The Inverse Laplace Transform

[@ChristopherLum]

In case it is helpful, here are all my ODE videos in a single playlist kzbin.info/aero/PLxdnSsBqCrrHHvoFPxWq4l9D93jkCNIFN. Please let me know what you think in the comments. Thanks for watching!

[@EdPalacios14]

AE501: This series on the Laplace transformations was really extremely helpful. The organization of the videos helped put all the concepts into perspective. Great series!

[@ChristopherLum]

Thanks! I'm glad you liked the series!

[@carlydunford2546]

AE 501: I really appreciate when you write out the steps in the videos, like steps for the Laplace transform. It is a good overall summary of the video and makes an easy section to reference when we need a review.

[@KevinCastaneda21]

AE 501: I really enjoy watching every step being displayed explicitly so that there is no mystery between steps and then I really enjoyed the step by step procedure at the end for Laplace Transfer, great video!

[@tonykuenzli2182]

AE 501 - The comparison of the three cases of poles to their signal in the time domain was very insightful

[@PathwaytoEngineeringDegree]

AE501: probably the most helpful lecture I’ve watched so far!

[@Andrew_Bruns]

AE501: Great video on the inverse Laplace Transform. I think showing the relationship between the pole locations and time domain response was helpful

[@ethanngo3203]

AE501: Love the Transformers analogy! That's a very interesting way to look at Inverse Laplace Transform

[@ChristopherLum]

Glad you liked it, there are more nerdy analogies coming in the future!

[@markykid8760]

You're wearing an Irish rugby jersey - nice ☘️ Your lectures are great Chris, thank you.

[@ChristopherLum]

I'm glad you like them. Please feel free to drop me a comment on any of the other videos that you find useful. Thanks for watching!

[@ryanmeinhardt81]

AE501 : Good layout of the inverse laplace process, and I always find the examples of the spring/ damper system very helpful

[@KennethWright-k2h]

AE501: Thank you for organizing the solution process into steps. This helps me approach these problems.

[@hshams28]

AE501: Great overall review and way to tie everything together!

[@jasonfranklin4614]

Great wrap-up to Laplace and the applications of the zpg format. It is very helpful

[@AlejandroMartinez-nv9ri]

AE501: I liked the graphs showing the relationship between the pole locations and time domain response. Helpful visual, thank you

[@FastLikeDar]

AE 501: No questions yet, but just wanted to say the layout and organization of the lectures has been great and the subsections in the video itself will make going back to review much easier, thanks! - Harold

[@paulpietrowicz3683]

AE501 Student- Good definition, steps and application of the inverse laplace method. Your steps make it seem so easy, now to apply it in the HW.

[@matthewbajamundi8774]

Great Transformer analogy. This video overall was helpful. Thank you.

[@Jenicek109]

Really helpful lecture, thanks!

[@ChristopherLum]

I'm glad it was helpful. I have a several more videos on ODEs on the channel. Please feel free to check them out, thanks for watching!

[@Jenicek109]

@@ChristopherLum I am going one by one, then I want to go through your Control Theory lectures and hopefully in the end I will be able to model my own dynamic system and controller. 🙂 So thanks again, you with Steve Brunton and Brian Douglas are like a holy trio of Control Theory on KZbin! 😄

[@jesusespinoza2349]

Very powerful method for solving ODEs

[@mrmateoable]

AE501, the discussion at 23:18 about how the poles govern the signal was especially helpful for understanding them, especially for hw2

[@ChristopherLum]

Matt, great, I'm glad it was helpful. Please keep me posted and let me know how things go as the quarter progresses!

[@LilanieAlfredaAbdur-Rahman]

Ae501: Thanks for the refresher!

[@Tamanaaaa1]

AE 501 - great review thank you

[@thomasireson1427]

Cool to see how it all comes together.

[@bryanliberman9732]

AE 501: Hey Chris! One of my favorite things about seeing the videos arranged in this way (and I guess binging them like I have been) is how clear the throughline is between what we want to do and how to do it. Its clear to see that: 1. We want to solve for a function that gives us the position of something at a time (x(t)) 2. We have a model of the behavior of our system, but it is a multi-order differential equation, and so a pain to solve traditionally. 3. So, we are going to do the following: a. Put it in the laplace domain. b. Solve for the function there. c. Partially expand our result d. Take the inverse laplace. And boom. You have your position at a given time. Or, if you don't feel like taking an inverse laplace, you can check if you can predict a study state with the FTV. I know what I said is kind of obvious, but for some reason this whole process wasn't as clear for me when I first learned it in undergrad. Thanks for helping connect all the dots now!

[@ChristopherLum]

Bryan, thanks for the clearly laid out observations. I'm glad this presentation order makes sense. On that note, if there is ever anything that you notice that can be improved, please let me know!

[@jacobgivens2000]

AE 501: Jacob Givens. I definitely really needed a refresher on this!

[@ericwang161]

What a great series of videos!

[@sunnysarkar7643]

AE 501: I thought that you adding the real/imaginary point on the plot and drawing the graph of how it impacts the inverse laplace was a great visual that helped my understanding.

[@jonathonlaird6279]

Thanks for the video!

[@melissawells8133]

Thank you for the help!

[@elijahleonen198]

AE501: The block diagram in the beginning was very helpful for understanding the rest of the video!

[@iremerkan0217]

AE501: I also agree that the video is a great review on the inverse laplace transform. Also thank you for showing the Mathematica part of it.

[@sajeew]

thank you really helpful sam

[@ryoonoue1076]

AE501. Gotta love the Optimus Prime and Megatron reference! haha. These type of examples are silly but actually make understanding so much easier. Thanks for the video Professor.

[@ChristopherLum]

Transformers G1 are great

[@ChaseSnow-w9f]

AE501: Great video.

[@AurashFilsoof]

AE 501 Great Video thanks!!

[@timproby7624]

[AE501] 44:40 Important for clarity on why having higher orders in numerator is not a huge concern since these systems are not really physically possible. I assume this can also act as a check if you are writing your differential equation of a system and get you higher orders in numerator, it means you've constructed the initial differential equation incorrectly.

[@masontelander3847]

Great video

[@evansteele7874]

AE501: Question on the Mathematica output starting at 38:09 - The Inverse Laplace of the X(s) function shows 1/2 - 2e^-t..., where on the board we calculated (1/2)*t + ... . Why is the first term 1/2, and not (1/2)*t ?

[@ChristopherLum]

This might be a typo, perhaps we can discuss at office hours?

[@trevorubrown]

Great vid

[@devarshpatel6063]

Greetings Prof, I am relearning engineering mathematics and matlab, and your lectures have helped me immensely. I would like to thank you for providing these high quality lectures for free. It would be very kind of you, if you could do a similar series (board + matlab + mathematica) for linear algebra. Thank you again.

[@ChristopherLum]

Hi Devarsh, Thanks for the kind words, I'm glad you enjoyed the video. If you find these videos helpful, I hope you'll consider supporting the channel via Patreon at www.patreon.com/christopherwlum or via the 'Thanks' button underneath the video. Given your interest in this topic, I'd love to have you a as a Patron as I'm able to talk/interact personally with all Patrons. I also take video requests and am able to answer questions on Patreon. Thanks for watching! -Chris

[@joewalker5753]

Great!

[@brentpaul7650]

I love Laplace

[@lukewideman1]

AE 501: where can we find the table that lists the common inverse laplace transforms and their respective t domain resulting functions in the textbook?

[@tranpham7120]

AE 501: I have a question related to why you use pole in your video versus roots in your notes?

[@ChristopherLum]

Good question, these terms are interchangeable so sometimes I accidentally switch the terminology.

[@sethwhittington28]

AE501: Provided that the function is set-up well coming out of the partial fraction expansion section, this step seems much simpler by comparison... assuming that you have access to laplace tables and don't have to perform those nasty integrations.

[@jakegalleryn6200]

And it all comes together.

[@ryanjorgensen8192]

AE 501: I like the Transformers analogy. Throw in Voltron and Thundercats and you will have pretty much summed up my entire childhood.

[@ChristopherLum]

Voltron is coming down the road 😊

[@RajChhabraUW]

AE501: Great video! For homework problems, can we refer to a Laplace Transform table if the problem does not ask us to explicitly derive the Laplace transform?

[@ChristopherLum]

Yes, feel free to use a table

[@connorbaldwin5845]

A E 501 This was a great recap on how to apply the laplce transform to Solve an ode

[@Richard_Le]

AE501 So if all the poles of a Laplace equation all fall on the y-axis, that would mean that the time domain response would be constant or oscillate around a constant range?

[@ChristopherLum]

Exactly, if you have only imaginary parts (no real part) then you have a pure sin or cos which is purely oscillatory.

[@TriMartz-f4x]

[AE 501] thank God the bus full of nuns are safe! 😂

[@SweetValleyKitten]

AE 501: Why do you use "pole" in your video versus "roots" in your notes? Around 26 mins into the video when you discuss that the types of poles actually influences the response of the system.

[@ChristopherLum]

Lila, good question. Poles and roots are used interchangeably as they mean the same thing. We'll soon see that eigenvalues also play a part in this discussion and they are also pretty much the same thing as poles and roots.

[@SweetValleyKitten]

@@ChristopherLum Thank you!

[@kacperbardecki3671]

*1-2s^2-3s @34:56

[@keyshawnb4845]

AE 501: This was a great payoff to the previous lectures on how the physical system is affected by the different poles :). I enjoyed the transformers references as well

[@ChristopherLum]

It's great to see people picking up on the nerdy analogies!

[@CodySmith]

AE501, Cody Smith.

[@atruon17uw]

[AE501] It looks like EMF is not the only Transformer in engineering now!

[@malachimorris1649]

AE501 - Malachi Morris

[@ardacetken9090]

AE501: Arda Cetken

[@daniellerogers5959]

Michael Bay should be ashamed of how much of a hack he is ruining for our nerd alerts, excuse me while I'm rolling laughing ... too funny

[@B_Foland767]

AE 501 Bryce Foland

[@BenLandes]

AE501: I'm impressed you can hold that tablet with one hand while drawing without dropping it

[@changlongwang5201]

[A E 501 student] watched - CW