get what the plot is.

@doktoren99 9 жыл бұрын

Ohh man this is great! I wish there were more videos of graphic understanding in mathmatics as well!

@jupatj24 10 жыл бұрын

Such knowledge, much appreciated, well done good sir.

@rajdeepchatterjee3549 10 ай бұрын

genuine and digestable. thankyou sir!

@hansi98 11 жыл бұрын

this is helping me so much understand the motivation of what i have to do thank you

@exmuslim3514 5 жыл бұрын

awesome explanation you give answer of lot of questions brother..

@nezv71 9 жыл бұрын

At 2m40s, the claim is way too broad. Exponentials are the only solutions to *homogeneous linear constant-coefficient* differential equations, or in physical terms, they are the only possible *transient* responses of *linear time-invariant* systems. For example, the linear time-invariant system y'' + y' + y = x^2 has a non-exponential (particular) solution y = x^2 - 2*x just due to its inhomogeneity. It'd be bad for people to believe an (incorrect) statement like "the solution to every differential equation is an exponential." That'd be an extremely powerful game-changer if it were true.

@zedlepplin9450 6 жыл бұрын

Can you think of a function or a signal (other than exp or any sinusoidal func for that matter) that if you take it's derivatives (1st, 2nd, etc) and if you add them all up will get a zero? With the mathematics that we know now, there isn't any. I'm not sure if there is a proof for that but for now it's a (very) valid statement.

@twilightknight123 6 жыл бұрын

I think you misunderstood what the original comment was saying. The video states that the solution to ALL differential equations are exponentials, sinusoids, or combinations of the two. This is just not true. It may be true for most physical differential equations such as Laplace's equation or the heat equation, but it is not true for ALL differential equations. Hell, most physically described systems are described by Legendre polynomials while are neither exponentials nor sinusoids. You can put sinusoids as the argument for Legendre polynomials, and most of the time you want to because of symmetries, but they are not inherently exponentials NOR sinusoids.

@eavids128 3 жыл бұрын

Thank god, I thought I was the only one who got super confused by the statement the video made. The first differential equation we learned in ordinary differential equations were ones where you could use simple integration to find solutions. However, I see how it could be a valid statement that every solution to a differential equation is *comprised* of sinusoidals and exponentials, as this is true of all signals.

@DDDelgado 5 жыл бұрын

2:30 interesting, solutions to differential equations representing physical phenomena results in exponentials or sinusoids, nice, it clears a lot of things.

@BrianBDouglas 11 жыл бұрын

You are correct the Fourier Transform returns a complex number. I think I confused a few people by only drawing one 3D plot (where I also drew the red line). But at 6:50 I explained that there was an imaginary and real component at that point. The graphic was just supposed to show visually how you fill in the S plane with information using the FT. Unfortunately, it didn't accurately represent the real and imaginary response. Does that clear it up a bit?

@horacechen5894 8 жыл бұрын

Excellent introduction!!! Thanks a lot.

@priced80 6 жыл бұрын

Wow. This is a really excellent explanation. Well paced too and clearly drawn. I like the fact I don't have to wait for you to write / draw things. That can get a bit tedious on Khan Academy

@squidcaps4308 8 жыл бұрын

Thanks for doing this in reverse, made so much more sense this way.

@inzepinz 5 жыл бұрын

Finally I understand what the laplace transform is for, thanks.

@samfisherXXI 10 жыл бұрын

Thank you for your brilliant explanation, I always hate when teachers "parachute" methods and equations without explaining the Why, well you did just the opposite and thank you for that :D

@danielurdiales2856 4 жыл бұрын

You are really good at explaining this material!

@rajeshkanna4124 6 жыл бұрын

Man your tutorials are awesome. Its a lot better to watch your tutorial than going to college. Applause !!

@quantummath 8 жыл бұрын

Thanks a lot bro, well done man.

@HassanAli-os3py 7 жыл бұрын

Such intuitive explanation!

@user-iz3rg3qq3z 9 жыл бұрын

Great Video! Your explanation is very clear and intuitive. Thank you =D

@sgtcojonez 8 жыл бұрын

You just blew my mind.

@BrianBDouglas 11 жыл бұрын

Hmm, I think this is a tricky question for me to answer. The thing is that we really don't perform the Laplace Transform and its inverse the way I explain in this video. The intent of the video was to give you a better understanding of what the LT is doing behind the scenes when you solve that integral ... or when you look it up in a table. By reverse I was just saying that you usually don't take the LP of the impulse response, you take it on the Diffy Q and solve for the impulse with it.

@averytieh 11 жыл бұрын

Great video to rough understanding on Laplace Transform!!!

@neilphilip2320 2 ай бұрын

These talks are stunning!!!

@Obyak 10 жыл бұрын

I really like your videos. You know your stuff 99.9%. please keep adding more vids on ME Controls. Thanks

@JordanEdmundsEECS 7 жыл бұрын

Wow. Well done. Very well done.

@Mordaxe 10 жыл бұрын

This video helped me a lot ! Thanks

@Arobinek 7 жыл бұрын

First, I was sceptic, but then!!! Great!

@IsaMelCoding 3 ай бұрын

MY IB LIFE SAVER!! THANK U SO MUCH

@theman83744 5 жыл бұрын

Thats a great overview. Thanks

@SafeAndEffectiveTheySaid 8 жыл бұрын

Thank you Mr Douglas!

@pp_01123 7 жыл бұрын

Brilliant Video (Y). Great Work!

@VrushangPatel9121992 8 жыл бұрын

great explanation, thank you sir.

@abhimanyupatwari4025 7 жыл бұрын

this is awasome lecture

@Rockstar1376 8 жыл бұрын

Splendid video, thanks!

@seinfan9 7 жыл бұрын

The black magic of math

@AngeloYeo 8 жыл бұрын

I have one question guys. At around 6 min in this video, when sigma=-1, "pre-multiply by that exponential..." ... how can the exponential be decaying? because what we multiply is exp(-sigma*t) isn't it? then exp(-sigma * t) must be getting bigger as time goes... Any helps?

@droxid666 7 жыл бұрын

You're right, it's most likely an errata. The function behavior is correct assuming the exponential doesn't have the negative sign, so the sigma sign is incorrect on the blackboard and verbal explanation. Happens to all of us.

@catalinstefanteodorescu2996 7 жыл бұрын

I also agree that the exponential should have been drawn as an increasing function with time. In other words, when sigma=-1, the exponential factor appearing under the integral of Laplace definition is exp(-sigma*t) which is an increasing function. Moreover, the integral might no longer converge in this region, where sigma becomes more and more negative: e.g., take x(t)= sin(a*t) which roughly looks like the function drawn by Brian on the blackboard. Its Laplace transform is a/(a^2+s^2) under the condition that Re(s)>0. One can check tables for this formula. Note that the 3D drawing of a/(a^2+s^2) is roughly what Brian has illustrated on his blackboard, however this 3D drawing makes sense only for the right half Re(s)>0, while for Re(s)0. As for the situation Re(s)

@andrerenault 5 жыл бұрын

This is the closest I've come to understanding Laplace. I still don't fully get it, but I have glimmers of it. Thank you so much.

@anoop5611 6 жыл бұрын

Very neatly put!

@deltaexplorer47 4 жыл бұрын

WOW !! IMPRESSIVE .... Thank you very much. An INSPIRING video as well. GOD bless you always.

@TheScottttttt 10 жыл бұрын

I think this might be quite a good idea! Having an image to quickly scan over to refresh my mind at the end of each of these videos would be quite useful. Thanks for the videos Brian.

@marwabarznjy3606 4 жыл бұрын

How I can get a good report about (Laplace transform and fourier series )

@Amb3rjack 10 ай бұрын

Wow! Just exactly what kind of a mind does it take to be able to just trip this stuff off the tongue like Brian does? I was mesmerized by this video and understood practically none of it . . . .!!

@BrianBDouglas 11 жыл бұрын

Hi MultiNova100 I just got like 20 emails from you! :) The "it" I was referring to was the impulse response. Now I'll go see about your other questions ... standby

@boling5755 3 жыл бұрын

I am reading your ebook. Thanks a lot for you kindly sharing.

@Friemelkubus 11 жыл бұрын

I only get half of this because I haven't gotten much of the mathematics yet (was just looking for Laplace transform because we vaguely saw it) but this is epic. I'll so dig into this after my exams.

@willashland 8 жыл бұрын

your videos are sweet bro, keep em comin

@gulshan1767 6 жыл бұрын

Excellent work !!

@thetompham 7 жыл бұрын

I am finally beginning to connect all the stuff Ive been learning as a electrical engineering student...wow.

@Nuke_Gunray 6 жыл бұрын

Cool video, thank you very much

@fatihsarikoc570 2 жыл бұрын

Hi Brian, That's the best explanation of Laplace Transform I have seen, which is touching on originating conceptual ideas. All your videos have this charecteristics. Sure, you have extraordinary talent and expertise. But, I would like to learn where this culture of conceptual understanding of you comes from. Is it related to university you graduated from or is there conceptual formal textbooks/resources that you can strongly suggest in this manner?

@ECOMMUSK 8 жыл бұрын

this is very good. thank you!

@pefrenos 10 жыл бұрын

THANK YOU very much for your time

@grpagobo 4 жыл бұрын

Thanks Brian.

@mbabaeevideos 11 жыл бұрын

Thanks Brian. I really like your drawings.

@rivera82nd 9 жыл бұрын

Awsome sir, well presented.

@ytano5782 6 жыл бұрын

Excellent!

@MrHashmi90 7 жыл бұрын

Brian thanks for this informative video and recommending this book " Steven W. Smith - The Scientist and Engineer's Guide to Digital Signal Processing "..... awesome book .

@arden_scott 4 жыл бұрын

Thank you this was really helpful

@meandyousomeofusfortwo 8 жыл бұрын

Helpful video.

@tarickgayle3145 7 жыл бұрын

awesome information. at first the maths class look boring but after know what i'm doing. it get pretty interesting. don't fully understand but i think i will get there