So grateful for these videos. I watched some other lectures from big universities and they don't really explain anything, just write terms on the board and expect it to be understood. You're a great teacher and I feel that I finally understand this topic; I always have a lot of questions that go unanswered in other videos so I appreciate the way you explain your steps thoroughly. Great video!
I am a computer science student, currently delving around machine learning and it brought me here. I once again am reminded of how beautiful mathematics can be!
you explained it so well i could skip through a lot and still understand it completely, my math professor didn't want to cover the basics, so thank you for going over them.
Perhaps this is the easiest video on Fourier series on UA-cam. Doing integration ( specially showing the value of delta (mn) ) makes this video unique. That's why I easily grasped the concept how to identify the co-effcient. Thanks a lot. My professor just messed up the topic and made it hard to learn.
I loved the derivation. I could only imagine how Fourier felt when he derived or invented this. Seems so clear but we know some steps. Also reversing the sum with the integral you said we know it converges to f(x). I thought that was what you were trying to prove.
Each of the 3 positions contains each decimal digit 1/10 of the time (if you count leading zeros). So each digit appears 3×1000/10 = 300 times. More generally: In a list of all possible n-positional integers (allowing for leading zeros) each base-b digit appears exactly n·b^(n-1) times, e.g. b=10 and n=3 is 3·10^(3-1) = 3·10² = 300.
That seems way easier than how I did it lol. My approach was: There’s 10 in the first 99 in the ones space (1,…,91) and then 10 more for #s 10-19, giving 20 total in 1-99; this repeats 9 more times for each set of 100 numbers giving 200 total, but then there will be 100 more for every number 100-199 (from the hundreds place) given a grand total of 300😊
Accompanying FREE worksheet courtesy of Maple Learn here: learn.maplesoft.com/d/DLEJJJNPPUILFLPNCTLRGSJHCTMHCRDJCTAUIRKKGSGPBSFHJNIFNRPODNPFBLJROIHMNIPIOUKLPHNIILISJMFLKULTNLGPHGNS
It's indded 0, if you plot cos(npix/L) on 2d, you will see that integral is the sum of area over -L to L Although cos is an odd function, but this integral will be still 0 due to area between x=0 to L/2 is the same of x=2/L to L. One is posivte,the other is negative,so they canceled out. For area between x=0 to -L is the same.
Hi. Im a 11th grade student. I didnt understand the part where: integrating the sin function, then inputting x=L gives zero (while deriving last RHS term for a0). I get why it happens for a cos function, we integrate it and it becomes sin, and every integer multiple of pi for sin is 0..... but for sin when we integrate, it become cos function... which is not 0 at every integral multiple of pi right? If you could clarify this doubt asap it'd be of help
Oh my, just came a minute shy to the end :) Tom, is there a way to describe a FT in terms of SU(2) Lie group? And I didn't watch the video yet - just in case the answer is out there - I'll do in a moment!
Hi Tom can you make a video testing the new AI chatGPT's maths skills by asking it a bunch of maths questions. I've used it a couple of times and it seems to be quite knowledgeable to a degree.
@@evazhang3232 0*1=0. In the integers, even times odd is even. It appears this is not analogous to odd and even functions, but this was just a passing remark that was irrelevant so it doesn't matter that it was wrong.
@@beachboardfan9544 Delta is a character from the greek alphabet. Just as in the roman alphabet, they have upper- and lowe-case characters. The lower-case delta is the "S" and the upper-case delta is the triangle.
Why is there no video on the internet giving a proof for the generalized by parts rule of integration? Is it just a mathematical trick without a proof or....simply put wtf is it??
Finally!!! Please, make a derivation of Laplace Transform!
I appreciate you really did the integrations and didn't just state the results.
So grateful for these videos. I watched some other lectures from big universities and they don't really explain anything, just write terms on the board and expect it to be understood. You're a great teacher and I feel that I finally understand this topic; I always have a lot of questions that go unanswered in other videos so I appreciate the way you explain your steps thoroughly. Great video!
I am a computer science student, currently delving around machine learning and it brought me here. I once again am reminded of how beautiful mathematics can be!
you explained it so well i could skip through a lot and still understand it completely, my math professor didn't want to cover the basics, so thank you for going over them.
Thanks!
Thank you for talking about the interchange of summation and integration and the property of uniform convergence!
Perhaps this is the easiest video on Fourier series on UA-cam. Doing integration ( specially showing the value of delta (mn) ) makes this video unique. That's why I easily grasped the concept how to identify the co-effcient. Thanks a lot. My professor just messed up the topic and made it hard to learn.
Studying physics rn, this helped soooooo much! Thx!!!
Great video!
Adding to the list of people suggesting this: would love to see how to derive the Fourier transform from Fourier series. 😊
I loved the derivation. I could only imagine how Fourier felt when he derived or invented this. Seems so clear but we know some steps.
Also reversing the sum with the integral you said we know it converges to f(x). I thought that was what you were trying to prove.
Why did u decide to integrate this eqation on 23:12 ?
For orthogonality, for m=n, you only covered m=n>0, the case m=n=0 has to be treated as a special case or else you are again dividing by 0.
I think he didn't considered it bc he was working with positive integers
Please make a video on Fourier, Laplace Transforms and Special Functions such as Bessel functions, Hermite , Legendre Functions.
Each of the 3 positions contains each decimal digit 1/10 of the time (if you count leading zeros). So each digit appears 3×1000/10 = 300 times.
More generally: In a list of all possible n-positional integers (allowing for leading zeros) each base-b digit appears exactly n·b^(n-1) times, e.g. b=10 and n=3 is 3·10^(3-1) = 3·10² = 300.
That seems way easier than how I did it lol. My approach was:
There’s 10 in the first 99 in the ones space (1,…,91) and then 10 more for #s 10-19, giving 20 total in 1-99; this repeats 9 more times for each set of 100 numbers giving 200 total, but then there will be 100 more for every number 100-199 (from the hundreds place) given a grand total of 300😊
Accompanying FREE worksheet courtesy of Maple Learn here: learn.maplesoft.com/d/DLEJJJNPPUILFLPNCTLRGSJHCTMHCRDJCTAUIRKKGSGPBSFHJNIFNRPODNPFBLJROIHMNIPIOUKLPHNIILISJMFLKULTNLGPHGNS
integration of cos would not be 0 at 30:43, would you please double check when you get a chance please?
It's indded 0, if you plot cos(npix/L) on 2d, you will see that integral is the sum of area over -L to L
Although cos is an odd function, but this integral will be still 0 due to area between x=0 to L/2 is the same of x=2/L to L. One is posivte,the other is negative,so they canceled out. For area between x=0 to -L is the same.
Probably pretty low-brow for you, but can you do one on induction proofs?
Hi. Im a 11th grade student. I didnt understand the part where: integrating the sin function, then inputting x=L gives zero (while deriving last RHS term for a0). I get why it happens for a cos function, we integrate it and it becomes sin, and every integer multiple of pi for sin is 0..... but for sin when we integrate, it become cos function... which is not 0 at every integral multiple of pi right? If you could clarify this doubt asap it'd be of help
Oh my, just came a minute shy to the end :) Tom, is there a way to describe a FT in terms of SU(2) Lie group? And I didn't watch the video yet - just in case the answer is out there - I'll do in a moment!
Hi Tom can you make a video testing the new AI chatGPT's maths skills by asking it a bunch of maths questions. I've used it a couple of times and it seems to be quite knowledgeable to a degree.
I had the opposite experience. It came upw ith some incorrect proofs for me but confidently thought they were correct.
16:00 Odd number times even number is even. Got a bit confused for a while
odd times even is odd
@@evazhang3232 0*1=0. In the integers, even times odd is even. It appears this is not analogous to odd and even functions, but this was just a passing remark that was irrelevant so it doesn't matter that it was wrong.
damn that's so helpful, thanks
I am very interested with!
too good bro. loved it
Is that an english thing, using the tall S as delta instead of the triangle?
it's the small letter delta.
@@MxIraAram Whats that mean? The triangle is only for numbers?
@@beachboardfan9544 Delta is a character from the greek alphabet. Just as in the roman alphabet, they have upper- and lowe-case characters. The lower-case delta is the "S" and the upper-case delta is the triangle.
@@ste1l1 Ahh thanks!
capital Δ lowercase δ
The sun(x) is a new one to me! :-)
Really im wating for that
Why is there no video on the internet giving a proof for the generalized by parts rule of integration? Is it just a mathematical trick without a proof or....simply put wtf is it??
I think the school is good
Does this guy have a youtube tattoo??? Wild.
A derivation of the fast fourier transform pwease
I feel help me the school please
Iam doing
Ouhhh
Wow, what kind of a lunatic does this this to his body?
You are extremely rude, what kind of a lunatic you are to leave such rude comment