Do you think there is any way that the difference between pointwise and uniform convergence can be visualized? I can understand the definitions with respect to the preservation of continuity, integrability, etc., but I still don't completely grasp what the difference in their primary definitions actually does (N being independent of x)
@tiyakeira972 yeah it is too late lol I'm not even a math student anymore I'm a full-time comp-sci employee now. Still, it'll help out anyone else having similar concerns
In most of the resources on this topic, in the definition for uniform convergence, it was stated that n >= N instead of strictly n > N. Is this an oversight in the video or is this intentionally different, and how important is this distinction? Otherwise, thanks for the great videos, I love them!
Maybe it's tied to the fact theat we are choosing N from Z+ instead of the set of natural numbers, as in most other literature I've come across today while studying this topic. I think this distinction would make sense if we consider Z+ as containing 0.
This video is a few years old at this point, but could one say that your example f_n(x) is pointwise convergent on [0,1] but uniformly convergent on only [0,1)?
can you make a video lecture on these topics of complex analysis 2 weierstrass function . elliptic function in term of weierstrass functions with same periods. Jacobian elliptic function and it's properties ??
The function of arctan is continuous, but the limit function is not. Hence, it is pointwise convergent. f(x) = arctan (nx) we know that arctan is continuous on [0,b]. But if x = 0 it will converge to 0. If x
Why don't you write for pointwise conv "there is a N=N(\epsilon, x) \in Z^+" and for uniform conv "there is a N=N(\epsilon) \in Z^+..." It would be no confusion then if N depends or not on x...just sayin'... :)
this video deserves thousands of likes, thank you so much.
Glad it helped!
Your videos are saving my life right now
Do you think there is any way that the difference between pointwise and uniform convergence can be visualized? I can understand the definitions with respect to the preservation of continuity, integrability, etc., but I still don't completely grasp what the difference in their primary definitions actually does (N being independent of x)
there is a great video by @cmodgamma1091 visualizing the difference between both, I know this is a little too late but you never know i guess
I know this is 4 years late but CModGamma made a TH-cam video on this and it’s great and worth checking out
@tiyakeira972 yeah it is too late lol I'm not even a math student anymore I'm a full-time comp-sci employee now. Still, it'll help out anyone else having similar concerns
Bro I love you so much , I have no idea what I’m doing and your videos are legit saving me 🙏🙏💙💙
Just found your channel and I already know it is going to help a lot haha, nice video!
This video clear up much confusion that I have on difference between pointwise convergence and uniform convergence
this was a great help, thank you :)
You are welcome😄
In most of the resources on this topic, in the definition for uniform convergence, it was stated that n >= N instead of strictly n > N. Is this an oversight in the video or is this intentionally different, and how important is this distinction?
Otherwise, thanks for the great videos, I love them!
Maybe it's tied to the fact theat we are choosing N from Z+ instead of the set of natural numbers, as in most other literature I've come across today while studying this topic. I think this distinction would make sense if we consider Z+ as containing 0.
It's not a huge deal, different books do it different ways.
Thx a lot my brother u helped me in my Exam
Thank you, great explanation
You are welcome 😄
So much helpful! Thanks a lot!
Thank you bro so satisfying
This video is quete helpful 👏
thank you so much
You are welcome 😀
did you follow this up with the video proving x^n does not converge uniformly? I am not finding it
you are so awesome. thanks for video a lot!
This video is a few years old at this point, but could one say that your example f_n(x) is pointwise convergent on [0,1] but uniformly convergent on only [0,1)?
Good explanation
thank you!!
can you make a video lecture on these topics of complex analysis 2
weierstrass function . elliptic function in term of weierstrass functions with same periods. Jacobian elliptic function and it's properties ??
Sure
or any link of complex analysis topics ?
yeah I have a playlist th-cam.com/play/PLO1y6V1SXjjOLpoC123XeiAX8hxbyY_2b.html
Thank you
You're welcome
Thanks a lot... could you pls explain now why arctan (nx) is UC/ PW convergent on [0,b]?
The function of arctan is continuous, but the limit function is not. Hence, it is pointwise convergent.
f(x) = arctan (nx)
we know that arctan is continuous on [0,b]. But if x = 0 it will converge to 0. If x
Why don't you write for pointwise conv "there is a N=N(\epsilon, x) \in Z^+" and for uniform conv "there is a N=N(\epsilon) \in Z^+..." It would be no confusion then if N depends or not on x...just sayin'... :)
👍
how does x^n tend to 0 when n approaches infinity??
It does, assuming |x| < 1
This topic is covered under calculus 3 in our institute can you tell me. WHICH OF YOUR PLAYLIST CONTAINS VIDEO ON THIS TOPIC SO I CAN SEE WHOLE TOPIC
Advanced calculus playlist has a few more
why pointwise convergence is called pointwise?
Cool Video.
'irregardless' is not a word
too bad i have no clue on how to solve this shit and my exam is the day after tomorrow