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:

@eigensteve on Twitter

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

[yevgeniyterekhin]

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!

[HackionSTx]

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

[AleeEnt]

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

[marioskokmotos]

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!

[ec]

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

[macchiato_]

As someone who's country's educational system is lacking in so many ways, I cannot thank you enough for this series. Thank you, truly.

[novelspace]

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

[andrewnorth]

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!

[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!

[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.

[brunoduartegomes]

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.

[ibrahimalotaibi]

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

[robvp]

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

[Elizabeth-nqly]

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!!!

[alejandrocarbon]

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.

[rudypieplenbosch]

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.

[abdussamad]

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.

[iheavense]

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

[dancollins]

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 YouTube comments, by doing so you will stand as a giant amongst global teachers. Onwards and upwards!

[vectorautomationsystems]

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