I am taking Optimal Control unit this semester and the idea of convexity has come up recently so I'm really grateful for your video - helps me understand its application even further now! Thanks!
Thank you for the video as always. Is there a topological definition for convexity or is that not useful or implicit in the definition of the above 3 already? Just to double check we would get concavity definition if we just turn around the inequality signs of the above 3 definitions correct?
@@drpeyam I tried to make a graph of f(x,y) = sqrt(x^2 + y^2) and it doesn't seem to be strictly-concave in some domain of (x,y) ie seem to be convex function. i think it is a nice idea for a future video (for both directions of the claim) :) thanks
Wait, is it really okay to look at whether ln(E(t)) is convex when E(t) is 0 at one of the endpoints? I think taking limits as y approaches t* outside of everything makes it work in this case, but I'm not sure it always works in general.
Alright, so my problem is: How do you interpolate a secant spline for asymptotically convex functions? There are infinitely possible ways to do that and i have no idea how
@@drpeyam Just because the function is zero at a particular point, doesn't mean it has zero derivative? Although I suppose if U(l,t)=0 for all t, its time derivative at x=l should be zero.
I'm loving these PDE analysis videos!
These videos are great to watch as I read through Evans' book!
I am taking Optimal Control unit this semester and the idea of convexity has come up recently so I'm really grateful for your video - helps me understand its application even further now! Thanks!
Nice!!!
love the video by the way thank you Dr Peyam
Thank you for making analysis so fun
Dr. Peyam please start a new series on : Essence of Calculus. that's a request please!
3b1b already has a series on that haha
: )
Cool ! Thanks.
Thankyou
Wow! I JUST started the Stanford Online course on Convex Optimization. This is unbelievably great timing, I’m quite lucky!
Nice!!!
Can you post a link to the course?
wow this is amazing
Great! 👍
Thank you for the video as always. Is there a topological definition for convexity or is that not useful or implicit in the definition of the above 3 already? Just to double check we would get concavity definition if we just turn around the inequality signs of the above 3 definitions correct?
Idk if this is just me or not (maybe just me) but i like when you're explaining through the whiteboard. ❤😬
Dr Peyam a video on graphing (-2)^x and equations of form (-c)^x please
if g(x)=f(x,y0) is convex in x for all fixed y0 & h(y)=f(x0,y) in convex in y for all fixed x0 -> is f(x,y) convex in (x,y)?
I feel the answer is no, but I might be wrong
Oh I think it’s indeed wrong, try f(x,y) = sqrt(x^2 + y^2)
@@drpeyam
I tried to make a graph of f(x,y) = sqrt(x^2 + y^2) and it doesn't seem to be strictly-concave in some domain of (x,y) ie seem to be convex function.
i think it is a nice idea for a future video (for both directions of the claim) :)
thanks
what virtual whiteboard programme does he use
Wait, is it really okay to look at whether ln(E(t)) is convex when E(t) is 0 at one of the endpoints? I think taking limits as y approaches t* outside of everything makes it work in this case, but I'm not sure it always works in general.
Yeah it really is ok, -infinity is still convex
Sir please make video on functions, please 🙏
Your way of teaching is amazing.
Functions? What 😂
@@drpeyam video on functions 😅 because iam not able to understand it.
Alright, so my problem is:
How do you interpolate a secant spline for asymptotically convex functions? There are infinitely possible ways to do that and i have no idea how
Wow !
Where did the [U_x U_t]_{x=0}^{x=l} go in E''(t)?
No boundary terms since they’re all 0
@@drpeyam Just because the function is zero at a particular point, doesn't mean it has zero derivative? Although I suppose if U(l,t)=0 for all t, its time derivative at x=l should be zero.
Exactly, if u(l,t) = 0 for all t then the t derivative is also 0
I love you
But you're uncertain about it.
Hi
hello
d(quality of the pun game) > 0