Differential Equations and Dynamical Systems: Overview

This video presents an overview lecture for a new series on Differential Equations & Dynamical Systems. Dynamical systems are differential equations that describe any system that changes in time. Applications include fluid dynamics, elasticity and vibrations, weather and climate systems, epidemiology, biomechanics, space mission design, and control theory.
I assume that students have taken some calculus (but might not remember it) and are interested in modeling the real world.
Playlist:
Course Website [will be updated soon]: faculty.washington.edu/sbrunto...
@eigensteve on Twitter
eigensteve.com
databookuw.com
This video was produced at the University of Washington
%%% CHAPTERS %%%
0:00 Introduction and Overview
3:54 Overview of Topics
10:41 Balancing Classic and Modern Techniques
13:11 What's After Differential Equations?
17:18 Cool Applications
22:38 Chaos
26:32 Sneak Peak of Next Topics

[@yevgeniyterekhin3711]

What you are doing is so important! The way you do it is so cool! I wish I had access to resources and lectures you deliver in my time, about 25+ years ago. Great respect!

[@onurkurum]

This! Thank you so much on behalf all life long learners

[@erikgutierrez3613]

@@onurkurum Thank you for all your paintings, Mr. Ross!

[@kenankenan6371]

Totally agree. Unfortunately in Soviet space this type of lecturers was in deficit and intuitive approach which is almost vital for math and engineering almost wasn't.

[@HackionSTx]

I can't believe you give us these invaluable resources for free prof. Brunton. I wish you all the success in the world.

[@AleeEnt863]

You are the future of the educational system. Keep doing what you are doing!

[@marioskokmotos8274]

Professor Brunton's excellent lectures consolidate at least 3 years of undergraduate (with a lot of graduate influences) mathematics and enhance it with fantastic example applications and even code! I wish I had these resources back in university. Everything would have made so much more sense! One of the best educators out there. We are forever grateful for this treasure professor!

[@michapeka2800]

Looking foward to!

[@goodfty]

Oh thank God, I'm so happy for this. Thank you so much!

[@novelspace]

Ive never hear of a rocket landing described as a pendulum. So simple and elegant. Brilliant. Thank you Steve

[@user-yr9ti4qz7f]

Just can't wait, thank you Professor.

[@christofferfink5049]

Someone give this guy a medal! Or maybe three.

[@Elizabeth-nq9ly]

Wow 😳 where have you been all my life? This is exactly how I want to be taught. With everything linked together. Thank you so much!!!

[@ryanj748]

Sooooo excited for this!

[@andrewnorth7000]

Thanks Dr. Brunton, I’m looking forward to this series! Your description of applied mathematics is inspiring and helps motivate my own journey of understanding on the subject. Love the historical framing and focus on modern applications and techniques. Also appreciate the black background, makes screen time way easier on the eyes!

[@muhammadsaadkhan9701]

Awesome . Thank you Professor Steve

[@AnimationsJungle]

Thank you for starting this lecture series........lots of love ❤️

[@AlexanderRodriguez-lk3hy]

You are awesome. Plain and simple.

[@ec6895]

The amount of resources, clarity, examples, graphics, and quality of the presentation. This is incredible! I think you got me hooked on ODE's

[@ibrahimalotaibi2399]

The way you deliver and share your knowledge is impressive, Professor. Thanks a lot.

[@brunoduartegomes2689]

Dear Steve Brunton, your videos are beyond great. In addition to your good teaching, there are also nice visual dynamics which really help with learning. Please continue and be aware that we will be always here supporting you and eager to learn more and more. Thank you very much indeed.

[@YenPitchayen]

Gosh! I wish I could have your lecture when I studied engineering class. I never knew the differential equation is fascinating and utilizing in every dynamic movement around us like this. Kudos to you Prof.Brunton! Your technique and the materials are very very awesome!

[@muhammadmobeen8682]

you are always impressive... looking forward..

[@khaldibel]

Sounds very interesting. I am teaching Modeling and Simulation and am looking forward to this series of lectures. Thanks for sharing this to a wide audience.

[@robvp71]

52 now... And again motivated to learn this beautiful subject! Great to see you being so enthusiastic and thanks so much for this material.

[@ahmadoqda1327]

I admire your passion for share such greatness of mathematics, you make it much easier and more glorious, thank you.

[@alejandrocarbon5483]

Amazing series. Thanks for compiling it. I am engineer aiming at refreshing concepts that I had forgotten or did not learn properly the first time around.

[@seivansalimibabamiri5268]

Thank you so much for your invaluable contribution to having free access to science. Your are an amazing teacher. these topics are very helpful.

[@mohamedghazali]

Thank you very much for this class and for the clarity of your overview.

[@tianyazhang7065]

Very exciting and fascinating lecture .

[@CodyKoehler]

I can't say enough good things about your videos. I just finished the vector calc series as a refresher after quite a few years. You are a wonderful professor, and these videos are such a nice way to share the information with the world. Thank you!

[@kalpitkatpara4363]

Steve Brunton is the legend, period!

[@AbidAli-bv2gl]

Excellent video, I was student of Real and Complex mathematics

[@moisesbeyond]

thanks for you time , effort and excellent information, from a former lover of Math now an engineer dealing with mundane things but always willing to learn , greetings from the Dominican Republic.

[@fabioragazzi5917]

This channel is simply incredible

[@balajiadmile496]

Oh my god what beautiful explaination we want more videos with visual animation

[@science_engineering]

More chaos, more chaos, more chaos:) favorite topic :)

[@jerimiah593]

Perfect timing since I’m about to start Math207!

[@kolapopoola3114]

I am looking forward to this. You motivated it well. The codes will definitely make it a worth while experience for me.

[@maxberghofer4775]

This will be absolutely fantastic! Thank you so much Dr. Brunton

[@Piipolinoo]

Exciting! Looking forward to follow it!

[@yashthakre]

just what I needed today. Thanks!!

[@hasibulhaque9452]

Just Love for the Professor, You are a blessing no doubt for math lovers.

[@iheavense]

An application perspective focused on PDE, is going to be a game changer for PDE teaching!

[@ManiKandan-zj2lr]

Thank u prof. Steve. You doing an excellent job. I don't know how to appreciate ur noble efforts

[@prashkd7684]

Perfect. Looking forward to the full course.

[@lksmac1595]

What you do is amazing for all engineering students! Love it, thank you!

[@stevenbacon3878]

Looking forward to it!

[@abdussamad4982]

why they did not use this metholodology while teaching mathematics. It makes so much sense listening to Professor Brunton. It is never too late to learn. Thanks Professor. I am learning.

[@mattijuntti7367]

Sounds interesting! Looking forward to the series, thank you!

[@vijaykrishnamenon]

I pretty much make my living with exactly the same stuff you teach .... Extraordinary .... Its like all Engineering in a formula... a Grand unification of all of Engineering Math.

[@mostafaatalla71]

Please continue the great job you are doing for the world of learners!

[@albertogarcia1278]

Thanks Prof. Brunton for this fantastic set of lectures. Amazing as a refresher for an engineer that got out of college 20 years ago. Also beautifully produced! (audio, slides, black background with 'glass' blackboard - all impeccable :-) )

[@kennethodhiambo1803]

This is Gold! I am one of them who studied these concepts about a decade ago and do not remember, but now I find myself in a situation where I need to understand them! Thank you very much! Best regards from Nairobi, Kenya

[@thawinhart-rawung463]

Good job Prof.

[@Mede_N]

Awesome. I'm so looking forward to this course. Thanks a lot!

[@alicanakca8116]

I will have taken this course this year. Looking forward to see your videos, thank you sir! ^^

[@dancollins1012]

Steve, I'm excited as you are about the upcoming videos! As an engineer rediscovering this material, may I emphasise a few high priorities? First and foremost: the intuition on all things eigen. I can use them, but lack the deep understanding as to what they're telling me about the system. Secondly, applications are critical - ideally I'd like worked examples of each topic across electrical, mechanical and fluid systems. Thirdly, the computational aspect is extremely welcome, but I urge you to include Julia language examples - its ease of use and outstanding performance make it a natural for these computations. I would trade it for Python in a heartbeat. Finally, thankyou in advance for engaging with students via KZbin comments, by doing so you will stand as a giant amongst global teachers. Onwards and upwards!

[@mehndiwalibaji6688]

you are a great person and great teacher indeed. respect and love. waiting for this program as well.

[@sal7391]

Thank you so much Steve. What you are doing is a great thing.

[@neurodiversidadetdah9599]

I felt in love with Differential Equations too!!

[@amaarquadri]

Love your videos! Looking forward to the series.

[@tinkeringengr]

Awesome, thanks for being my professor!

[@lioneloddo]

Does someone feel, like Leibniz, that differential equations are out of the world ? Poincaré explains very well the different approches between Newton and Leibniz about differential equations. The Leibniz approach is so beautiful ! Leibniz invents the differential calculation but also the monadology. And it's so instructive to read the monadology with the idea of differential calculation in mind !

[@riteshparmar4687]

I am second year undergraduate student I have read ordinary differential equation in 3rd semester and with partial differential equation course of 4th semester I will watch this masterpiece made by you. Thanks sir, for this wonderful course lectures

[@bernardorinconceron6139]

Thankyou very much Prof. Brunton. I find your videos really interesting and very well-delivered lessons.

[@benceweisz1063]

Super excited for this series! I'm hoping to do research in physics based animation so I think this series is going to help me a lot with understanding the models. Also I was wondering where I saw that cylinder fluid flow model and remembered I saw it at a talk your student gave at the UofT Geometry Colloquium. Great work!

[@usmanmuhammad5061]

Please upload all videos fast. I need this course desperately.

[@Eigensteve]

Top secret tip: if you go to the playlist, all videos are there now, even before they are publicly released.

[@dimpap9659]

Wow, the teaser was already more plausible than all the explanations I've already received from professors and teachers why an eigenvectors and eigenvalues ​​are used. thanks for that

[@rudypieplenbosch6752]

Looking forward into following this series, especially the practical examples you mention for Matlab and machine learning and control systems. I have been following your previous lessons and am amazed by the quality and the work you put in them 👏. Wow stabilising a double pendulum, this I never saw before, amazing.

[@An_Attempt]

Yes, that was quite the spectacle; to think that that is secretly built into our brains is even more remarkable.

[@jimlbeaver]

Awesome…this is going to be great! Thanks very much

[@johnkim1048]

This is exactly what I was looking for as a civil engineering trying to get ahead for college during my summer break. Thank you so much!

[@hurstcycles]

Fantastic, really looking forward to this series, Python at the ready!

[@mauYair]

love your videos! 11:06 Leibniz, pronounce EI like your do in eigenvalue

[@Eigensteve]

Thanks, and good call on "L-eye-bniz" not "L-ee-bniz"... :)

[@__--JY-Moe--__]

nice! super brush-up! U teach so well ! good luck!

[@ichaa3tech]

really excited to start this journey with you. very interesting indeed

[@uddipanbaruah6021]

Thank you so much sir.. I know thank you is not enough but I really appreciate your work.. Really excited for the course sir

[@jb3065]

Absolutely brilliant. Wish I could have had a professor like him 30+ years ago. Thanks for providing this content, it's wonderful.

[@maifilms]

Thank you so so much I’m taking a course right now with this exact course title and I’m struggling, looking forward to actually understanding stuff after this video

[@yanjnus]

Thanks for the excellent lectures!

[@terrym2007]

Great Stuff. I would love to get your ideas on two important books..1. Where Mathematics Comes From, Lakoff, Nunez. 2. Godel Escher Bach, Douglas Hofstadter. Thanks again

[@tikarambhusal8657]

Continuity in your progressive teaching has helped globally,thanks a lot.

[@user-su4jh4sp9b]

You are the best lecturer I have ever learned from!! (and I learned many years from many lecturers). Thank you so much for this course!

[@lorenzosalomone8635]

I really like that fact that this video other than just being a nice introduction is also an amazing motivational video

[@martinsanchez-hw4fi]

Awesome!!

[@josematas6278]

Hi Professor, it is really cool that you share all this material. I now follow you. We love you 💓💓💓💓💓

[@naimaware]

This is the best course I have seen on Engineering math , thankyou! I am reviewing those concepts after I studied time ago and now are getting more clear.

[@marcfruchtman9473]

Sounds amazing. Thank you for making this educational video series.

[@magicalblade9503]

Thank you so much Professor Brunton. I am learning a lot from your lectures, they are a million times better than the courses I took in university.

[@murraypatterson9190]

Never ceases to amaze me how practitioners of “dynamical systems” and “systems dynamics” are both others existence … particularly as they both purport to model nonlinear systems. We live so often in narrow minded worlds.

[@plekkchand]

Wonderful, generous, sane, intriguing, brilliant....

[@drgali7230]

I'm actually a dentist but this set of lectures are ughh , I'm so obsessed ❤️

[@marklondon9004]

I'm a data scientist, but my crown just broke off. Could we exchange skills?

[@drgali7230]

@@marklondon9004 of course

[@drgali7230]

@@marklondon9004 yes let's do this

[@adekunlerenner7675]

Can't wait to get started

[@mingusbingus6746]

You the man. I’m trying to learn more DEs to apply to ecological modeling. Very fun

[@TheChemicalProcessEngineer]

you made me more than just excited! thank you!

[@TylerMatthewHarris]

Can’t wait

[@markusm2538]

Honestly i didn't think I'm a math person, however your courses fit well into my brain. Great thanks.

[@JohnSmith-ut5th]

Thank you so much for a MODERN course on differential equations. This is how it should be taught in universities. Can you do a lecture series on Calculus of Variations and maybe one on Continuum Mechanics?

[@gean7917]

a course like that on youtube is just insane

[@abdallaismail2191]

This fantastic I'm glad I stumbled upon your channel, much love

[@michaelwood2292]

I agree with all the positive comments provided here... If you are taking additional requests, I'd REALLY love to see more vidoes like the "Gental Introduction to Modeling with Matrices...." This is the first video I watched and I can't explain to you how much it made sense and how all the components "linked" to oneanother... Thank you for your time and energy for making these videos and hopefully more in the future.

[@eduardocarmona8157]

I'm a film production professor, but this is addictive!

[@martinsanchez-hw4fi]

The double pendulum stabilized was shocking!