The Laplace Transform - A Graphical Approach

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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!

Опубликовано:

25 янв 2013

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Комментарии : 406

@fatihersoy7559 4 года назад

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

@ad2181 3 года назад

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 года назад

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 года назад

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

@georgeclooney6208 5 месяцев назад

@@vaughnmonkeynot begging fakin paying for them to teach us

@MugiwaraSuponji 7 лет назад

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.

@fzigunov 8 лет назад

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!

@SeraphisQ 7 лет назад

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.

@marialey7658 8 лет назад

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

@pratibharacheljohn3814 3 года назад

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!!

@bboysil 6 лет назад

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.

@BrianBDouglas 11 лет назад

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 года назад

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

@shishirsks 9 лет назад

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

@Ropsch 11 лет назад

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

@poppyblop484 5 лет назад

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

@DanT2990 11 лет назад

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 года назад

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!

@90ben09 11 лет назад

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.

@apoorvvyas52 8 лет назад

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

@rileystewart9165 7 лет назад

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

@Chadwikj 10 лет назад

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

@MarkNewmanEducation 6 лет назад

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.

@faifai4 7 лет назад

This video is insanely good.

@dericc8611 8 лет назад

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

@allenkkwong 10 лет назад

Direct and clear in explanation! Great lecture.

@RexGalilae 8 лет назад

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

@alanly3780 7 лет назад

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

@GonzaloBelascuen 9 лет назад

Amazing Video, thank you!!

@closingtheloop2593 7 лет назад

Always a good refresher. Thanks!

@Beudd 6 лет назад

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

@achimbuchweisel2736 8 лет назад

Great visualization of the Laplace Transformation! Made my day.

@ludwigrasmijn8218 6 лет назад

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

@shekharyadav380 6 лет назад

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

@rajatjadhav1061 2 года назад

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

@Centuries_of_Nope 8 лет назад

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.

@rajeshkanna4124 6 лет назад

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

@speedbump0619 11 лет назад

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.

@squidcaps4308 8 лет назад

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

@inzepinz 5 лет назад

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

@maksoff Год назад

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

@ricojia7322 7 лет назад

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.

@jamesheadrick7206 7 лет назад

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!

@hansi98 11 лет назад

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

@BrianBDouglas 11 лет назад

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

@rajdeepchatterjee3549 11 месяцев назад

genuine and digestable. thankyou sir!

@jupatj24 10 лет назад

Such knowledge, much appreciated, well done good sir.

@neilphilip2320 3 месяца назад

These talks are stunning!!!

@danielurdiales2856 4 года назад

You are really good at explaining this material!

@horacechen5894 8 лет назад

Excellent introduction!!! Thanks a lot.

@user-iz3rg3qq3z 9 лет назад

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

@HassanAli-os3py 7 лет назад

Such intuitive explanation!

@averytieh 11 лет назад

Great video to rough understanding on Laplace Transform!!!

@priced80 6 лет назад

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

@BrianBDouglas 11 лет назад

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?

@exmuslim3514 5 лет назад

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

@quantummath 8 лет назад

Thanks a lot bro, well done man.

@Mordaxe 10 лет назад

This video helped me a lot ! Thanks

@sgtcojonez 8 лет назад

You just blew my mind.

@doktoren99 9 лет назад

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

@IsaMelCoding 4 месяца назад

MY IB LIFE SAVER!! THANK U SO MUCH

@Obyak 10 лет назад

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

@BrianBDouglas 11 лет назад

Hi Shouvik, great suggestion! I've just filled out the form to get my channel reviewed by RU-vid 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.

@pp_01123 7 лет назад

Brilliant Video (Y). Great Work!

@samfisherXXI 10 лет назад

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

@anoop5611 6 лет назад

Very neatly put!

@funcionamaldito 8 лет назад

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 лет назад

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

@SuHAibLOL 7 лет назад

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

@grandlotus1 7 лет назад

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 лет назад

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 года назад

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.

@JordanEdmundsEECS 7 лет назад

Wow. Well done. Very well done.

@theman83744 5 лет назад

Thats a great overview. Thanks

@nezv71 9 лет назад

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 лет назад

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 лет назад

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 года назад

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.

@Rockstar1376 8 лет назад

Splendid video, thanks!

@DDDelgado 5 лет назад

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

@Arobinek 7 лет назад

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

@VrushangPatel9121992 8 лет назад

great explanation, thank you sir.

@gulshan1767 6 лет назад

Excellent work !!

@andrerenault 5 лет назад

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.

@marctison1039 6 лет назад

It's this video that made me finally click. Can't thank you enough, I'm buying your book

@willashland 8 лет назад

your videos are sweet bro, keep em comin

@BrianBDouglas 11 лет назад

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!

@SafeAndEffectiveTheySaid 8 лет назад

Thank you Mr Douglas!

@boling5755 3 года назад

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

@lectrix8 7 лет назад

This video was great!

@abhimanyupatwari4025 7 лет назад

this is awasome lecture

@ECOMMUSK 8 лет назад

this is very good. thank you!

@thetompham 7 лет назад

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

@Amb3rjack 11 месяцев назад

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 . . . .!!

@bartek89k 11 лет назад

Definitely YES! you're great!

@mbabaeevideos 11 лет назад

Thanks Brian. I really like your drawings.

@arden_scott 4 года назад

Thank you this was really helpful

@deltaexplorer47 4 года назад

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

@pefrenos 11 лет назад

THANK YOU very much for your time

@Nuke_Gunray 6 лет назад

Cool video, thank you very much

@tarickgayle3145 7 лет назад

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

@jfpatxo8707 7 лет назад

excellent video !!! thanks !!!

@meandyousomeofusfortwo 8 лет назад

Helpful video.

@ytano5782 6 лет назад

Excellent!

@jean-michelgonet9483 5 лет назад

I’ve got it. Wow. Very nice explanation.

@rivera82nd 9 лет назад

Awsome sir, well presented.

@Friemelkubus 11 лет назад

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.

@grpagobo 4 года назад

Thanks Brian.

@BrianBDouglas 11 лет назад

If you look at w^2/(s^2+w^2) you'll notice that it's a classic 2nd order system with damping, zeta = 0. Which means if you put an impulse into this system an undamped oscillation will be the output, or a sine wave as expected. Remember that with Laplace Transform the only numbers that mean anything are the poles and zeros. In this case the poles are at, S = sqrt(-w^2) which is +- w*i. So there are two poles and both are on the imaginary axis, which again means undamped oscillation.

@maudentable 5 лет назад

AWESOME AWESOME EXPLANATION

@TheScottttttt 10 лет назад

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.