ODE | Phase diagrams
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- čas přidán 15. 09. 2012
- Examples and explanations for a course in ordinary differential equations.
ODE playlist: • Ordinary Differential ...
In this video we explain how to construct a phase diagram (or phase portrait) for an autonomous first order differential equation using the example of the logistic equation. With one dependent variable, our phase diagram is a phase line. We also give examples of stable and unstable equilibrium points.
I rarely comment on these videos but this 5 minute video, most of which I skimmed through, explained more than I'll ever learn reading the corresponding chapter in this piece of crap 200 dollar textbook. Thanks for the videos man.
+Roger Li +
True
Zill? Or are you using a different POC textbook?
Felt so lost in my differential equations class, but not anymore! really clear and helpful!
I was reading a research paper in Controls Theory which talked about phase diagrams, and I had no idea of what it was. I'm aghast at how a 5 minutes video was able to teach me it! Excellent video!
I dont typically comment on videos but this video explained more to me than a 1 hour lecture and a full chapter in my textbook, and it did it in 5 minutes. Thank you so much and i hope to see more videos!
Thank you for blessing the comments section with your admiration for the creator... 😜
You are simply AWESOME!!!!! I have an ODE exam this Friday and I am going over all you videos and this is helping me a lot! Thank you!!
Hello sir, your voice is heavenly and your explanation is Godly. Thank you so much. This is possibly the best explanation I have seen so far.
+1
This video needs more views. Lifesaver before my first exam.
Your explanations and videos are great quality, and easy to follow. That is why you need to make more videos!
Many thanks for the video! Especially for the questions in the end that stimulate thinking!
Differential equations is so confusing, but once I get a grasp of what’s going on, it’s really cool to see how we could examine solution curves without even touching the DE
thank you for explaining this topic so well and adding accurate captions! ❤❤
Simply put! It makes for a better understanding. Thank-you!
thank you for doing this, a service to humanity!
How to find Equil Phase Portrait of three (x,y,z)
Awesome! Keep it up! You're helping a lot of people :) Thank you!!!
saving grades on a daily basis, thanks man
This is incredibly well explained. Many thanks ✌️
You deserve a medal.
Just an AWESOME explanation. Thanks :)
Very helpful video, thank you for making these!
Thanks. Nice Simple, Clear Video, Clear Audio. Your legibility sense is good. Thanks for eliminating thin hairlines which are difficult to see. You get the videofountain .. Clarity Award for September 2013.
Your a blessing from God.God bless you sir.Your the best!!!!
my favorite in the series
That. was. AMAZING! Thanks.
Awesome video! Thanks man
it was good. I watched about 5 videos and didn't get a thing, but now I do.
Cheers
Concise and perfect.
really helped with me undertasnd this segmentof my differential equations class
Clear interpretation!
really helpful! thanks a lot!
Very useful, thanks man. Que Dieu vous protège.
wow, this is a very good explanation of a phase line. I appreciate it.
How to find Equil Phase Portrait of three (x,y,z)
Hi and thanks a lot for your help! My problem is the following: I would like to draw a phase portrait for a system of 3 differential equations.
Wonderful explanation
I was sooo lost idk why I didn’t watch this video thanks man
I believe the answer to the first challenge is have a point of inflection - thus cubic (in x) 'dx/dt'.
There's a time symmetry in the slope field, I noticed, so 'unstable' and 'stable' solutions are precisely dual w.r.t which way the film runs in the projector. This does suggest we can have stable inflections as easily as unstable ones - and thus have the 'full set'.
Are you intending to do any 'numerical' (iterative) methods of solution in this course I wonder?
easy and clear...Thanks
Dude I love you.
I don't understand why uni's don't just hire guys like you to make content like this for their courses. Why do millions of people each year have to sit through incomprehensible multi hour long lectures and then come to youtube for better understanding in 5 mins, it blows my mind.
Hi and thanks a lot for your help! My problem is the following: I would like to draw a phase portrait for a system of 3 differential equations.
Thanks!
So, for the first challenge/question I came up with the equation dx/dt = x^2 and this gave me a solution where two arrows where pointing in the same direction. So I just needed confirmation of whether what I did was right or wrong. And for the second challenge I am guessing for every configuration of stable and/or unstable equilibria the exists an ODE which matches those equilibrium points. Please correct me if I am wrong or add remarks on your opinions of the solution.
for the first challenge, i was thinking add a third multiplying factor where when x is a certain negative integer i it equals zero. that way, from x = 0 to x = i (neg number), both will always be pointing downward toward -infty thus creating a semistable equilibrium point at that negative integer i
where do you answer your challenges by the way, i'm curious to see the answers! Thanks!!
Super helpful! You are very good at explaining things simply and quickly. One question: So you have to draw the slope field in order to be able to draw a Phase Line?
No, the sign of f in a particular interval gives you the direction of flow.
Do you need to have a directional field in order to draw the phase line?
y' = (4-y^2) * (y^2) is an example of one with going in and going out for one of the C.P. And I think we can create any phase diagrams and come up with a diff. eq. Let me know if I am right or wrong. Thanks
thanks!
thought this was khan academy for a sec, incredible video!!!!
Thank you for the video. I just wished that you explain more in detail why dx/dt is 0 by the formula x( 1 - x).
after you find the equilibrium in which case it's 0 and 1. Pick a point at the following intervals [-oo,0] , [0,1], [1,oo].
So if my x =2, I will have 2(1-2) = 2(-1) = -2 a negative value and that's decreasing.. my arrow should be going down if I have a vertical phase line or left if it's horizontal... x = -2 for [-oo,0] = -2(1-(-2)) = -2(3) = -6. Again decreasing...
now x = 1/2 will have 1/2(1-1/2) = 1/2([2/2-1/2) = 1/2(1/2) = 1/4 that's positive and I should have an arrow going up.
It is helpful
may god bless you
Then how do I find x(t)?
Nice
How to find Equil Phase Portrait of three (x,y,z)
what if it's an equation like dx/dt = -x^2 +4x-4 where it has one zero and it's negative on both sides?
Just understand how to draw the slope field and follow the directions on the y-axis basically. Idk why my professor made it sound way more complicated 😅
dx/dt = x^3 - x^2 the task
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I don't see why we shouldn't be able to create any phase line, we can draw any line and then describe the line with a function... right?
If you got an arrow pointing up from below, and an arrow pointing down from above, you are forced into a stable equilibrium point. That is what he means by "gluing points" and hence food for thought.
@@hybmnzz2658 I'm not really sure what your point is.
you tricked me. i thought this was a khan vid because of the software in the thumbnail
you forgot semi-stable
Semi-stable was the one on the lower right of his screen, where arrows went in on one side and out on the other.
S Green was thinking the same thing.
Why does my book try to explain this concept in the least-intuitive way possible? I swear.