2x2 Systems of ODEs: Sources and Sinks
Ғылым және технология
This video investigates a 2-dimensional linear system of ordinary differential equations with either pairs of positive real eigenvalues or pairs of negative real eigenvalues. These solutions are known as unstable sources and stable sinks, respectively. We investigate the solutions using eigenvalues and eigenvectors, as well as with phase portrait pictures.
Playlist: • Engineering Math: Diff...
Course Website: faculty.washington.edu/sbrunto...
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This video was produced at the University of Washington
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0:00 Overview of sources and sinks
1:56 Writing the solution
2:53 Recap: How to compute matrix inverse
12:24 Drawing an unstable source in phase space
21:01 Drawing a stable sink in phase space
Пікірлер: 34
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 ❤
thanks for producing these videos @steve - they are great.
Amazing lectures.
Great! Love the graphs! ❤ 😊
Really excellent lectures, would be interested in seeing a video about how you think/approach teaching in general
@cerbahsamir5119
Жыл бұрын
Agree 💯
Excellent lecture
awesome explanation
Beautiful pictures 🙂
Great videos. Stupid question: how do you make them?
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?
best lectures ever
@Eigensteve
6 ай бұрын
Thanks!
Wooow, I did not see this coming
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
Жыл бұрын
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.
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
Жыл бұрын
There’s a course website and book listed in the description
@rajinfootonchuriquen
Жыл бұрын
His book jajaja
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?
@user-ck9fc5yf6o
Жыл бұрын
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
Жыл бұрын
@@user-ck9fc5yf6o 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
nice drawings
It's like a 4 point perspective drawing.
💛💛
Had to use Maxima back in the day, that's a real pain in the arse
T is a special matrix known as the Hadamard
와아~~1등이다. 언제나 감사합니다.
is he writing backwards??
@damsaddles9911
5 күн бұрын
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
5 күн бұрын
@@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
First (English)
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