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
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
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.
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!!
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.
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.
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.
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!
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.
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.
I am a Data Science student and I thank RU-vid'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!
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.
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!
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!
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
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.
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.
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.
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!
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.
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
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.
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.
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.
Hi Steve, I am a postdoc and have found your lectures useful when learning new concepts or brushing up old ones. I also find the mode of the lecture recording fascinating. Would it be possible to share an overview of the process of how your lectures are recorded? Thank you and keep up the good work.
The trick is actually simple. The lecturer stands in front of a glass board and writes notes on the board normally as we have in class, and a camera records the process from the other side of the glass. Then, after the video is recorded, use editing software such as (opencv) to flip every images (left -> right) recorded in the video. That's it!
I think it would also be interesting to briefly show why is not so simple to perform the inverse Laplace Transform. I mean, some Engineer courses don't have any complex Calculus lectures, so it is quite common to students try to perform the inverse Laplace integral without describing the path on the complex plane given by s = gamma + i*omega.
Great point. In my ME565 course (all videos in a playlist), I spend 6 lectures developing enough complex analysis to be able to take the inverse Laplace transform. Definitely not as simple as the forward transform.
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!
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?
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.
So technically the Laplace transform is a generalized Fourier transform (as it handles more non-well-behaved functions), but really the Laplace transform uses a Fourier with extra conditions attached?
Dear Prof. Brunton, I have a question. Isn't the inverse derivation process starting 11:46 missing out the Heaviside function? Or is it so that the inverse only valid for f(t) for t > 0. I tend to think I am missing something in this derivation. But I have to thank you a ton for the amazing way of teaching. Deriving the intent behind the transform is so much more interesting and insightful. I loved the Fourier transform series as well.
Very nice lecture, professor, thank you! However I would like to notice, that it's not perfectly correct to say, that Fourier Transform is unapplicable to ugly functions like constants and sins (in general non rapidly decreasing functions). A Fourier Transform can be generalized to such functions by defining FT of a generalized function aka distribution. This generalization allows to handle ugly functions and work with things like deltas in a mathematically correct way. And I belive that it's more appropriate to call this type of generalization a "Generalized Fourier Transform". I'm not saying that you are wrong, it's true that classical Fourier Transform has problems with this ugly functions, but generalization through distributions solves this problem just as good as the Laplace Transform.
You are definitely right. I was glossing over some more technical details here, but you are right that with generalized functions it is possible to FT these "ugly" functions.
Can you talk about why some functions have different Laplace and Fourier transform despite Laplace being a generalized version for example sinusoidal Laplace is different from sinusoidal Fourier.Similarly the step function has different transform in Fourier and Laplace.Also it would be helpful to know why we always use Fourier in communication subjects rather than Laplace which is way easier to handle
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)
@@王珂-k7d No: the whole frame is mirrored. There is a clear window between him and the camera. He writes normally on his side of the window, but that makes it reversed left-to-right from the camera's view. Mirroring the video applies to both him and the writing. This is much, much simpler than, say, deriving the Laplace transform. Or learning to write backwards. Not that he couldn't have learned to write backwards; I once learned to write backwards, but that was on a dare.
imo this isn't a sensible convention and should be ignored: you should consider your functions as only being defined for t bigger than or equal to 0. Indeed, all information about f(t) for t
These are v good . Check out Prof Kutz's lectures. You'll find how to uncover the Terminator signal. You won't know what I mean till you watch em :) . He's v good too.
Really loved your Fourier transform video because it explained the mystery why people use Ohm's law with the imaginary j term in multiplication and addition arithmetic. But I am afraid to watch this episode with Laplace because I don't know where this is going. Loved your glass board because it showed from the beginning to the end, all in one picture, of why calculus differential disappeared with Fourier.
The essential difference, is that instead of multiplying and dividing by j*omega to account for calculus operations, you multiply and divide by s. The s-variable for the Laplace transform is called complex frequency, which is a combination of sigma+j*omega. The sigma is the domain variable of a spectrum of exponential decays, and the omega is the domain variable of a spectrum of frequencies. The Fourier transform only considers the steady state, while the Laplace transform considers the approach to the steady state, from the initial conditions.
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.
I don't understand wtf it is, in my collage, i know only integration but luckily I got promoted in 2nd sem because of corona, luckily i escaped from electrical and electronics subject because of corona, i know god helps me✌️,
Dear Steve, nice explanation. Maybe you already have a plan for this upcoming playlist about Laplace transform. If I could wish some content, pls explain how Tustin transform method works and where it's useful. There's too less explanation and examples about that. Thanks and take care!
