Laplace Transforms and Differential Equations

This video describes how to use the Laplace transform to simplify differential equations.
@eigensteve on Twitter

This video was produced at the University of Washington

[NowanIlfideme]

I can't get over the fact that these lectures really excite me in ways many of my professors didn't. :)

[JonOlaivar]

I'm not sure that words can describe the positive impact you've had on peoples math education. Such great lectures, I really appreciate you putting the time and effort into them.

[xiaowenzhang]

I just spent 2 days binge watching this series of videos, they are so intuitive and clear and I've learned a ton. Thank you Prof. Brunton!!

[jha]

Best math lectures on youtube i have ever seen.

[House]

amazing! I've never seen a better summary of a Laplace ODE physical example, with the final glimpse of how control theory gets in the way...

[rajendramisir]

Indeed! Extraordinarily cool. I really enjoyed your crystal clear approach to and explanation of solving this spring motion dynamics ODE. I like the control force part and would like to see how you handle it. I got a good grasp of the Laplace/Inverse Transform and used them to solve ODEs in my Differential Equations class taught by Professor Leif at KCC(CUNY). I recall using a lot of exponential and trigonometric identities to solve those ODEs. Laplace was a clever and intelligent French Mathematician - one of my favorites.

[andinosa]

I loved your videos on the Laplace transform. Your explanations is simple and to the point.
However, I want to mention for the enthusiasts out there: except for very simple ODEs (e.g.nlinear with constant coefficients) you never use the Laplace transform to solve an ODE. For real life problems you use numerical methods like RK4. Numerical methods can easily solve any ODE, however complex. They should be taught above all else in engineerinf. Unfortunately many old school professors still waste student time with strategies to solve ODEs analytically.... Conceptually interesting but useless...

[vnickleswitter]

Thank you for taking the time to discuss these topics. I appreciate it.

[danielhoven]

This brings back memories from sophomore year :) Thanks for the excellent content professor!

[BentHestad]

An excellent, little lecture! Could hardly been done better. Thank you, Sir!

[LucasDimoveo]

I apologize for the non-mathematical comment, but I must ask - are you writing backward on a transparent board? If so ... that is amazing. Simply skillful. Thank you for your awesome work.

[alexli]

Wonderful lecture! I am really looking forward to see the lecture about solving PDE with Laplace transform.

[pengfeixianyu]

Thank you Brunton for these wonderful videos.

[wiloberlies]

Great presentation again Dr Brunton, thank you for making this available!

[toraibo]

As I see your lecture, I want to become a professor one day :)
Incredible videos, you really helped me out.
Greetings from Germany.

[sachinr]

Sir, thanks for the lectures.
I am following your DMD book exercises problems on flow past cylinder.
I want to try these methods on new data, (jets, plumes data).
its request for you can please mention some PIV or other image data sets.
Thanks

[Unidentifying]

[Gordon Ramsey voice] beautiful . Now just a drizzle of olive oil

[SRIMANTASANTRA]

Hi Professor Steve, tremendous and excellent lecture, Thank you

[PetrGladkikh]

4:59 - I think itwas necessary to mention that laplace transform has linear properties and that is why one can apply it to each term separately.

[jtlee]

Hey Steve, first off your videos are great! I am a fellow educational YouTube (nowhere near your scale), and I was thinking about making a mini series about some controls theory topics. Are you planning on continuing your Laplace topics? I am thinking a good place for me to start with the series I’m considering would be with how maths work in the Laplace domain and what it’s implications (for things like CLTF) are. If you are covering this, I will probably just skim over it and link to you- no need to reinvent the wheel. But if not I would love to do some episodes on that, but would need to start writing scripts in advance. Anyway, not sure if you will see this, but if you do It would be great if you would just let me know your thoughts. Thanks so much! And PS, my video style is super different (I animate everything and tend to do broader overviews aimed at getting a basic intuition, you do MUCH better at fine details), I would love to try and collaborate some time since they are complimentary styles if you would be interested