Matrix Systems of Differential Equations

[@felipegabriel9220]

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

[@benanderson9189]

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

[@fabiofarina9579]

I have to admit that without squeaking, I concentrate less

[@whootoo1117]

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.

[@WayneLinorice]

Thanks for the videos. I think I finally understand why the Kalman Filter actually works now. It's because if you pick those eigenvalues correctly the difference between estimated and measured values settle to zero.

[@Eigensteve]

Glad it was helpful!

[@실버벨-f8i]

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

[@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 KZbin, and so brilliantly created. Big fan.

[@bendavis2234]

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

[@agrajyadav2951]

pulling an all nighter watching ur videos, absolute treat

[@kalpitkatpara2720]

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

[@et4493]

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

[@ChristinaRichardsonFitness]

You are always so excited!!! I love it!!

[@anishsharma6702]

writing a comment down here , this is such a good video along with such enthusiasm shown by our prof .

[@tommyhuffman7499]

This is my new favorite series!!!!

[@unsearchablethings8167]

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

[@ryantanner1210]

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?

[@michaelchristinarichardson9660]

If you watch at the pen tip you can see that Dr. Brunton has to write backwards our left to right but his right to left. He is behind the glass. That is my perspective at least.

[@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!

[@jritts]

Thank you - you’re a phenomenal teacher.

[@soumyaayegou2757]

what a beautiful picture of math u made ! thank u for the heart

[@deeper1993]

Excellent series of lectures on solving higher-order ODEs. I would request you to make a separate video that talks about the geometrical interpretation of the solution. In my opinion, the interpretation is like this; each of the eigenvalues corresponds to the exponential rate of divergence along the eigenvectors of the Jacobian matrix A. So if x = c1 exp(lamb1 t) + c2 exp(lamb2 t), then there is a eigenvector associated with c1 and c2. The solution can be written as u1 exp(lamb1 t) + u2 exp(lamb2 t). This would lead to an eigenvalue problem where u1 and u2 are the eigenvectors of A. The solution x can now be expressed as c1 u1 exp(lamb1 t) + c2 u2 exp(lamb2 t). This solution can be interpreted as how the vector(solution) grows or shrinks along the axis(u1 and u2). The eigenvectors would be the basis of the solution and lambda's would tell us how they grow in those directions(eigenvectors u1 and u2).

[@minder3761]

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

[@manfredbogner9799]

ask KZbin?

[@copernicus6420]

I wonder that too

[@idrisShiningTimes]

this video is a gem ❤️

[@curtpiazza1688]

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

[@roman54634]

Nice explanations

[@vijaysinghchauhan7079]

It is a gem.❤

[@olivierdewith1948]

how do they film this?

[@naimaware]

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

[@KingOf_B]

How does he record these? Like is there a pane of glass between him and the camera that he writes on or what because it was cool but confusing. Also, is he writing mirrored?

[@carultch]

He's probably not talented enough to write mirrored and have it look natural. It is probably mirrored video footage. One way you could do it, is by digitally flipping the video. Another way, is to use an optical mirror.

[@ΚωνσταντίνοςΛαζαρίδης-ξ9ι]

thank you sir!

[@AJ-et3vf]

awesome video. thank you

[@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?

[@manfredbogner9799]

Very good

[@yugantarbhasin1914]

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

[@manfredbogner9799]

More please

[@pablobronzone6498]

Amazing. Thank you!

[@Sebastiaan-ev9rc]

How do you film these videos?

[@couchpotato3239]

recorded normally and then flipped

[@synocx4785]

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!

[@ichaa3tech]

No this can't be so smooth, something is wrong lol

[@andreizelenco4164]

Thank you for your amazing content. I share your videos all the time on social media. I might be wrong but I don't understand what happened to the minus sign of the characteristic polynomial at the end of the video. Other than this, thank you very much for your effort!

[@GabrielDubatti]

-equ=0 is -1*equ=0 --> equ=0/-1 --> equ=0 (and the minus is gone)

[@baylee2448]

thank you so much, ily

[@albertmendoza8330]

I miss when math was this easy…

[@nerd2544]

this is easy??? 😔😢

[@albertmendoza8330]

@@nerd2544 Depends on the field you go into.

[@CigamMan12]

Does this guy write backwards or something??!

[@carultch]

He mirrors the video footage. If you saw him in person, the writing would be backwards from your side of the glass.

[@isanewday]

Tõõ small

[@maciejmikulski7287]

It's surprising that to get cha. poly. we assumed the form of the solution (exp(lambda*t)) while with the matrix method we didn't do any assumptions and arrived at the equivalent form.