Excellent lectures--I wish I had you for my math classes. It took me a long time (I am 57+) but learning this lesson from Prof Ramakrishna was so gratifying. Thank you so very much for posting this on RUclips
But at 12:24 you can still pick a alpha(x) such that the integral is zero. Just make it a sinus curve with a period of x2-x1 and a phase such that it is zero at x1. Am I missing something?
If h(x) = sin(x) and the interval is [0, 2*pi]; then we know that integral( sin(x)cos(x) dx) in the interval = 0 but that does not mean cos(x) = 0 everywhere?? Can someone please clarify?
cos(x) is right for sin(x), and satisfy the integlal, but dosen't work for all the functions in C. Remember that you are working with a space of functions and the condition have to work every posible function in C. a(x)=0 satisfy the condition for every h(x) in C.
@@claudiocan41 I figured that out reading the Lemma very carefully. I wish this was emphasized in the lemma and the case of orthogonal functions discussed. But I guess mathematicians read very carefully because ideas are represented very succinctly. I am a 57+ lifelong learner trying to learn advanced math on my own. No mathematicians in my social circle and so your response was invaluable--thanx a bunch!
@@GoutamDAS-ls1wb That's nice. Any case, do you know why the second lemma is general for any function ? I know that the derivation is right but why chosing that h(x) works for every function in C1
@@claudiocan41 Thank you for your prompt response. It is great RUclips allows people from all across the world to assist each other. I am in the process of understanding the second lemma. Thanks a bunch once again!
@@claudiocan41 I understand the second lemma now. I would have done it differently--using integration by parts and then using Lemma_1 to show that since (alpha(x))' would have to be zero then alpha(x) must be a constant.
Excellent lectures--I wish I had you for my math classes. It took me a long time (I am 57+) but learning this lesson from Prof Ramakrishna was so gratifying. Thank you so very much for posting this on RUclips
A mind blowing teacher!!! So cool!! Exceptional lecture👍👍👍🙏
What a lecture, exceptional
Where can I find the other lectures of the same series?
Can anyone point me to the lecture where Professor Ramakrishna talks about Taylor Series. I would very much appreciate it.
My doubt is in the 1st lemma : if alpha(x) = 0 then whole integral will be zero no, because anything multiplied by zero is zero only.
I think u are a genius
But at 12:24 you can still pick a alpha(x) such that the integral is zero. Just make it a sinus curve with a period of x2-x1 and a phase such that it is zero at x1. Am I missing something?
The issue is, would the integral be GUARANTEED to be zero for ANY h(x) i give you? The answer is no.
@@jehushaphat thnks for u both
If h(x) = sin(x) and the interval is [0, 2*pi]; then we know that integral( sin(x)cos(x) dx) in the interval = 0 but that does not mean cos(x) = 0 everywhere?? Can someone please clarify?
cos(x) is right for sin(x), and satisfy the integlal, but dosen't work for all the functions in C. Remember that you are working with a space of functions and the condition have to work every posible function in C. a(x)=0 satisfy the condition for every h(x) in C.
@@claudiocan41 I figured that out reading the Lemma very carefully. I wish this was emphasized in the lemma and the case of orthogonal functions discussed. But I guess mathematicians read very carefully because ideas are represented very succinctly. I am a 57+ lifelong learner trying to learn advanced math on my own. No mathematicians in my social circle and so your response was invaluable--thanx a bunch!
@@GoutamDAS-ls1wb That's nice. Any case, do you know why the second lemma is general for any function ? I know that the derivation is right but why chosing that h(x) works for every function in C1
@@claudiocan41 Thank you for your prompt response. It is great RUclips allows people from all across the world to assist each other. I am in the process of understanding the second lemma. Thanks a bunch once again!
@@claudiocan41 I understand the second lemma now. I would have done it differently--using integration by parts and then using Lemma_1 to show that since (alpha(x))' would have to be zero then alpha(x) must be a constant.
che ce frega de leo messi noi c'avemo padoiiiiiin!