Real teacher teaches hardest concept in easiest simplest way possible and. I found you are the one who does beautifully Thankyou sir for giving such insight which we never thought possible without you "Love and huge respect from INDIA "
This is becoming my favourite math channel to extend the current knowledge with subjects that interest me. And youtube algorithm deserves a hats off as well. It just suggested your fourier series video series where finally it's not just introduction of what fourier does, but explaining how to use it or approach it. Like giving instructions to how to use a hammer to actually nail something.
For those wondering why we need cosine as well as sine, one way of seeing this is to first observe that any function f(x) can be written as a sum of an even function and an odd function: f(x) = even(x) + odd(x) where even(x) = 1/2 (f(x) + f(-x)) odd(x) = 1/2 (f(x) - f(-x)) Now the sin(nx) terms approximate the odd part (as sin(nx) is always odd, a sum of them will be odd) and the cos(nx) terms approximate the even part (as a sum of even functions is even) the all we need is a constant offset as the average value of sin(x) or cos(x) over [0,2pi] is zero.
Thank you Dr Trefor, you're a very excellent teacher, i've been trying to understand what fourier series is in other videos but I couldn't until I saw yours
You are the absolute GOAT of youtube teachers. I learn so much from you. You are getting me through DiffEQ right now. Best place to review for a test ever!!!!
i cant thank you enough Dr Trefor but your enthusiasm towards this topic helped me really focus on some underlying concept on fourier ,you really enlightened my mood this evening,thank you Sir
I am so happy to watch this video - I understood concept of Fourier series with the happiest teacher I even seen. Much better understanding that in my university Thank you a lot❤
I came to your playlists for the topic I didn't understand from books or any source available on the internet. And I got my concepts here!! Some serious Quality work sir!! ❤️
I really dig how you end the video with questions to be answered later (but which a student could start thinking about ahead of the next lecture). I am learning how to teach mathematics effectively and your videos are incredibly helpful and inspiring. Thank you for the wonderful resource and I hope you don’t mind the compliments!
Wow great video, I didn't saw this perspective of the Fourier series before. This is one of the subjects in mathematics that I like the most because at the beginning(when I was in college) it was difficult to me to understand it but once I discover what it does and how it's related to the Fourier transform it just blew my mind. Thanks for such awesome explanation videos!
Thanks to this video, I was able to explain a problem with a machine filling bottles. The machine was capable of filling 4 bottles at the same time. If a bottle would not be present the machine would not filled the bottle. But the weight in the bottles after that would vary too much and cause deivaitions. I was able to save the company about 1.2 Million per year. The product is very expensive.
There is a beauty to your explanations. You're an amazing teacher. I'll be sharing your work with my readers and viewers a lot. Please keep making videos
@@bazsnell3178 grant is amazing no doubt. However in terms of technical level, his are more directed towards beginners. He does help one appreciate the beauty in Math though
Great video. When I was first trying to understand this, my math prof told me, "The idea is any periodic function can be built up from sums of cos and sin. And... with a sufficiently warped mind, ANYTHING can be considered a periodic function." Even the Big Bang!! (hehehe... we don't know the 'period' yet, but one might consider it 'periodic') :)
You are great! I was a graduate in mid-90, but it reminded me the weakest point of maths to data analysis when facing decision making in complex analysis of contour integral that missing momentum-oriented formula.
When I see how well some random profs online can teach the broad strokes of Fourier Series, it makes absolutely no sense why other profs who, I'd assume are equally knowledgeable with regards to the basics, can't do a better job teaching the material.
You clearly understand the math, but your knowledge of platforms and tools to make pictures is what sets your presentations apart. P.S. Love your Latex tutorials, too, as even formatting goes a long way towards clarity. I sure hope there’s something for you in all this, because it’s invaluable, and yet free, for all of us. The Internet has caused its fair share of problems, but helping to educate is where it has shone brighter than anyone imagined, I think.
Man, I have a final test on this topic on Friday. Pretty doubtful you would upload all vids related to this topic by then. Still, an amazing video tho! I’m motivated to learn now :D
A really cool derivation of this is the Continuous Least Square Approximation with the Sin(nx) and Cos(nx) as the basis functions. Showing they are orthogonal, and how that simplifies the linear algebra
The Dirac delta function(t) is 1 in fourier domain. That means that we need all sine waves of equal amplitude. cos(x*1/5)+cos(x*2/5)+cos(x*3/5)+cos(x*4/5)+cos(x) looks like an approximation to the dirac delta function, and it makes sense. Mathematically I don't understand why it's cos instead of sin, graphically I understand why. If we integrate by dividing with iw we get 1/(iw), which in time domain is a heaviside step function. That makes sense. 1/(iw) means that we want all sine waves, phase shifted by 90 degrees and their amplitudes decay on the form 1/(frequency). sin(x*1/5)*1/5+sin(x*2/5)*2/5+sin(x*3/5)*3/5+sin(x*4/5)*4/5+sin(x) doesn't look like a heaviside step function at all. Where am I thinking wrong? My gut feeling tells me that the heaviside step function is basically just a square wave of infinite period, shifted up and scaled down so it goes between 0 and 1. Sorry for coming here with such a mathematical question. But I thought it was very related to the video.
sin is an odd function (sin(-x) = -sin(x)) while cos is even (cos(-x) - cos(x)). The Dirac delta function is even (it is the limit of even functions) therefore needs to be approximated by sum of even functions.
It may be worth noting that there's no mention of time in this explanation in the form of frequency . He says the period is 2*pi. When X gets replaced with w*t is when time enters the picture and the time domain is entered.
Will you please make a long lecture serious regarding integral equations and then another series on integro differentail equations. Please also tell us why we use integral equations.
@Dr. Bazett - Great work. Enjoying your videos. Can I request Laplace Transforms, please? Perhaps this once I could figure out where it all came from. Only you can do this.
Awesome channel, thank you. Gibbs phenomenon is to be expected, though. One is trying to approximate a non-continous function by an infinitely differentiable function. If one was trying to draw this with a pen, it would necessarily overshoot due to its inertia (like in d²y/dt² here)
2:53 I would be nice to simple graph the difference/deviation as an intermediate step. You will see the triple frequency in it and that it is not try and error of what you're doing in 3:13.
Real teacher teaches hardest concept in easiest simplest way possible
and. I found you are the one who does beautifully
Thankyou sir for giving such insight which we never thought possible without you
"Love and huge respect from INDIA "
I don’t usually comment on TH-cam but I’m a 2nd year physics student and I have to say you are the best source of maths help on the entire internet
Thank you so much!
May the soul of Fourier subscribe to your channel
This is becoming my favourite math channel to extend the current knowledge with subjects that interest me. And youtube algorithm deserves a hats off as well. It just suggested your fourier series video series where finally it's not just introduction of what fourier does, but explaining how to use it or approach it. Like giving instructions to how to use a hammer to actually nail something.
For those wondering why we need cosine as well as sine, one way of seeing this is to first observe that any function f(x) can be written as a sum of an even function and an odd function:
f(x) = even(x) + odd(x)
where
even(x) = 1/2 (f(x) + f(-x))
odd(x) = 1/2 (f(x) - f(-x))
Now the sin(nx) terms approximate the odd part (as sin(nx) is always odd, a sum of them will be odd)
and the cos(nx) terms approximate the even part (as a sum of even functions is even)
the all we need is a constant offset as the average value of sin(x) or cos(x) over [0,2pi] is zero.
I will never understand this... 😔
@Dont Check My About Page Link
Why do people do this stupid shit.
Another JEM on TH-cam after 3B1B .... Beautiful 💞💓
Exactly. Just so perfectly explained ❤
Better than 3brown 1blue
FINALLY!!!!
It's "GEM", not "JEM"!
Ss
Thank you Dr Trefor, you're a very excellent teacher, i've been trying to understand what fourier series is in other videos but I couldn't until I saw yours
You are the absolute GOAT of youtube teachers. I learn so much from you. You are getting me through DiffEQ right now. Best place to review for a test ever!!!!
i cant thank you enough Dr Trefor but your enthusiasm towards this topic helped me really focus on some underlying concept on fourier ,you really enlightened my mood this evening,thank you Sir
Thank you my esteemed professor for making my Fourier class smooth......big up from Kenya
Dr. Trefor deserves every possible award in the world. He is amazing at teaching. This video beats 10 hours of my prof's lectures.
I just fan of you how amazingly you explain such difficult concept in such a amazing visualization way. I love it. ❤️
Thank you so much 😀
He's like the "Brian Greene" of mathematics. He explains all these abstruse mathematical concepts in a very succinct, lucid, and visualized way.
Just what I needed. It's like this guy knows exactly what i need every time
Haha awesome!
One of the BEST introductory explanations I've heard of a Fourier series. It's motivating & interesting.
Watching this video brings me back to my university days taking Applies Physics - keep 'em coming!
YES!!! YES!!! YES!!! I’ve been dying to learn about Fourier Series for the longest time
Nice, they are so cool!
I am so happy to watch this video - I understood concept of Fourier series with the happiest teacher I even seen. Much better understanding that in my university
Thank you a lot❤
I came to your playlists for the topic I didn't understand from books or any source available on the internet. And I got my concepts here!! Some serious Quality work sir!! ❤️
I really dig how you end the video with questions to be answered later (but which a student could start thinking about ahead of the next lecture). I am learning how to teach mathematics effectively and your videos are incredibly helpful and inspiring. Thank you for the wonderful resource and I hope you don’t mind the compliments!
Very nice video
Wow great video, I didn't saw this perspective of the Fourier series before. This is one of the subjects in mathematics that I like the most because at the beginning(when I was in college) it was difficult to me to understand it but once I discover what it does and how it's related to the Fourier transform it just blew my mind. Thanks for such awesome explanation videos!
Awesome work, guys like you are the future of education
Been watching your videos since you had 30k subs, amazed you are on 100k now, keep up the great content Dr. Trefor :)
Nice!! Thank you so much:)
Thanks to this video, I was able to explain a problem with a machine filling bottles. The machine was capable of filling 4 bottles at the same time. If a bottle would not be present the machine would not filled the bottle. But the weight in the bottles after that would vary too much and cause deivaitions. I was able to save the company about 1.2 Million per year. The product is very expensive.
This deserves millions of subscriber.
Your recent posts are outstanding, thank you!
Glad you like them!
Another excellent video from the best math teacher in the planet. Thank you!
Thank you so much!!
There is a beauty to your explanations. You're an amazing teacher. I'll be sharing your work with my readers and viewers a lot. Please keep making videos
Also excellent is TH-cam channel '3Blue1Brown'.
@@bazsnell3178 grant is amazing no doubt. However in terms of technical level, his are more directed towards beginners. He does help one appreciate the beauty in Math though
Amazing way of explaining things by Prof Trefor. Wow.
just in time when my professor introduced fourier series in our analysis II course....Youre a savior
Great timing!
Great video. When I was first trying to understand this, my math prof told me, "The idea is any periodic function can be built up from sums of cos and sin. And... with a sufficiently warped mind, ANYTHING can be considered a periodic function." Even the Big Bang!! (hehehe... we don't know the 'period' yet, but one might consider it 'periodic') :)
Difficult concept explained with an easy approach,I appreciate your efforts.
You are great! I was a graduate in mid-90, but it reminded me the weakest point of maths to data analysis when facing decision making in complex analysis of contour integral that missing momentum-oriented formula.
I had no idea what’s going on in my class before watching this video. Thanks for the amazing explanation!
Thanks!
Thank you so much!!
Wow It's just how fascinating is this ! Thank you so much You have the gift of explaining hard topics in an amazingly simple way.
Glad you enjoyed!
When I see how well some random profs online can teach the broad strokes of Fourier Series, it makes absolutely no sense why other profs who, I'd assume are equally knowledgeable with regards to the basics, can't do a better job teaching the material.
Your way of explanation is awesome
Hatsoff to you 🤓
Just when I need it!!Great work!!Greetings from Greece!!
Awesome! Thank you!
Came here to understand Fourier transforms from a medical imaging perspective. Your images are intuitive, 😊
Thanks alot, My discrete mathematics test went great today only bcauz of you🙏
Congrats, that’s awesome!
@@DrTrefor Your explaining skills are legendary
You clearly understand the math, but your knowledge of platforms and tools to make pictures is what sets your presentations apart. P.S. Love your Latex tutorials, too, as even formatting goes a long way towards clarity. I sure hope there’s something for you in all this, because it’s invaluable, and yet free, for all of us. The Internet has caused its fair share of problems, but helping to educate is where it has shone brighter than anyone imagined, I think.
Man, I have a final test on this topic on Friday. Pretty doubtful you would upload all vids related to this topic by then. Still, an amazing video tho! I’m motivated to learn now :D
One more coming on thursday lol, but good luck regardless!
How am I in college and a professor explains this but it’s gibberish, and this is so clear and it’s free!
Maybe after your videos I will finally understand this topic. Thanks for great work)
If only every body could explain this well ! Thank you.
thank you, it is a beautiful think to anderstand the basic idea of topic
Thanks for the passion you show while teaching!!
Great wideo. It's always good to talk about mathematical actions in this explenatory, human way.
Thank you doctor for beautiful explanation ever ❤
This kind of videos are so awesome thank you so much, keep doing this
Thank you, I will!
People r doing big stuffs like fourier transform and here I am. just celebrating my 500th like on this video :')
Sir, you always explain so well! Thank you so much!
hahaha! Found it just when needed! Thank you Dr Bazett
Glad it helped!!
Thanks for the intuitive explanation Trefor!
You’re most welcome!
You really help me a lot in maths! Thank you!
Woah congrats on 100k subs!
Thank you so much!!
Amazing man this is one of my wishes ,thanks .
Your videos are really helpful for me. Thanks and keep making more...
You are my favourite teacher
The visualization helped a lot. Thank you so much!
Absolutely amazing video, thanks for the intuition.
How beautifully explained sir !
Love the way you explained : )
Great presentation. I wish you make a series on Wavelets.
Can't wait to watch the next video! Thanks professor for your awesome videk
Glad you enjoyed!
You are just what I needed! Thank you!
superb motiation for this interesting topic. Thank you so much.
A really cool derivation of this is the Continuous Least Square Approximation with the Sin(nx) and Cos(nx) as the basis functions. Showing they are orthogonal, and how that simplifies the linear algebra
Thanks for this Dr. Bazett!
Thank you sooooo much for this amazing explanation!
This was a very good explanation, I really enjoyed this video. I wish the audio wasn't so crunchy on the video though.
insanely good intro video
Nice clear explanation with some interesting twists and details!
You are the best!! Thank you so much sir
Finally a video which doesn't assume the student knows eigenvalues
This is absolutely amazing
I love it, you explain so clearly and intuitively. Best math channel with 3Blue1Brown !!!
Wow, thank you!
great visualization
The Dirac delta function(t) is 1 in fourier domain.
That means that we need all sine waves of equal amplitude.
cos(x*1/5)+cos(x*2/5)+cos(x*3/5)+cos(x*4/5)+cos(x) looks like an approximation to the dirac delta function, and it makes sense. Mathematically I don't understand why it's cos instead of sin, graphically I understand why.
If we integrate by dividing with iw we get 1/(iw), which in time domain is a heaviside step function. That makes sense.
1/(iw) means that we want all sine waves, phase shifted by 90 degrees and their amplitudes decay on the form 1/(frequency).
sin(x*1/5)*1/5+sin(x*2/5)*2/5+sin(x*3/5)*3/5+sin(x*4/5)*4/5+sin(x) doesn't look like a heaviside step function at all. Where am I thinking wrong? My gut feeling tells me that the heaviside step function is basically just a square wave of infinite period, shifted up and scaled down so it goes between 0 and 1.
Sorry for coming here with such a mathematical question. But I thought it was very related to the video.
sin is an odd function (sin(-x) = -sin(x)) while cos is even (cos(-x) - cos(x)). The Dirac delta function is even (it is the limit of even functions) therefore needs to be approximated by sum of even functions.
@@gibbogle Ah, of course, so intuitive! Thank you!
Very nice video as always. I'm eager to learn this series :)
I'm so excited!!!
haha, awesome!
Fourier series is half the truth of the universe.
Awesome video! Thank you!
It may be worth noting that there's no mention of time in this explanation in the form of frequency . He says the period is 2*pi.
When X gets replaced with w*t is when time enters the picture and the time domain is entered.
Drrrrrr you help me so much ❤️
Thank you so much for this video!!! You really helped me out a lot.
Great Presentation
Will you please make a long lecture serious regarding integral equations and then another series on integro differentail equations.
Please also tell us why we use integral equations.
Thank you so much Dr.Trefor, Could please help us with deep understanding to Bessel equation and it's solutions
Oooh, that would make a great video
Dude, I love you.
Thank you for making these videos
@Dr. Bazett - Great work. Enjoying your videos. Can I request Laplace Transforms, please? Perhaps this once I could figure out where it all came from. Only you can do this.
I have a whole playlist on this, check out my homepage!
Thank you so much for your work - I wish you had a Patreon page, if everyone just contributes a little that would only be fair!
I don’t have a patreon, but I do have a TH-cam membership (it’s the join button). Regardless, thanks for even thinking about that, much appreciated:)
@@DrTrefor Thank you Sir, I will consider doing this
Love you sir. Mesmerising
Awesome channel, thank you.
Gibbs phenomenon is to be expected, though. One is trying to approximate a non-continous function by an infinitely differentiable function. If one was trying to draw this with a pen, it would necessarily overshoot due to its inertia (like in d²y/dt² here)
No, not really. Think for example splines!
2:53 I would be nice to simple graph the difference/deviation as an intermediate step. You will see the triple frequency in it and that it is not try and error of what you're doing in 3:13.
Greatly greately lenegdary explaination
thx mr Trefor
Thank you this was perfect 👌