OMG this is amazing. you are literally my hero for posting this derivation. THANK YOU.
@umarbashir7196 Жыл бұрын
The video was really educating. I really enjoyed watching it.
@md.khurshedulislam17627 жыл бұрын
very good explanation for beginners. Keep it up sir. Want more video
@funtofun3216 жыл бұрын
Very nice video. It helped me to understand the concept of linearization around a critical point..., lot of thanks. Keen to watch your more videos..
@ytjoemoore943 жыл бұрын
Imagine the expanding brain meme that starts with Kahn Academy and ends with this guy!!
@man9mj2 жыл бұрын
Very excellent demonstration. Thank you
@jnxmaster6 жыл бұрын
Great videos. You have a new subscriber.
@biaschatterjee98364 жыл бұрын
Very helpful video, thank you sir😊👍
@marrytesfu31636 жыл бұрын
Simply WOW!!
@loganthrashercollins7 жыл бұрын
What exactly is meant by "very small perturbations"? Is this related to limits or is does "very small" simply denote that it is within a small enough interval that the behavior doesn't change? Also: great job explaining. I really enjoy these nonlinear dynamics videos in particular. I look forward to the rest of the series!
@FacultyofKhan7 жыл бұрын
Thank you! It's not related to limits, even though I've used epsilon (the same greek letter you see in the epsilon-delta limit proofs). Small epsilon just means that the amount by which we disturb the particle from its fixed point/steady state is so small that epsilon^2, epsilon^3 etc are negligible. For example, if epsilon were 0.01, then 0.01^2 = 0.001, which is very small (1/100th) of the original epsilon. When epsilon^2/^3 etc are negligible, we can safely apply the linear approximation as I did in this video. The main caveat is that you're restricted to looking at disturbances in the local area of x_f. You don't know about global behavior via linear stability analysis. Hope that helps, and feel free to ask more questions!
@tjmitchell215 жыл бұрын
Wonderful video, thanks! It's really helped. :)
@shivrajahirwar43345 жыл бұрын
nice explanation
@farzanehazargoshasbi2842 жыл бұрын
Your videos are very useful.Thank you very much🙏🏻
@pierreretief Жыл бұрын
Stunning. Thanks
@薛启谭2 жыл бұрын
thanks for teaching, it's helpful
@TheCerebralOne2 жыл бұрын
@6:00 to clarify, if the derivative f' at the fixed point is zero then the linear stability analysis is inconclusive?
@dantecalanza13303 жыл бұрын
Thank you po Sir.☝️
@VictorHugo-xn9jzАй бұрын
But when would we actually make use of a large perturbation to analyze a stable point? Why would global fixed points be of interest?
@FilipeSilva15 жыл бұрын
Thank you.
@harshitjuneja94623 жыл бұрын
so it is basically the second derivative test from single-variable calculus, right?
@FacultyofKhan3 жыл бұрын
It's similar, in that it allows you to determine the nature of the point where the first derivative is 0 (i.e. the fixed point). The difference here is that you're differentiating dx/dt = f(x) with respect to x as opposed to taking the straight second derivative (i.e. d^2 x/dt^2).
@اممحمد-ق2ه3 жыл бұрын
Can you help please How classification of critical points of system in three equation in 3d
@aissamaissam56184 жыл бұрын
Thanks alot for this nice video. I want know the condition that makes the following discrete system stable: x(k+1)=Ax(k)+B Where A and B are a known square matrices an x' in R^n. Thanks in advance sir.
@rajatmishra41892 жыл бұрын
Thanks a lot buddy 😁
@hayleycoyle97262 жыл бұрын
You totally lost me at f'(x_f) = -1 . Where did this come from? How did you figure this out?
@Noumankhan-nx9nz4 жыл бұрын
thanks alot
@maurocruz18243 жыл бұрын
You make that exponential solution for epsilon. That reminds me of the generator of a Lie group. Is there any connection?
@zhiyongli75264 жыл бұрын
4:34, The fixed pint is not the stationary point, why should it be zero.
@FacultyofKhan4 жыл бұрын
For this video, they mean the same thing. A fixed point is where the function x(t) is momentarily fixed (i.e. dx/dt = f(x) = 0), and a stationary point is where the function x(t) is momentarily stationary (i.e. dx/dt = f(x) = 0).
@zhiyongli75264 жыл бұрын
@@FacultyofKhan Ok, thanks for the explanation. That is a stationary point other than a fixed point. Fixed point x(t)-t=0, stationary point: dx(t)/dt=f(x)=0.
@trantrang15905 жыл бұрын
i love you
@XanderGouws6 жыл бұрын
It's nearly been a year :(
@FacultyofKhan6 жыл бұрын
Aww don't worry man, the next Nonlinear Dynamics video is in the works and should be up this week!
@XanderGouws6 жыл бұрын
Faculty of Khan EE :D
@XanderGouws6 жыл бұрын
Faculty of Khan EE :D
@FacultyofKhan6 жыл бұрын
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