Matrix Systems of Differential Equations

This video describes how to write a high-order linear differential equation as a matrix system of first-order differential equations. This is a major step towards solving general ODEs using eigenvalues and eigenvectors, leveraging the full power of linear algebra.

@eigensteve on Twitter

This video was produced at the University of Washington

%%% CHAPTERS %%%
0:00 Overview
1:54 Introduce New Variables
7:11 Writing as Matrix System of Equations
12:12 Summary and Takeaways
14:51 Eigenvalues of Matrix System are Roots of the Characteristic Polynomial
17:40 Example 3x3 Matrix System of ODEs

[minder]

Why is that so hard to find material on systems of differential equations? This video doesn't even have a lot of views.

[felipegabriel]

Those last lectures about ODEs are seriously one of the best ones I've seen on Youtube! Really enjoying it, keep it up :D

[benanderson]

2:17 "I actually opened up a new pack of markers because I'm so excited about this lecture" hehe the enthusiasm is infectious

[whootoo]

You made me love math and calculus which i hated a long time. The different ways of math notations, best explanation and relationship between linear algebra and ODE is just a thing that can make me study math soon.

[toastrecon]

New pack of markers! Man, I really should buckle down and watch all of these videos as a refresher. I struggled to really comprehend them during my undergrad, and it'd be nice to finally feel like I fully understood.

[RotBaron]

i wish i had these videos when i was in my EE program. back then 3blue1brown started to emerge but he couldnt carry me alone there!

[CigamMan]

Does this guy write backwards or something??!

[et]

Steve was feeling himself in this one 🤣 a mixed of math and stand up comedy. Loved it

[ryantanner]

Every time I see someone teaching on one of these glass panes, I'm always perplexed at how it is being done. Is the video mirrored or is he writing backwards? Also, if it is mirrored, how is he oriented in relation to the class?

[StaticMusic]

Haha I love that you drew a heart at the meeting point of linear algebra and diff equations.
Thanks so much for all these presentations - honestly some of the best material on YouTube, and so brilliantly created. Big fan.

[bendavis]

I love when two different areas of math connect to each other as shown here with linear algebra and diff. eq.. So satisfying!

[실버벨-fi]

I like searching good lectures on Youtube. This series is as best as Strang's Linear algebra!

[curtpiazza]

"Polly Polynomial"....Linear Algebra. ❤ love it! 😂

[kalpitkatpara]

Absolutely Exceptional explanation how linear algebra combines with the calculus to solve differential equation! I am feeling blessed to find this videos on YouTube! we love you lectures!!!

[tylersculpts]

at 18:50, when I do the matrix multiplication with the vector I get an extra x2 by itself without any a coefficients. However, in the equation below there is only a single variable without an a coefficient. where does that go?

[unsearchablethings]

Matrix systems of differential equations……
I’m so thankful for them!

[naimaware]

what if the equation isn't omogeneous and the coefficients aren't constant but dependant on a variable?

[yugantarbhasin]

can you please explain how do we represent odd powers as physical spring mass systems as addind additional spring and masses is just providing even power linear ode's

[synocx]

Hello Prof. Brunton, thank you very much for your video and your contributions. I wanted to ask if you can cover the mathematical background of the message from AlphaTensor. DeepMind reports that they have developed an AI-based algorithm that accelerates matrix multiplications.
Thank you very much!

[agrajyadav]

pulling an all nighter watching ur videos, absolute treat