very useful but needs to go in more detail. Especially when f(x) is a function that is very difficult to draw (eg. x/(a+x)-x ) how do you determine the sign of the slope then ..
That's right. This video only talks about the graphical approach. For functions that are difficult to graph, an analytic approach might be better. That happens in the "next video" mentioned at the end. If you click on the above link to see the Math Insight page where these videos are embedded, the analytic approach video appears below. Or the analytic approach video is availble at: The stability of equilibria of a differential equation, analytic approach.
If an equilibrium is not stable, then that equilibrium is unlikely to be observed in a real system, as any small change could move the state of the system off the equilibrium. Similar to how it is hard to have a pencil setting on a stationary table and balanced on its point.
10 minutes of pure learning:
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very useful but needs to go in more detail. Especially when f(x) is a function that is very difficult to draw (eg. x/(a+x)-x ) how do you determine the sign of the slope then ..
That's right. This video only talks about the graphical approach. For functions that are difficult to graph, an analytic approach might be better. That happens in the "next video" mentioned at the end. If you click on the above link to see the Math Insight page where these videos are embedded, the analytic approach video appears below. Or the analytic approach video is availble at: The stability of equilibria of a differential equation, analytic approach.
An extremely helpful video! Your explanations were clear and easy to follow. I enjoyed every minute!
Why can't people teach like this. You compressed 20 years of guess work into 10 minutes of reality...for that, I say, THANK YOU!
Your explanation is brilliant. I was really struggling with the concept of stability and your video helped me greatly. Thanks alot. :D
Thank you. You have made it easy to understood.
Great Video. Thanks a lot!
Amazing explanation, thank you.
u should be my lecturer for dynamical systems.
great videos :)
I was the *1000th* like ! 👍
Thank you! This is wonderful.
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Great explanation!! thank you!!
You're welcome!
what is the need of stabilty of a differential equation
If an equilibrium is not stable, then that equilibrium is unlikely to be
observed in a real system, as any small change could move the state of
the system off the equilibrium. Similar to how it is hard to have a
pencil setting on a stationary table and balanced on its point.
THANK YOU! Be my lecturer!!!