Thank you very much for uploading this video. I couldn't understand this concept by watching any other video I watched. It's been 10 years and you're still the best !
Thank you so much for uploading this! I'm a physics student in my first semester and your tutorials help me greatly to understand the topics discussed in class. :)
Thank you! You have a very clear manner of explaining, your effort is greatly appreciated! Especially the way you explain why certain theorems are useful.
If the logic used at 6:22 of part 1 is applied to to the series of functions at 1:46 of part 2, you would incorrectly conclude that the sequence is not uniformly convergent. Am I misunderstanding something?
Dan, that is a good question. I think my explanation of uniform convergence in Part 1 was a little too vague, and that is creating some confusion with this particular example in Part 2. You are right, in this example, it appears that the value of n needed for the inequality |f_n(x)-f(x)|
Rob Shone I'm clear now. I think what might be confusing is simply the use of the word "uniform," which intuitively is a bit different from the actual behavior. The Wiki page on uniform convergence also states the speed of convergence doesn't depent on X. My interpretation of speed would imply the curves remain equidistant, which is not generally the case for uniform convergence. Thanks for the quick reply.
Hey Rob, thanks for such a simplistic explanation. I've got a question. For the example fn(x) = (nx)/(1 + nx), when you show the plot at 2:12, and if we consider an epsilon > 0, wouldn't the value of N be dependent on x as well? So by using the plot, the function does not come to be uniformly convergent but you've proved it to be so using the helpful theorems. Where am I wrong?
thank you sir the explanation is amazing , I have a doubt , i haven't understood why , at 5.20 we can surely tell that the sup is 1 , i mean we know just that n is a natural number , can't it be big enought to "compensate the really small value of x" in 1/(1+nx) ?
Rob - many thanks for this helpful video. I was wondering whether "Helpful Theorem 1" has a recognised name, or if not, whether you can point me to a source that I can quote. I am particularly interested in seeing a formal proof of the theorem. Many thanks!
Sir I have a confusion In example fn(x) = nx/1+nx If we see it's graph We find that for a fixed epsilon the value of n is different for different values of x Please sir clear my doubt by showing geometrically the uniform convergence of the above sequence
Thank you very much for uploading this video. I couldn't understand this concept by watching any other video I watched. It's been 10 years and you're still the best !
9 years already and I'm here claiming you are my biggest savior
Man, you are awesome. This is saving my butt right now. Thank you for being so clear.
Thank you so much for uploading this! I'm a physics student in my first semester and your tutorials help me greatly to understand the topics discussed in class. :)
Thank you! You have a very clear manner of explaining, your effort is greatly appreciated! Especially the way you explain why certain theorems are useful.
Hello,
du génie en barre !! Amazing pedagogy, I'm glad you decided to become a teacher !!!
wow nice video, you explain it way better than our professor
If the logic used at 6:22 of part 1 is applied to to the series of functions at 1:46 of part 2, you would incorrectly conclude that the sequence is not uniformly convergent. Am I misunderstanding something?
Dan, that is a good question. I think my explanation of uniform convergence in Part 1 was a little too vague, and that is creating some confusion with this particular example in Part 2.
You are right, in this example, it appears that the value of n needed for the inequality |f_n(x)-f(x)|
Rob Shone
I'm clear now. I think what might be confusing is simply the use of the word "uniform," which intuitively is a bit different from the actual behavior. The Wiki page on uniform convergence also states the speed of convergence doesn't depent on X. My interpretation of speed would imply the curves remain equidistant, which is not generally the case for uniform convergence. Thanks for the quick reply.
Hey Rob, thanks for such a simplistic explanation. I've got a question. For the example fn(x) = (nx)/(1 + nx), when you show the plot at 2:12, and if we consider an epsilon > 0, wouldn't the value of N be dependent on x as well? So by using the plot, the function does not come to be uniformly convergent but you've proved it to be so using the helpful theorems. Where am I wrong?
I would also like to the answer to this question too
the same question.
DR. SHONE U ARE THE MVP TY!!!!!
thank you so much this has saved my neck!!!! oooh man you made it so easy to understand, thanks
thank you sir the explanation is amazing , I have a doubt , i haven't understood why , at 5.20 we can surely tell that the sup is 1 , i mean we know just that n is a natural number , can't it be big enought to "compensate the really small value of x" in 1/(1+nx) ?
Very clearly explained. Thank you.
thanks. this is an awesome course on this topic.
Rob - many thanks for this helpful video. I was wondering whether "Helpful Theorem 1" has a recognised name, or if not, whether you can point me to a source that I can quote. I am particularly interested in seeing a formal proof of the theorem. Many thanks!
very nice explained.
good job man
thumbs up. .....very helpful
Thank you! That was a perfect explanation :)
Sir please upload mn test
Sir I have a confusion
In example fn(x) = nx/1+nx
If we see it's graph
We find that for a fixed epsilon the value of n is different for different values of x
Please sir clear my doubt by showing geometrically the uniform convergence of the above sequence
let f:R→R be a continuous function such that 〖Lim〗_(x→±∞)〖f(x)〗 exit and finite. Prove that f is uniformly continuous on R.
Qué buen vídeo. Gracias.
Really helpful!
excellent!
You are amazing!
Thank u very much
very nice
please add more vedios