2x2 Systems of ODEs: Sources and Sinks

[@noahgilbertson7530]

this whole series is really good. I regretfully didn’t pay attention in these lectures last year so this video series will serve me well ❤

[@stonechen4820]

Really excellent lectures, would be interested in seeing a video about how you think/approach teaching in general

[@cerbahsamir5119]

Agree 💯

[@OtterMorrisDance]

thanks for producing these videos @steve - they are great.

[@kambizmerati1119]

Amazing lectures.

[@curtpiazza1688]

Great! Love the graphs! ❤ 😊

[@prashkd7684]

I am really enjoying this series however can I request you to recommend couple of good books to go along with each of the topics ? Call me old fashion but I find it easier to relate to written material ans only use videos such as this to argument my understanding. Thanks a lot for all your efforts and making this course available to masses for free.

[@stonechen4820]

There’s a course website and book listed in the description

[@rajinfootonchuriquen]

His book jajaja

[@wentaowu3070]

best lectures ever

[@Eigensteve]

Thanks!

[@dimitrisnentidis797]

Greatly appreciate the series so far. My understanding is that the phase diagram you drawed for the stable sink is mistaken. I think that the positive ξ2 side should be different. The way you drawed it, it seems that the ξ1 is growing faster that the ξ2.

[@erayyildiz9562]

For me it seems proper because if you follow each individual line, you can realize they have tendency to go faster to the infinity in ξ2 directions.

[@mauriciocarazzodec.209]

awesome explanation

[@FormalSymmetry]

Beautiful pictures 🙂

[@何承燁-i5p]

Excellent lecture

[@sherifffruitfly]

Seems like your "run the tape backwards" intuition at the end, switching source to sink could also have been achieved from the other direction: replace t with -t in the original solution, and pull the negative sign OUT?

[@andy_lamax]

Wooow, I did not see this coming

[@GeoffryGifari]

Hmmm hearing about eigenvectors and how you can have motions (modes?) that have nothing to do with each other (decoupled) makes me wonder if having eigenvectors is still possible in nonlinear ODES. I've read a lot in physics where variables are so strongly coupled and nonlinear that its hard to have tractable calculation. In which cases can we decompose dynamics into decoupled eigenvectors?

[@何承燁-i5p]

I bet you've already known the answer as new videos are uploaded. Just in case, it's covered in the future lectures: linearization near fixed points.

[@GeoffryGifari]

@@何承燁-i5p ah yes, i don't really watch the videos in order and the comments are what comes in my mind about the lecture at that moment

[@afoondun4986]

Great videos. Stupid question: how do you make them?

[@lioneloddo]

It's like a 4 point perspective drawing.

[@wenzhang365]

nice drawings

[@superuser8636]

T is a special matrix known as the Hadamard

[@lecturesfromleeds614]

Had to use Maxima back in the day, that's a real pain in the arse

[@armanbarghi6052]

💛💛

[@dongyeonkim2790]

와아~~1등이다. 언제나 감사합니다.

[@john4556]

is he writing backwards??

[@damsaddles9911]

He is left handed. And the video is mirrored. We write from left to right, so we write starting at our left side and toward our right side. Notice that he starts writing from the same side as his hand that is holding the pen, therefore….left handed.

[@john4556]

⁠​⁠@@damsaddles9911 wow this is so simple that I want to believe I made the comment as a joke. But looking back at it I know I was 100% serious… I guess the left-handedness kind of adds to the illusion though

[@reactorfour1682]

“How to invert a matrix” easy just use your calculator

[@TNTsundar]

First (English)

[@sohailtabarhossain6096]

Greetings Dr Brunton. I'm graduated in civil and environmental engineering, currently studying finite element analysis, I'd like to be granted having your insight and guidance in my future studies. May I send you an email? Sincerely, Sohail Tabarhossain