How to compute a Fourier series: an example

[sepia2008]

very well explained thank you sir! :)

[davidfof13]

I really appreciate your work Dr Tisdell. Your explanations are very clear and you speak slowly allowing us, the viewers to easily adapt to the rhythm. many thanks. this vid has widened my vision of fourier series

[spacewesterns]

Very helpful, thank you!

[ManusCelerDei]

Such a hero! Many thanks Dr Tisdell

[fingerboy18]

I haven't seen too many Australian people on these sort of videos.  There's something about the accent that I love even though I'm American! Great work Chris.

[Hakkology]

U truly are a lifesaver.

[ammarshaikh1000]

This was very helpful!

Thank you Dr. Trisdell

[varungargg8]

good for my bigiening in fourier analyses

[0000robbin]

what if sin(nπ)? i know that cos(nπ) = [-1]^n. is there any way to simplify sin(nπ)??

[mwray100]

@0000robbin sin(nπ) is always zero, regardless of n

[liamreidy7]

@0000robbin sin(nπ) is just 0, for all n

[29Ocelot]

Will you please be my dad?

[aluminous0]

Thank you so much! I was smashing my head against the wall for hours trying to figure this out before.

[NikIzzat91]

thanks for very clear explanation

[josiahsavino]

Best video on this topic yet. Love it

[ros343va]

chris tisdell is the reason y i pass math :)



[dpowerfool]

Thank you very much for this video. It's great!

[vivaliberte]

thank you very much doctor.

[sandslash123]

On behalf of all the undergraduate viewers I THANK YOU for your videos.

Science bless technology advanced 21.st century.

[mostafa8998]

im so happy that i learned how to do this ..yayyy

[colonelangel12]

You explain very well, I never understood anything to these f****** Fourier Series and now I got it all! Thanks

[vesperala]

Thank you!

[321815730]

can you show how you plot a FFT on maple please

[FaithLovesMath]

Great video!

[ph1ly]

I don't get how lecturers can suck so much! I learnt more in that 8 minute video than i did in 5 hours with my useless lecturer

[EgyptianKid22]

Aussie Aussie Aussie

Oi Oi Oi!!

[andyweg]

legend. good vid..very clear. cheers!

[anoxious90]

Hello there sir... I'm from Malaysia n i learn lots from your maths video... Thumbs Up!

[Trombonerist]

Very good video explains it very well

[check9264]

Excellent job mate!

[Lownayto]

Thanks for uploading this, can't understand my actual professor. I love you forever good sir.

[fcdog555]

Thank you very much for the vid:D

btw it's pronounced four-ree-aye just a heads up:D

[DrChrisTisdell]

@fcdog555 potato po-tar-toe tomato to-mar-toe :D

[fcdog555]

@DrChrisTisdell lol I guess you got me:D

and thanks on reply to my other comment on the other Fourier video.

[fingerboy18]

@fcdog555 Haha, yeah. Fourier was a French man, therefore it is pronounced "4-E-A" Haha!

[jsy012792]

@fcdog555 it's actually foo-yay. it's a french name

[fcdog555]

@jsy012792 I know it's French and it is not pronounce foo-yay lol

[jsy012792]

@fcdog555 ...it is...all my french friends say so. my complex analysis math professor says so as does a french translation site and wikipedia.

[fcdog555]

@jsy012792 meh I used a French Translation site that have people say the words in French and the way I wrote it is the way they pronounced it.

Your friends must have learned it wrong then"[

[jsy012792]

@fcdog555 wow, the ignorance. wikpedia /wiki/Fourier, forvo /word/jean-baptiste_joseph_fou­rier/

[fcdog555]

@jsy012792 You're not seriously still worked up on this? lol

[JQ322]

thanks.. helped me out a little... Im in a vibrations class, and we have to find fourier function of a graph, not a function given to us.. (so i guess its just a small extension of what you provided here) Thanks again

[MutantNinjaFly]

Whats an odd function or an even function?

[DrChrisTisdell]

@MutantNinjaFly 2:26

[mexico442]

Wonderful job Dr. Tisdell. I should let you know that I've passed calculus because of your videos. Thanks!

[PokemonParadise2010]

Dr. Tisdell

You have done a wonderful job with this video. This is excellent. I learn a lot from your videos. Please make more videos. You are great.

Regards,

SO

[gvsfgdf]

U iz da best... me take DE class and u help me well. I like.

[heyandy889]

You saved my booty for my Linear Algebra project. We have these challenging problems, mine is "Find the Fourier series for the func f(x)=abs(x), -pi<=x<=pi". Now I have an idea about where to start

[troid]

Thank you for doing this! It means a lot for us students and learners. You've just covered two weeks of class in our school (which is sad). I just hope teachers would learn how to teach like you. Some of them feel they knew everything that they don't even want to learn new things (better way to teach).

[11phax]

what happens if we integrate a product of two even functions?

[11phax]

what happens if we integrate a product of two even functions?

[FallofDarkness55]

@11phax integration by parts?

[pedrosa3142]

@11phax

Two products can be integrated using the method of parts. I am not sure how to visually describe this but it can be found as a definite integral.

[kingrobin12]

Man this is AWESOME!! You saved my exam!

[chevon1920]

I literally LOVE this man. This helped me soooo much!

[ew0054]

Thank you so much for this video! You have taught me in 10 minutes what I have not been able to learn in class for the past month. I will be sure and pass this along to my friend who is equally struggling.

I would like to ask, at 4:35, when you double the integral and 1/2 the length, what property allows this?

[ew0054]

@ew0054 Actually, I think I understand now why an = 0: An odd * even = odd (180° rotational symmetry), so the integral has to be zero because of symmetry.

I think I answered my own question: If you integrate y=x^2 from -1 to 1, or integrate y=x^2 from 0 to 1 then double, you get the same answer (2/3).

[blasos1983]

What a legend

[jackofnowhere]

i'm bit confused as to why f(x) is an odd function at 3:25

f(x)=3, f(x)=-3 can be reflected across the y-axis just fine

and i dont understand how it is interpretted as odd when there are no "x" to compare with the definition -f(x)=f(-x) with -(3)=(3)

[DrChrisTisdell]

@jackofnowhere Did you watch the video linked at 2:27? Maybe the best (and simplest) way to understand odd functions is to rotate the graph of the function 180 degrees about the origin and to see if you get the same graph as the original function.

[jackofnowhere]

@DrChrisTisdell hmm thanks, =D

i understand it now, i was mistakenly looking at the graph of x=3 and x=-3 individually rather than the graph of f(x)={3,-3}

afterward i understood the rest, excellent video by the way

i like your accent too lol

[manuel729]

So many thanks from Dominican Republic, a VERY simple way to teach no simple things

[PartizanBeograd]

Well described video... you have a very pleasant voice

[jnctrockstar]

im so thankfull to you sir, regards from india :) may god bless you :)

[rcomid]

Thanks a lot Dr. Tisdell for this video and please accept my warm regards from Iran.

[banytoshbot]

Awesome explanation :D thanks alot Mr Tisdell!

[DrDread]

Thanks a lot for the brilliantly laid out and thorough example. Saved me a lot of headache!

2nd Year Mechanical Engineering student at University of Nottingham

[ciaphas2037]

@DrDread sure beats Kostos Soldatos. I understand more from this 8 minute lecture than I got all term from him.

[0availableusernames]

@DrDread

lol same here

[AryaSravaka]

Dear Sir, Thanks for these videos & I find them very useful. very Noble work.

2nd Year Maths student at Queen Mary University Of London

[InfamousShogun]

Dr. Tisdell,

I thank you for all the efforts you made in creating these videos... Thank god there are people like on this planet.

I'd love to donate to express my thanks; do you have a paypal account or something of the like.

Best,

ATG

[DrChrisTisdell]

@InfamousShogun Hi ATG. I'm really enjoying the feedback from everyone on my videos (both positive and negative) and view them as very valuable donations! Best wishes.

[marcjdesjardins]

how do you know whether its even or odd? im confused on that and as well as at 4:40, why can you do this (doubel integral and half the boundary conditions)?

[DrChrisTisdell]

@marcjdesjardins Click on the link in the video to learn more about odd functions. See my comment below on doubling the integral.

[HangLooseMig]

Thank you so much, this was a great video to help refresh my memory for my final exam

[TheJroyer]

very good

[sai1120]

My life would be a lot easier if you are my maths lecturer, Thanks a thousand!!!

[ronalddlelariarte]

can i ask, Dr. why did you double the integral?

[DrChrisTisdell]

@ronalddlelariarte I doubled the integral, but halved the length of the interval of integration. The reason is that it is nice to have 0 in the integral sign sometimes because is simplies calculations. It comes back to thinking of the area. Instead of the areas cancelling (as is the cases with a_0 and a_n), with this b_n the area is repeated (doubled). Hope this helps.

[motoxidation]

@ronalddlelariarte graphically it is because of the symmetry associated with f(-x) = -f(x), which is a property of odd functions.

[griessman76]

@ronalddlelariarte

The function he wrote was even, meaning it was symmetric about the y axis in this case. If you take the integral (area under the curve) of the function from an interval -L to L of an even function, it will have the same area if you just took the area under the curve from 0 to L (which is half of it) and multiply it by two.

[pusikcat]

@ronalddlelariarte That is because we changed the limits of integration from -1 to 1 to 0 to 1.

[FallofDarkness55]

@ronalddlelariarte Whenever you see symmetry i.e. an even function you can integrate from 0-n where n is some arbitrary number and multiply the whole integration by 2.

[canadaonly2]

those 5 who disliked must have aids or something?

[TheAnatomias2]

Really nice explained Dr Chris,keep up the good work!Thanks

[PCGamerPortal]

Saved me on a take-home exam emegency!

[KiSsInTHERainxo]

ummm what if you aren't given that the period is two? how do you it's two? --Suppose, even, that the domain with which you are given in the piecewise is not the typical (-L, L). What do you do if it's like 0,2*pi???

[patvan2020]

Thank you so much Dr Chris for making this clear to understand I am busy with a mechanical engineering degree and the pace is hectic... I am studying part time and work full time, finding it hard to get sufficient practise... but your explanation is more clear than my lecturer. I have exams in January we have moved on to Z transformations have you any other videos you recomend. Thanks again

[jensstoltenberg]

thanks alot

from norway

[convolucion1981]

Hi, Why in the interval f(x)=F(x+2) the period is 2L=2? Thanks

[BarGesq]

@convolucion1981 It's not an interval. By saying f(x) = f(x+2) you repeat the defined function over and over with period 2 (when x reaches a value, f(x) will be the same as the value x-2 and x+2)

[23rdnova]

Dear Dr Chris i would appreciate is you could make a video explaining how to compute a complex function

[23rdnova]

Now i can go and kill that Math2 exam...Thanks Dr Chris

[saadamiens]

You are the best teacher on youtube 

[hugoalfa]

@saadamiens I aprove this answer, FACT

[ecdmuppet]

Dr. Tisdell,

Thanks for this video. Could you post a more complex example with perhaps a sawtooth or triangle wave? The integrals get hairy when f(x) is more than just a constant.

[WaqasKhan411]

Thanks Dr. Chris for uploading such an informative video

[silentnodes]

Dr Chirs........you made my day........Sir....Thanks for such a great help.....i have a question....can you please guide me about it.....i am using proakis book for ref:, my topic is to find the fourier representation of Sawtooth Wave...and finding its coefficient too....i would be very great if You can provide me some guideline....

[silentnodes]

@silentnodes

Sir the actual question is:

Find Fourier coefficient & Avg power of Sawtooth Wave

[MrDjnickos]

many many thanks from Greece DrChris!!

[niftyusername]

Very clear and awesome. Understanding is such a stress relief!

[lifematch]

can you make more video of Fourier series. i really need to grasp this concept and your video was the clearest among other vids in terms of what to do with Fourier series. i would very much appreciated as will other students around the world. nonetheless thank you soo much for the lesson.

[k1k0xiii]

what if the function given is neither odd or even ?

[DrChrisTisdell]

@k1k0xiii Just use the given formulae in the video for a_0, a_n, b_n that rely on integration over [-L,L]. Best wishes, Chris.

[k1k0xiii]

@DrChrisTisdell ok thanks .. good explanation and video .

[tbartley]

Excellent. Thank you!

[irfaanfr1]

Thanks a lot!!

[mistergmedina]

Please, On 1:50 why the funcion is odd ?

Thanks in advanced again !

[masteralo2234]

@mistergmedina because if a function is odd, it basically mean that it is symetrical about the origin. or if it satisfies the definition of an odd function, which is -f(x)=f(-x)

[Waqarahmedkhattak]

Why do we need to use Fourier Series.

What does it do.

Does it make money ?

[HaBaBaMBiZ]

I didnt understand how product of odd function and odd function is even because simple example : 5 x 5 = 25(odd)

[masteralo2234]

@HaBaBaMBiZ an odd function doesnt necessarily mean its odd in the same way in which 5 is. it just means it has a certain type of symmetry. and same goes for an even function. an odd function means it is symmetrical about about the origin, and it satisfies the definition of an odd function, which is -f(x)=f(-x). similarly, if a function is even, it means it is symmetrical about the y-axis. the mathematical definition of an even function is f(x)=f(-x).

[sivar144]

@HaBaBaMBiZ in fourier series these are following conventions

even X even = even

odd X odd = even

odd X even = ODD

do not mix it with simple maths multiplications.

good luck

[supercoolperson14725]

WHATS 4+4 LOL

[mistergmedina]

Dr , please to clear this issue: How do you get x values on 5:25 and how do you get Cos NPi -1 (I want to clear -1) on 5:48. Thanks in advanced again,

[mrbluesky323]

@mistergmedina

He gets the x values from the limits of integration. He's integrating from 0 to 1, so you must subtract the lower limit (x=0) from the upper limit (x=1).

[smithynakka]

Finally someone who teaches in clear, easy to understand English with clear writing! Great!

[inshtain2]

i can only say thank you so much



[ultln9562]

thats was great

do you have one as an even function

[shilly123]

your awesome!!

[Jonorocks999]

Top Video, really clear. Now Fourier is sorted for my exams...

[jsm666]

As always, you're crystal clear and your examples are easy to follow, even for someone who hasn't had formal university maths. I could quite happily watch these vids all day.

[888Xristos]

It's really helpful that you have the formulas pop onscreen when you use them.

[ravenflutterby]

This was awesome, thanks for the help!

[darwyn13]

i wish you're my professor!

[thegreatgiginthesky]

Thank you - you just helped me to pass my University Maths for Physics exam! The clearest example I have seen.

[melbourne2112]

thanks a lot

[khalid97899789]

i love ur vids

[Beriszle]

Hello, I am an aerospace engineering student getting ready to start my second year and I am just curious about this sort of thing. Just wanted to say very clear explanation and VERY interesting!

[MonterreyLegend]

thank you doctor, i got an A in my exam :D

[mayabentz]

Real stupid question, but can anyone tell me how to know if a function is real or false please?

[resmond]

@mayabentz

Do you mean odd or even -

Odd is 180 degree symmetry about the x axis; even is symmetrical about the x axis

If you meant real or imaginary -

A real function (not sure if you'd use that term) has no imaginary parts (being = j = sqrt (-1) ).

[mcdowesj]

Very very helpful!!!

[fezzy247]

thanks for taking the time to do these

[wkrepelin]

Nice one Dr. Chris. Do you have a recommendation ( or a desire to do a video on) the completeness of Sin(nx) and Cos(nx) or even the completeness of the powers of x? I know that the orthogonality of Sin(nx) and Cos(nx) is a simple (relatively speaking) exercise but I'd like to see the completeness proof. Cheers.

[yankeesfan811]

I appreciate this so much! my professors is so confusing, but you made this look so simple!

[wall12390]

Why can't you be my calc teacher instead of the inept idiot I have who gives examples on a rare occasion. Pretty hard to learn when you only use variables all the time and never actually give us a real problem.

[mcardlel90]

I wish you were taking my lectures! I can actually understand what you are saying... Thank you

[trevdawg911]

i love how i pay 340 dollars a unit to go to a four year university, yet ive learned 90 percent of my math and science material from youtube.....if only youtube gave out degrees......thankyou Dr. Chris I really appreciate you sharing this knowledge :)

[was0here]

@trevdawg911

haha, same!

[grinninghanis]

@delkhairio

Agreed. Dude, I'm learning at a uni where the professor speaks perfect english and it's still hard as balls to understand anything...

[queenmari89]

Thanks a lot :)

[mdawg414]

very nicely done, you just made this homework assignment so much easier. especially considering i have never even seen a fourier series before. thanks!

[NYMT19]

Thank you so much Dr. Tisdell

[nikan4now]

Thanks Chris. Very helpful.

[shultzgary]

thanks alot! i was looking at my notes from class though and are you sure that for Ao you use 1/2L not 1/L.

[alreadytakenindeed]

A guys like you, Chirs are giving the math a good name. You gave me hope :)

[system0system0]

wow dude you have a great writing tallent It look so pretty

[mahishimi50]

thanks chris great vid well explained

[adjamainstone]

great, really nicely presented and answered many of my questions. I need to figure out what you mean by odd and even. havent see that method used in our lectures but i like that...

is cos always even?

and sin always odd?

or is a cos 3 even and a sin 3 odd?

so that a cos 2 would be odd and a sin 2 even???

thnk thats how it works....???

[Anonymiusen]

An even function is so that f(-t)=f(t). An odd function is so that f(-t)=-f(t).

Take a look at the sine and cosine function, and you will clearly see what is meant by it.

[gremlinextreme101]

it can be quite easily proved that any continuous function can be written in as a unique sum of an odd and even function.

An even function can be written in the form (f(x)+f(-x))/2

and an odd function can be written in the form (f(x)-f(-x))/2, you can use these definitions to show general cases of odd*even or odd*odd and to show that a differentiable odd function has an even derivative.

[aegeanseamusic]

Thanks so much professor. I have a Diff. EQ final next week and this will help a lot. I also enjoy the characteristic way you write your x variables. I write them the same way, a backwards c next to a regular c. People would always make fun of me for doing so and it's good to know I'm not the only one.

[tuchelnumerouno]

Great stuff Dr. Chris! Thanks a ton.

[rrrikin]

thank you so much!

[diegoflo]

Thank you very much!

[madgary187]

mate you make fourier series look soo simple unlike any of the maths professors at university of edinburgh.

[ProfanityToInsanity]

Well said, most of our lecturers are shite.

The worrying thing is that the maths lecturers are the best ones.

[geezezy]

is there a video for even functions? do you do the opposite whereby even*even cancles leaving zero and then even*odd gives area? please help, cheers

[mangyOpi]

ei, what if f(x) is not given. our professor just gave as a graph so, we don't know how to compute the or where do we start the calculations... plss help us

[mangyOpi]

ei... what if the 'f(x)' is not given... my professor just gave as a graph.... we don't know what to do or where do we start... plss reply. thnx

[moaf06]

tx, ur much better than the other's, do u have any other video's conserning fourier series?

[sisip123]

I'm currently cramming for MATH3121 .. this was good revision. thanks!