Laplace Transform Examples

[@PanMaciejK]

I finally found professor that explains not teaches the formulas. It's amazing how simple concepts many professors over complicates with not not naming what is that they're doing. Great lecture, hope You'll live long and good life!

[@juliogodel]

Can you keep publishing new videos forever? Thanks, as always a great explanation.

[@Adeltraut]

I am viewing your videos to catch up with something I had to learn years ago and I love it. Your in depth explanations motivate the subject just enough to get the viewer interested in the method itself rather than the "why do need this and how do I calculate it quickly" that is seen more frequently.

[@Eigensteve]

That is really nice of you to say! Finding the balance of high-level and depth is always tricky.

[@p_square]

From today, I encountered you randomly and I would not lie but YOU ARE A GENIUS. You taught Laplace Transform better than any other KZbinr. As soon as I finished the video of Laplace Transformation, I immediately subscribed you. PLEASE keep making such great videos forever.

[@codebits4461]

As a self taught math enthusiast, your video has opened my mind on Laplace and fourier transforms🔥

[@emilienlegrand6591]

This playlist content is really great and helped me to link many mathematical, computational and physical concepts together. Thank you.

[@alirezanazarahari8342]

I have just binge-watched 35 videos of your Fourier series playlist. I can just say "Thank you!"

[@nikolaalexanderphilipp968]

I am watching your videos to better understand the things I'm learning at university, and the explanations are so simple and elegant, its incredibly fun to listen to you. At certain points in the video I went: "wow, that's so cool!", which I definitely didn't at my lecturers explanation. Thanks a lot! :)

[@JosephRivera517]

I am always in awe listening to you. This makes my understanding of Laplace deeper.

[@mahdirezaei7365]

watched all of this playlist lectures and all i say is Thank you for making me more interested in math and scinece and relations ! i really appreciate it man

[@bhupendrasharma2705]

At 12:17 how did you set e^(+infinity) to zero. Please explain

[@doubleezee]

This series is great! I’m glad someone finally makes videos about this transform!

[@sbhhdp]

Could you refer to an article or video of laplaces work on stability of planetary orbits

[@wesleyfarriss7684]

You’re a fantastic lecturer. Glad I found your channel

[@AmirHosseinSoltanzadeh]

Thank you very much for your yet another insightful lecture. I always enjoy watching your lectures. Just a couple of side notes: @2:22 df/dt looks to be v_dot instead of dv (dv is df/dt times dt). Same happens with du=-s.exp(-s.t) @3:46. @4:20 the upper bound of exp(-s.t).f(t) is guaranteed to be zero only if f(t) is of an exponential type function ( |f(t)|

[@muthuramalingamperumal4747]

Hi Professor Steve, I enjoy watching your series. Complicated concepts made clear. I Like your awesome voice.

[@VeteranVandal]

I'd say that, after all this years, it is the first time "I get" the Laplace transform. The problems I had with it probably came from excessive focus on doing the inverse.

[@SRIMANTASANTRA]

Hi professor Steve, nice lecture, thank you so much.

[@Ninguempensonesse]

Great content. Congratulations professor for your domain in the field and superb teaching skills. And a question. Where are the following lectures?

[@samuelleung9930]

So you really have forgetten to post the link of that convolution video Sir.

[@iooooooo1]

I think it's kzbin.info/www/bejne/o4DMimSchLeChck

[@koheder]

Thanks from Spain. You are a great teacher

[@MathTeacher80031]

Really great video! At t=4:19, I think we should add "assuming f is of exponential order."

[@antonnilukshan935]

The physical systems usually take t=0 as the starting point so the 'one sided', and the stable systems by definition have to be stable so 'weighted' in order to introduce the negative gain along the timeline. Is that a correct way of generalizing the practicality of the Laplace transform in control systems theory? By the way, Thank you so much for this brilliant lecture Sir!

[@IvoryOut]

SO HELPFUL. I wish you were my professor.

[@omarfarouk3848]

Hey, i guess multiplying by e to -gamma t doesnt solve the problem except for functions that go to infinity slower What we fo for the other class of functions ?

[@GTORIDERS]

Hey Steven, thanks for the video. Do you think you could do an example where you solve some couples PDE or ODE. Maybe something like heat transfer with reactions or something like that? cheers

[@andinosa]

RK4

[@Niels1234321]

Shouldn't the Laplace tranform of f(t)=exp(at) be f_bar(s) = { 1/(s+a) if s>a, else -infinity }? You argue that gamma is chosen such that the boundary of the integral at infinity will always be zero, but gamma doesn't show up in these equations. Is it the case that we assume a

[@nikolayfx]

Thank you for the series, the book is amazing too.

[@valor36az]

What a great education and for free!

[@wailrimouche1171]

How is the limit of exp(-st) in plus infinity zero if we do not know the sign of s?

[@ChaoS-pn3ic]

From his previous video we see that by definition of Laplace transform s=a+bi with a>0.

[@ChaoS-pn3ic]

@anusmundianer Agree, your statement is more rigorous. Just one thing to mention here: in practice, the Laplace Transform that interests us is a Laplace Transform that converges. Therefore, if a Laplace Transform of a signal f(t) does not converge, it is usally of no practical use.

[@jamma246]

Yes, he just assumed that f(t).exp(-st) converges to 0 as t -> infinity. That might depend on s, or it might not even happen for any s, if f(t) grows super-exponentially. So we're assuming here that f(t) doesn't grow too quickly, and then also that s is chosen large enough so that f(t).exp(-st) converges to 0 as t -> infinity.

[@Metalhammer1993]

quick question: COuld I "inverse transform" a Laplace transformation by recognition For instance i have an ODE the La place transform after all the algebra just looks like the La place transfrom of sine. I checked it three times "yup if i LT sin(2t) I get that" Could I just skip the inverse transform and say "yup the solution is sin(2t)" and only use the more complicated inverse transformation only if I don´t have something working in my tables?

[@Metalhammer1993]

@anusmundianer thank you.

[@0GodJudges0]

Forgive me if im forgetting my math classes from years ago, but why do we treat s as a constant when we integrate? Isn’t it the variable of the laplace transform?

[@carultch]

s is a constant in the time domain, but it's a variable in its own domain. What you are doing with this transform, is scanning the original function as a superposition of exponential decay functions and sinusoidal oscillations. The s is the exponential decay rate when it is a real number, and frequency when it is an imaginary number. Or a multiplicative combination of the two behaviors, when it is a complex number. So if we fix frequency & decay rate, and integrate the function, we generate one piece of the information to find the transform. If we keep this as a variable, we get all possible results of integrating in the time domain, and put them together as a spectrum of amplitudes as a function of s. The Laplace transform result, is a spectrum in the s-domain.

[@zhichaozhao172]

you didnt link the video of convolution part.

[@JoceliMayer]

Prof. Brunton, how do you set up this mirrored blackboard ? It is amazing, I would like to employ similar apparatus. Thx.

[@swaree]

kzbin.info/www/bejne/i6PXfZehjbWFhLM

[@JoceliMayer]

@@swaree thank you!

[@Bravo_L]

dude i love this guy. he so good. writing backwards and shit. super talented man.

[@lukejagg]

I bet he just flips it horizontally

[@Bravo_L]

Good point. But good ass idea. Looks cool lol

[@abdjahdoiahdoai]

how come video 40 in the Fourier Analysis playlist is private :(

[@Eigensteve]

Whoops, this was an old video that had a small issue. I released the same video without the issue a while back. So not some secret video or anything :)

[@abdjahdoiahdoai]

@@Eigensteve ahhh I see, love this series. I didn't fully understand Fourier conceptually even I was doing probability theory at a graduate level course. This been super helpful!! Binge watching Chapter 3 now!!

[@federicogottardo4869]

Very clear explanation

[@kevinallen9106]

What do you mean ‘we assume we multiplied this by e to the gamma t so this decays to zero’? We didn’t, f(t) is a positive exponential and we said the LT handles functions that don’t tend to zero at plus/minus infinity. You did ‘A Laplace’ on us there! I’m confused. Otherwise loving these lectures!

[@feraudyh]

I remember reading about Laplace Transforms many years ago, while not being very awake to the fact that s is a complex variable.

[@gaugustop]

wonderful classes!!!!

[@IceTurf]

"And next time I'm going to show you how to simplify ODE's by..." this is the last video in this series but it refers to a future video that will be added in the future?

[@r1a933]

Great effort. Thanks ❤️

[@sophielerouge8835]

thank you very much...

[@Eigensteve]

You're most welcome

[@TranquilSeaOfMath]

Great explanations!

[@Eigensteve]

Thanks!

[@manjumanl222]

Thanks ,Are you familiar with Matlab Dr Steve ?

[@lernenmitrobin]

He definitely is, have a look at his playlist

[@jsc3417]

Are you writing on glass backwards?

[@jsc3417]

Oh, you flipped the video, that's clever.

[@mikemironov7551]

5:00 this is so cool!

[@FunPHYSICZ]

The most impressive thing here is that he appears to be writing all this backwards on the other side of a glass window. But I imagine that it’s probably been digitally modified to appear that way.

[@carultch]

He's left handed. You can see him writing with his left hand in his earlier videos on a regular whiteboard. The video is flipped, so the writing appears normally to us.

[@lukejagg]

Awesome video!

[@psxinformation]

Great job Welcome to Pakistan

[@fhz3062]

Everyone enjoys the basics. Back to basics.

[@Ralfonso_Di_Rosetto]

nice channel , greats from germany

[@yuxianghuang-ty6mm]

His lectures are as handsome as himself!!!🤩

[@TheStreamline1998]

so good dude

[@danielhoven570]

Couchy and Riemman went to get lunch, they ate Bromwiches.

[@el_witcher]

Now I know who started the "by mere observation" thing; or "trivially" or "it's clear to see that..."

[@jms547]

The convolution video that Steve forgot to link to: kzbin.info/www/bejne/o4DMimSchLeChck

[@johnwt7333]

Hahahaha your Twitter is EigenSteve, we see what you did there Sir....

[@saitaro]

magic.

[@0GodJudges0]

Imagine if he sneezed on the glass

[@dcselfdefensekarateassn.8310]

English majors keep dis liking this video. 😄

[@foolwise4703]

"Its easy to see" is NOT kind of fun :D