Oh my God, if this existed 27 years ago it would have been so much easier to learn. You are a genius teacher

@DrTrefor

3 жыл бұрын

haha I sometimes wish I could go back in time and watch my own videos:D

@gurumayummadan2646

3 жыл бұрын

@@DrTrefor haha bless you Sir

@dj_b1627

2 жыл бұрын

@@DrTrefor weird flex but ok

@VCT3333

2 жыл бұрын

Wait till you hear him teaching the better series ... Fiveier Series.!

@LittleWhole

2 жыл бұрын

@@VCT3333 I'm more of a Sixier series type of guy, but I respect your opinion

There is something just so magical about when stuff like this finally clicks. Makes you feel like you've unlocked a new understanding of reality. Thank you so much Dr Trefor

Can't wait for fourier transforms The way you explain things is magical

@DrTrefor

3 жыл бұрын

Me too, they are so cool!

If anyone asked me to show them who a teacher is, I would point to you and say Dr. Trefor Bazett. Thank you life saver and be blessed.

You might already know how impactful your videos are on people. But let me tell you how it helped me personally, i am from India (south), i really had a tough time getting my head around Fourier series (cuz without animation, it's very difficult to just imagine) and i can't afford to join tuitions or get paid courses for all my doubts (i am still a student), and there are hundreds of thousands of such people around the world for whom you have helped and made a difference in their learning/education. Thanks a lot 🙏🏼.

@RobinYuan

Жыл бұрын

same here, he is a magician that made fourier series easier to understant

@anonymous9217w2

Жыл бұрын

where in South?

@movrew

Жыл бұрын

​@@anonymous9217w2south

Sir we are lucky that you are giving such a information for free and you teaches us what our lecturer takes 2 hour lecture to explain us , but cant explain properly.

I love the way you explain, you have a real gift for teaching, thanks so much!

I am able to understand this in only 10 to 15 minutes which I would take weeks to understand from books.This justifies how can a human learn faster through visuals.Thanks again for such wonderful demonstration of Fourier series

Wait a second, all this time I've been calculating Fourier series problems without knowing why. And now I Know. Thanks professor!

I don't know anything about Fourier series yet I can understand ur video.u r doing a great job

Simply the best the most intuitive explanation which I was able to find. Many thanks!

you are a very good teacher , your students are blessed , not even a Engineering guy explained it so well

Oh my GOD you can't understand how helpful this video was I have an exam 4 days later and this saved my life thank you so much

Im very drunk while watching this but I still understood, this physics degree gonna be bussin now, thanks doc!

Absolutely incredible sir. I've been out of practice for a dew years and I just picked up PDE's,so this was more than helpful. Thank you!

Fascinating video! I understand it completely

Such a great explanation, thank you so much, I really got the point behind the equations. Best wishes to you

Absolutely loved your presentation 👏 👍 😀 ❤ this made my learning so much easier and intuitive 😀

Just *beautiful* , that's enough. Thank you Professor 💖

1 of the best explaination. Unfortunately underrated video.

Professor, you are a national treasure. I love you

You're doing gods work here and I hope you know that.

What a great video! This deserves 0 dislike (which currently is, per 05-08-2021) and many of likes!

Thank you for this informative video.

Good work...very simplified,thanks alot

Great video, thanks. Much much much better than any textbook explanation I've ever scratched my head over...

This teacher is good, like really good and should be appreciated alot more

That's quite a good explanation! I learnt it through the complex exponential function but it's basically the same. You have a cos term for the even component, sine for the odd component and a constant term for the DC component. That's why your a0 term is zero in your example in your introduction.

Great explanation and editing :)

👍You explained so clearly Sir, thank you.

Please do transforms too. This is the most intuitive and motivated explanation of Fourier series I’ve ever seen! Great job!

@DrTrefor

2 жыл бұрын

That's the plan!

@user-qy6tu9ip9v

2 жыл бұрын

@@DrTrefor I just don't get this stuff man... it makes me so sad.

thank you, sir, you are great!

You are saving my life right now. I have a DiffEq final today, and this has made it so much clearer. Thank you!

@DrTrefor

2 жыл бұрын

good luck!

@user-qy6tu9ip9v

2 жыл бұрын

Dude... fourier transforms and fourier series seems impossible to understand

Wow this clarified so much for me, all the textbooks would not do what you did by 4:30

Very good. Thanks

this is the first time this clicked for me, thanks a lot

You're a very talented teacher

Great explanation

This helped a lot

This was video was a pleasure to watch. It would have been nice if you had discussed the conditions under which we can interchange the infinite summation and integration. I guess we would need to use something like the dominated convergence theorem, with some appropriate conditions on f.

My savior!

Very good

Super clear explanation!

@DrTrefor

2 жыл бұрын

Glad you think so!

super sir beautiful explantions

Thank you very much for the video❤️

@DrTrefor

3 жыл бұрын

You're welcome 😊

Such an excellent explanation! Thank you!

@DrTrefor

3 жыл бұрын

Glad it was helpful!

For general half period L the formulas for a_n and b_n should include L as well!

Hi, thanks for this new series, I'm so excited to be learning about Fourier series! Quick question: When you were talking about the 3 important integrals, must m and n be integers?

@DrTrefor

3 жыл бұрын

Thanks! And yes, m and n are integers.

@dovidglass5445

3 жыл бұрын

@@DrTrefor Cool, thanks!

@telodemuestro7384

3 жыл бұрын

@@DrTrefor Hi, do you mean "They could be integers" or "They must be integers"? thanks for your work!

@2001herne

2 жыл бұрын

@@telodemuestro7384 They must be. If you throw it into desmos, non-integer values of m and n result in values that are not 0 or pi

Thank you so much. I observed that vibration monitors record peak particle velocity with time. then there is option in the software to convert into frequency domain using Fourier transform. i have no confuse on the graph of peak particle velocity in time domain. it simply shows the sensor recording with time. if higher amplitude at 10th second, i understand there is higher vibration at 10th second in machine after starting. if i plot a graph having 10 amplitude readings from sensors with time, that may be a wave form. how can i convert into Fourier series form from the practical readings (i.e. sensor readings)? is it mandatory to form Fourier series to get frequency domain of the wave form ? Again the question, how to create Fourier series form (i.e. mathematical form) from actual vibration sensor amplitude readings? i don't know whether the question is correct or not. Thank you.

you oscillate to peaks of genuine excitement and interest at a periodic rate that can I can now transform into binary to teach a robot how to effectively stimulate students... thanks

Hi I was wondering why do you change an and bn to am and bm. Thanks

terima kasih

Do we also write the general Fourier series for the even as well instead of only the odd fns.

Wish your channel existed when I was in college in the last decade :(

great!

Excellent explanation, thank you. I have an old unsolved question that perhaps you can answer: in electronics we often consider the spectrum of a signal as the “frequency content” of a signal, intended as a sum of sinusoidal functions of certain frequency. However the Fourier series describe a signal as a sum of *sine* AND *cosine* terms. How do this relate this with a spectrum of a signal?

@andrewharrison8436

Жыл бұрын

For a specific frequency there will be, in general, sine and cosine terms. These can be rewritten as a sine term with an offset. To see this look at sine and the angle x an offset of k we get sin(x+k), this becomes sin(x)cos(k) + cos(x)sin(k) so by picking k appropriately we get constants cos(k) and sin(k) to turn the sum of the sine and cosine terms at that frequency into just one oscillation at that frequency but offset.

in the example, what happened to the part of the function that is 0? I know you changed the integral range only to fit the value of 1, and I would guess that if you did the integral of the part 0 with its corresponding integral it would be 0, what happens if its -1?, do you do it as well? how do you add one coefficients to form one series? are they just added?

This is amazing sir.... Always waiting for your new series..

really nice would have been nice to say that m,n have to be natural numbers for the Integral to work like that :)

Can you discuss on Lagrangian mechanics .

@DrTrefor

3 жыл бұрын

I hope to, but going to be a bit:)

How can u put m=0 ,when m is in denominator.

Please make a video on how u plot these on desktop or just tell us in comments. Thanku so much U r great

@DrTrefor

3 жыл бұрын

Nothing fancy just MATLAB

Well I don’t know how to say it Dr. , but i love u 😍 ❤️

Sir we are waiting for fourier transform please make that video....🙏🏻❤

At 10:07 and 12:08, you suddenly introduce an "x" into your equations. Do you mean "t" where you wrote "x"? If not, please explain where the "x" fits into this entire discussion. Many thanks!

At 2:15 shouldn't there be condition that m and n are integers?

@darlingdarling2943

2 ай бұрын

Yes. That part through me off so bad and I was questioning things, but your comment clarified what they meant; yeah, this is only true for integer values. It’s also not true if abs(m) = abs(n) (accounting for m = -n).

Why can't the Fourier series be applied to non-periodic signals?

thank you for the great lecture. Can "m" be a non integer? Because the cosine plot you showed for the "m" values included points for all possible "m" continuously. But then you picked only integer values of m. Can the function be approximated with only integer frequencies? What if the function has the frequency 1.4, or 3.7 in it, for an example? Thanks

@DrTrefor

3 жыл бұрын

For now, yes, an integer. This is a discrete fourier seriers. There are other continuous options, but that is quite beyond the current scope.

@douglas5260

3 жыл бұрын

@@DrTrefor thank you.

There is a mistake in the general case a_0 is equal to 1/2L times the integral not 1/L.

2:32 Values of m and n must be integers

Your first video was very nice and so helpful but this one confused me so much and i didnt understand at all ...

Thank you for sharing these first class lectures .Please advise on the convergence of the Fourier series of a function f(t) =t^2 ( t squared) if 0

Great explanation. However, is the piece wise continuity of the function and its derivative also necessary condition or is it just sufficient? I wanna go deep. Throw Lebesgue spaces at me if it is necessary.

is this definite integral done from 0 to 2pi only. Why didn't you find the integral from zero to say pi/2

1:50 Isn't this dependent on m and n being integers, which you don't specify? When I try computing for values of n that are fractions of m, very close but not equal to m, it doesn't evaluate to zero. Assuming so, that would also explain the interval from 0 to 2*pi, as you're essential looking at two multiples m and n of a base harmonic frequency of 1 and its period 2*pi. Maybe that's implied but I didn't get right away why I couldn't confirm this in mathcad for all values m and n. Otherwise great explanation.

Why are you going from 0 to 2pi instead of -pi to pi? I assume it makes no difference and it's easier to compute, but according to the general function, we need an interval [-L, L), where you can't plug in 0 and 2pi. Is this just something you can do with sin and cos? It's the same for [-pi, pi) and [0, 2pi) in this case?

@carultch

Жыл бұрын

It's an arbitrary choice. Ultimately, you want to complete the integral over 1 full period, how ever you chose to assign it. In this particular case, it is equally as easy to integrate from 0 to 2*pi, as it is to integrate from -pi to +pi. The interval from -pi to 0, and from pi to 2*pi, both give a value of the original wave function of zero, and thus are both trivial to integrate.

Hi a bit confused about the last part of the full example, aren't you only doing the integrals for the function f(x)=1 from 0 to pi? is the part where f(x)=0 from pi to 2pi not relevant? Thanks :)

@kevthedorkslayer9848

Жыл бұрын

I am trying to understand that too its very confusing

@jacobmcgregor4359

2 ай бұрын

@@kevthedorkslayer9848 From Pi to 2*Pi we're just integrating the value 0. For an indefinite integral (an integral without limits) we would write '+C' to indicate some constant. But our integral is definite (has limits Pi to 2*Pi), and the definite integral of 0 is just 0. I may be wrong in my thinking, but you could also think of "Integral = Area between the curve and the x-axis". The line f(x) = 0 is just the x-axis itself. So there is no area between them. And again, no area is just 0.

One question: the derivation in the start is for period 2π?

@DrTrefor

2 жыл бұрын

Yes

2:41 how you could explane it in this imagen way 🥺🥺❤️

2:08 i think these are only true if (m) and (n) are (integers) or at least it is always true in that case but not necessarily other cases

@DrTrefor

3 ай бұрын

Yes they are implicitly assumed to be natural numbers

Hey Can u please cover mensuration 3d😶

Anyone else learn this by the sampling vector then the complex Fourier series first ?

@ 11:36 I THINK in the cosmt it would mpit/l

pleas explain n ,and m why its only interger ? what excalty m ,n is ?

@carultch

Жыл бұрын

They are multiples of the fundamental frequency. For this introductory example, he's sticking to the discrete Fourier transform, where they are integers. There is a continuous Fourier transform where n isn't necessarily an integer, but it is beyond the scope of this introduction.

How did Fourier discover all this 😳

Is a_n the same as a_m and b_n the same thing as b_m?

@DrTrefor

2 жыл бұрын

Yup just different notation

For a(o), why is it 1/pi instead of 1/2pi? I thought the formula was a(o) = 1/T and so on, where T is the period

Sir what happened to the summation when we get the value to the coefficients.( At 4.19 min )

@pratikyadav6036

2 жыл бұрын

What will summation do there when its cosine function is not there, as cos nt got cancelled, it went away with it

In the example at 7:13 what if we want to calculate the coefficients of f(t)=1 from 0 to 2pi instead?? i have a feeling this would give f(t) = 1 always 😂😂, maybe that's the midpoint thing in the the theorem 😅😅 anyway if anybody could help with my confusions plz let me know in the comment

why is a0 considered to be the period of sine?

@carultch

Жыл бұрын

It isn't. It is more like a constant that depends on the average value of the function being integrated. In an electronics application, this would be called the DC offset.

@sroydetroy6404

11 ай бұрын

Sorry for the late response but thank you very much!!!@@carultch

Math is so beautiful

Definite integrals of sin * sin or cos * cos always equalling 0 or pi if the m & n terms are different or same… I don’t think I was taught that trick lol

i know it's too late , but it would be good if you could normalize the audio of your videos, you go from shouting to whispering. I am using an extension to compress the audio to mitigate the problem. great videos by the way, thanks!

@IntisarJabir-zj3zl

2 ай бұрын

Teachers tend to use that method to attract attention on matters that truly matter, maybe reduce your volume idk 😅

the author says nothing about infinite orthonormal basis of this Fourier Series form and projections of function f(x) upon orthonormal functions… and that’s key for understanding Fourier Series

Dear sir , if you integrate sin(mt),cos(mt) from 0,2pi it's not ALWAYS equal to zero. Just see sin(1.2t)

@FaranAiki

3 жыл бұрын

Dear sir, summation cannot have floating numbers. Summation can only have *integers* whereby the equation is true.

Cut down on caffeine bro 😂

@siphosethuharleyzwane1640

14 күн бұрын

😂

How are lectures so bad at showing how simple the concept behind calculating these coefficients are. The first things my professor did was throw some complex constructions at us overwhelming us with what happens only to spend the next 1 hours and 20 minuhtes to talk to teach the 2% of students that he hasn't lost at that point

This man is the Jordan Peterson of math

Best maths video i have ever watched, i am an electrical and electronic engineering student and when we came to communication systems the fourier series seemed to be extremely inportant but no one told me ( even in the provided reading material) the important 3 identities such as sinmtsinnt cosmtcosnt which means i would write 10 lines of equations to calculate a single coefficient! thank you Dr, youve helped me a lot with my future study.

right, I swear all these damn fourier tutorials use the most simple numbers 1 and 0! what?! how am I meant to understand what happens to one with say 9 and 7? this is not a direct example, you didn't calculate something you just went over the equation that I already knew?