Intro to Fourier series and how to calculate them

[arienette820]

This video is the only reason I got any of my homework done. Thank you so much!

[texxmexxtexx]

Thank you for this great, and easy to understand lesson. It is much appreciated.

[abekmuratov]

The way u teach is easy to understand and ur voice nice to listen! Thanks from Kazakhstan! Keep it up!

[MacacoPulando]

Thanks alot for these videos. I had a class last semester that dealt with fourier series but I never really understood the point of them until today.

[nvrfollowb5]

You make a great online math tutorial. One of the best I have seen. Thank You! Keep the PDE stuff coming!

[shinakuma9]

Hi there, are the documents you used in the video available anywhere to download?

[DrChrisTisdell]

@shinakuma9 Please read the annotation at the start of the video for directions.

[lugiachan]

i want to know how do you simplify cos (n pi) to (-1)^n ?

many thanks indeed!

[lugiachan]

and.. why 2k-1? where does it come from? thanks!

[DrChrisTisdell]

@lugiachan Because n = 2k-1 is always an odd number (whenever k is an integer) and we are only interested in summing over the odd values of n.

[DrChrisTisdell]

@lugiachan Consider the even values of n, so n = 2,4,6 etc Can you see why cos (n pi) = 1? Consider the odd value of n, so n = 1,3,5 etc. Can you see why cos (n pi) = -1. Put these cases together and the result follows.

[lugiachan]

@DrChrisTisdell

thank you! i just reckon that im too silly to ask these !

[DrChrisTisdell]

@lugiachan Don't worry about it. You are not too silly. BTW, I have a real fondness of Hong Kong. I spent some months at HKU and CityU as a mathematician in 2006 and 2009.

[Rmpf22]

@DrChrisTisdell How did the 2/pi become 2/(n*pi)? You just integrated the sin (nt), did you?

Thank you

[DrChrisTisdell]

@Rmpf22 Yes, :08:16 "integrate with respect to t".

[ELT626SSN]

when should Ao be divided by 2 in the fourier series equation?

as presented in this video the equation given the first coefficient is just Ao while my text book has Ao/2

[DrChrisTisdell]

@ELT626SSN Some texts prefer to have a_0/2 in the Fourier series (rather than just "a_0"). In that case there is no "2" in the (integral) definition of a_0.

[airman665544]

Why use Maple when you can use our old friend MATLAB :) Just kidding :D

[PenguinRecordings]

I know people don't say this a lot on education videos, but I think I am going to have to break the replay button for this one...

[19hashan93]

Wow this is brilliant. Thanks a lot sir! Couldnt understand heads or tails of this at my lecture but thanks to you its crystal clear now. Off to try out some problems now! :-)

[ThePerfectElite]

@TheMunkification he needed to multiply by n/n to get the 'n' in there so he could integrate. He then pulled out the 1/n and integrated

[TheMunkification]

Where did the "n" and the -2 in -2/(n*PI) come from at 08:24 ?

[barryj106]

yo dawg yo videos so dope i gone go git me some motherfucking A's bitch

[biloocabba2]

thank you sir ...i study in 1 years master Electrical Engineering, and i hope that ..benefit from your extensive experience  bilal

[biloocabba2]

thank you sur but ... do you dimenstaration ...how we foawd B0,An,Bn relation

[DrChrisTisdell]

@biloocabba2 You can see all the details here /watch?v=KeT6CB6Qi10

[himerobine]

Thanks so much for your explications it so helpful and kind of easy to understand ^^

[afg987654321]

@DrChrisTisdell How do you calculate these integrals on a TI Calculator? I have a TI 83

[DrChrisTisdell]

@afg987654321 At UNSW we do not use these kinds of calculators, rather we use programs like Maple, Matlab and Mathematica. So I can't answer your question - sorry.

[Bairdyboy1980]

This is really helpful... you explain it really well.... thanks!!!!

[mostafa8998]

i love you dr chris...you illuminated my world of fourier series....i was blind now i can see

[hbz241]

amazing thank u so much

[Damianbambambosiacki]

this is dank

[olifannar]

Awesome video, thanks alot

[Sasotzu]

Thanks a lot, very useful video for a frenchie who wanted to work for the holidays :)

[Dosalt]

Regarding the answer to the practice question at the end, the function seems to be neither odd nor even.

Also the final answer has all three components a0, a1 and b1.

Someone correct me if it is not the case.

[DrChrisTisdell]

@Dosalt Please see my earlier comment about this. 

[Jdonovanford]

@DrChrisTisdell Sorry, we can't find the earlier comment. Could you just answer the question?

[DrChrisTisdell]

@Jdonovanford If you download the associated PDF for this lesson (UnderstandMath.tv), then you'll see a generous hint in the answers to the practice question. .

[Dosalt]

Regarding the answer to the practice question at the end, the function seems to be neither odd nor even.

Also the final answer has all three components a0, a1 and b1.

[KwasiYe]

what was the answer to the question set at the end?

[DrChrisTisdell]

@KwasiYe Please see my earlier comment about this. Best wishes.

[commelions]

ok i see it now !! sin (nt) = -1/n cos (nt), sorry i guess i was over thinking there !. thanks for the help.

[commelions]

hi im new to this integration stuff, i got a problem with the Bn part, when the integration is done on the 3 line of the bn coefficient you have no t squared left when you move the N outside the brackets. why ?

[DrChrisTisdell]

@commelions Why would a $t^2$ appear? We are not integrating $t$, we are integrating

$\cos nt$. If you're new to integration then Fourier series are quite a challenge. They usually appear in a third university course in calculus, whereas integration of something like $\cos nt$ appears in a first course in calculus.

[Wilsonnyo2]

definitely helps my cramming for the coming unsw math exam :p

[Wilsonnyo2]

@Wilsonnyo2 and thank you very much! :D

[SarahStarmer]

These are really good explanations of Fourier Series but I am so fed up of watching the same advert again and again and again.

[cantabriver]

thank you so much for this!

[lminors]

What's the solution to the problem given at the end?

[DrChrisTisdell]

@lminors Please follow the Annotation at the start - download the PDF from UnderstandMath.tv to find out!

[lminors]

@DrChrisTisdell In this answer, why does a0 go to a half, even though it is odd. I got the wrong solution and I can't see why, is there a worked answer?

[DrChrisTisdell]

@lminors There isn't a worked solution because the aim is for *you* to think hard about the question and to keep going! The function isn't odd BTW. Good luck!

[lminors]

@DrChrisTisdell There is no way the function is even.

[DrChrisTisdell]

@lminors Correct - the function isn't even (I didn't claim that it was). Think of shifting the curve down 1/2 a unit to produce an odd function and calculate the FS for that. Then simply add 1/2 to your answer. Over and out.

[KwasiYe]

@DrChrisTisdell genius. thanks, i would never have thought to shift the graph down by 1/2 to make it an odd function. i hate missing things like that in maths! but thank you so much pal.

[patarthenry]

Thank you for this example with explanation.

[rkjab]

Hello! I have a question. Does all cosine and sine functions of period 2pi are orthogonal to each other, even if we take L as 2L? or in other words take frequency 0.5?

[Haroson]

You are amazing. I was about to give up on this if it had not been for this fantastic video. Thank you. 

[kashmoney2011]

i wish i went to UNSW instead of UWA.

[deathidoo]

thank you!! m so happy that i finally understand this :D

[mchei]

i hv a problem that why odd*even=0

and odd*odd=even and why then you can double the integration and get result?

also, for even function, (even function)*cos is even, thus can i say that

when the product of 2 function is even that i can double the integration and get result?

[mchei]

@mchei

let me reply myself....

i found that :

The product of two even functions is an even function.

The product of two odd functions is an even function.

The product of an even function and an odd function is an odd function.

and

The integral of an odd function from −A to +A is zero

The integral of an even function from −A to +A is twice the integral from 0 to +A

[mchei]

EEEEEEEEEEEEEEEEExcellent!!!!!­!!!!!!

[fcdog555]

I think I know why this is, but if you were to move all of the function to the right by pi/2, would it not become an even function?

[DrChrisTisdell]

@fcdog555 Indeed, my friend. :D

[mosawimmz]

wow, really good video!!! thank you

[FallofDarkness55]

Thanks for this video, man! I have a project on Fourier series and you clarified this confusing mathematical concept for me.

[kazifhei]

why we can replace n by 2k-1 ??????sorry i just don't understand :).

[kazifhei]

why we can replace n by 2k-1 ??????sorry i just don't understand :)..

[DrChrisTisdell]

@kazifhei See my comment answering this question below.

[lorenz0laplace]

@kazifhei because n is odd brah

[viktorgoa]

this helped me finally understand it, many thanks!

[csGolddragon]

Correct me if I'm wrong, but isn't an odd function * an even function = an even function?

In that case, the cos parts of the fourier series do not = 0!!

[csGolddragon]

Otherwise great vid!

[DrChrisTisdell]

@csGolddragon No, what I've said is correct. If h(x) = f(x)g(x) with f odd and g even then h is odd (ie, h(x) = -h(-x) for all x). You can prove this (or just confirm it with on wikipedia).

[SHITONASTICK1100]

hmmmm am i being stupid or is the equation that starts at 8:29 wrong.... should it not be + 1???? sub in pi and 0 u get (-cosnpi - 1 ) take out factor -1 it turns to cosnpi +1??? no?? probably me being a douche i dunno......

[SHITONASTICK1100]

odd multiplied by even thing is a bit confusin..... but i c sed the blind man, it eventually clicked, i drew the graphs to c that odd times even stayed odd. ha ha ha. Nice lesson man you can actually teach! A rare talent in universities or at least mine.

[NevermindVzla]

Alright alright I have an exam in an hour and a half and I must this really helped a lot but I'm still confused with that thing you did at the end with the cos... how did you turn that into (-1)^n ? will it always be like that ? is there a different transformation for sin ? please help

[DrChrisTisdell]

@NevermindVzla Yes, it will always be like that (can you see why?). There is also one for sin, but I'll leave it to you to determine it. Good luck with your exam!

[NevermindVzla]

@DrChrisTisdell I figured it out, thanks !

My exam was postponed for today, any last minute advices Dr ?

[nukerl]

Thanks for video and it is very very life saving..

My question is could you please tell that how did you draw the graphs.

I need to learn it very soon. Thanks for your helping..

[adastra123]

Thanks , you have a very elegant way of explaining it. Thanks so much for uploading this. People like you make the internet a toy of the gods and worthwhile.

Thanks again so much.

[SantaMain]

I have a question! If we take a harmonic wave added to another harmonic wave, and then want's to calculate with them. Lets say that we have f(x)=3sin(3*pi*x)+4sin(4*pi*x)­, this will result in f(x)={6,8381 0<x<1, and -6,8381 -1<x<0 f(x)=f(x+2) .. Now my question is, do i just do the same as you did? Just follow the steps and then just calculate with reel numbers, instead of whole numbers? Or do i have to make any changes?

[SantaMain]

@SantaMain My problem is that, You have worked with square waves right? and this one is a sine wave.. which makes in more,. non square :D And then i just wonder if it's the same.

Thanks :D

[Cytozone]

Thanks!

[jprigby91]

what happens if there is two odd functions in the integral? good video aswell by the way, my lecturer's been explaining it for 12 weeks and i only understand now after your 13 minute video.

[higgo86]

awesome.. where can i find more?

[1989AndyL]

Great vid, really big help!

Is 10:18 supposed to be sin( n pi t )?

[shyamnarain]

Amazing Explanation Dr. Tisdell . I would like to know if you have a video explaining Complex Fourier Series. Please guide me if you have lecture notes or explanations on complex Fourier series.

[DrDread]

You, my good sir, are amazing. Your effort is much appreciated. Knowledge is power!

[ronalddlelariarte]

this is more rocks and understandable than the chinese guy who speaks 550 syllable per seconds.

[maizul85]

how do you know f(t) is odd? 

[DrChrisTisdell]

@maizul85 3:53

[golnar]

Thank you!

[golnar]

So we basically have to always substitue something for 'n' at the end, and it has to match the type 'values we're summing' ?

[DrChrisTisdell]

@golnar Yes, if you want to "simplify" the sum. It would also be OK to leave it without  changing to 2k-1 (or 2k if you are summing over the even terms). It depends on your preference.

[golnar]

Where did the 2k-1 come from, at the end?

[DrChrisTisdell]

@golnar 2k-1 will always be an odd number and it appears as we are only summing over the odd values. Hope this helps.

[aandreya]

OMG, omg, omg. I must say marveoulus! I don't have anything to do with math anymore since i'm done with uni. But that explanation of odd and even is brilliant. I was trying to figure out f.s. for a while, but then I decided I just won't learn them. Now I see it's pretty logical.

Keep up a good work. It might save a lot of nerves for some people.

[DrChrisTisdell]

@aandreya Many thanks for your comments!