How to compute a Fourier series: an example

Free ebook tinyurl.com/EngMathYT
This video is a demonstration on how to compute a Fourier series of a simple given function. I discuss how to calculate the Fourier coefficients through integration and the simplifications involved.
Fourier series are an important area of applied mathematics, engineering and physics that are used in solving partial differential equations, such as the heat equation and the wave equation. Fourier series are named after J. Fourier, a French mathematician who was the first to correctly model the diffusion of heat.
Fourier series are seen in 2nd-year university mathematics.

[@MadeyeMoody492]

You know what they say. Better 2 hours before your final than never...

[@965productions9]

I have been trying to understand this for the past 12 hours and this video from 12 years ago is the biggest help I've found. Thank you so much sir!

[@Murphyalex]

After such a frustrating day trying to organise all my printouts and really make a dent in my understanding of this, your video comes along at 1am and now I feel like I can sleep tonight. THANK YOU.

[@DrChrisTisdell]

Wow - I'm really glad and humbled to receive a comment like yours. If you liked this video then there are lots more examples in my new (free) ebook, where each lesson is linked to a video of mine. The link is in the description. Good luck with Fourier series!

[@bloomingbeautybyjessblesse1519]

The book is no longer available ): do you have another link? please help!

[@RossJenk1]

You are quite literally, single handedly saving my degree. My lecturers notes are shambolic compared to those which you produce, just a shame you're not my Engineering Mathematics II lecturer!

[@frozenrats]

How is life for you now 10 years later?

[@RossJenk1]

@frozenrat pretty good, thank you. Engineering wasn't really for me, I had a better head for business. So that's what I did, set up a medical engineering company and now hire 4 engineers.

[@diags_1109]

@@RossJenk1 That's cool, also interesting looking at a video you watched 10 years ago haha

[@Ensign_Cthulhu]

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.

[@mikey071113]

If only there were more professors like you online, I'd have a much greater understanding of all my subjects! Thanks!

[@arialamoosai3966]

The best lecture i have seen on the Fourier Series ! Thank you .

[@alokkumarsethi2668]

Thank you

[@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

[@2020LLL]

finally someone who doesn't take for granted that everyone is born genius. Excellent tutorial and wonderful practice for us starters who have full-time everything going on yet wants to better themselves in understanding step by step and not skipping just because we should already know this... Please, more examples; and as you get more in depth, your followers will become more as well but with a greater concept than those who were born engineers.

[@anannyauberoi7984]

Great explanation! Love the little simplification in the end- thanks a ton!

[@DrChrisTisdell]

Thanks for the feedback. Glad you are finding these things of some use. Next year I'll post a full course on PDE with a new, free ebook. Good luck with your studies.

[@Tofumoode-jy6ro]

wow, you managed to explain what I've spent for over 6 hours trying to yet understand. Many thanks. :D

[@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).

[@ASFAnarchist]

Great! I remember learning this a few years back, but I urgently needed a refresher. This was exactly what I needed. Thank you!!

[@RossJenk1]

Well my university have decided to screw me over because I had to get an operation and long story short I am now sitting this exam. Again. This video for a second time has helped me more than I could have imagined and the PDF is great! The one thing I'd suggest is possibly worked solutions but I appreciate how much time has already gone in to it out of your own goodness. Keep up the good work, much preferred channel over others such as Khan Academy. If I could hire for private tutoring I would!

[@Andiotic]

Thank you very much sir, this is one of the most straight forward, easy to understand example I've seen so far.

[@ortek87]

Sir, thank you for this. I think the true instructor should possess the characteristics that you have. Ours are always reluctant to give details about how to calculate, they even skip the intermediate parts in examples, they say it is our duty to find out how the calculations are carried out and our job to refresh our memories from calculus to carry out difficult integration by parts etc. 4.5 hours to my final exam and thank you for making these available to us. You sir, are a great man!

[@martafajlhauer8877]

I had 100% on my ODE mid-term thanks to you, now it's time for my final. I would love to repeat my score :) As my lecturer is not the best I can say that I had my score only thanks to Dr Chris. Thank you.

[@martafajlhauer8877]

Ha! Thanks for the reminder. Do you know that I got 80%+ for my ODE in the end and I have studied for a week or so. I work as Data Scientist contractor at the space industry company. I think that these ODE went pretty well but will revise them one day. Highly recommended!

[@luthandondlovu8613]

DAMN DAMN DAMN WOW.......You have simplified the workload for me after trying many videos

[@sanchezdel8]

Wow! This is the explanation I've been looking for. VERY CLEAR. THANK YOU!!

[@DumboSanchez]

Youre a legend Tisdell love your teaching style!

[@jackdavy9182]

This really helped me to understand when you can integrate from [0,L] instead of [-L,L]

[@ortek87]

I got a total of 83 from differential equations course and got a BA. In the past, I would be walking on the clouds for such a grade, but now I feel for that missing AA :))) Thank you Dr. Tisdell, blessings to you

[@DrChrisTisdell]

Hi - thanks for the kind words. I have been at UNSW, Sydney for 10 years. During that time I, too, have learnt a lot from my colleagues. I've had a bit of experience with teacher training and get the trainee teachers to "critique" some of my videos, eg "What would you do differently?". You may also like to use YT as a learning tool in your own classroom at some stage. Good luck with teaching!

[@RandyLott]

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.

[@parveensharma75]

Amazing explanation Chris Keep up your good work.

[@Arnab1actor]

definately the easiest way on the internet to understand the concept of fourier series.. kudos!!!!!!

[@cemcalsar7367]

thats what ı have been searching for, so you made it simple ,hocam thanx to you so much

[@Fatkaido]

Thank you Dr Tisdell. Im having an exam tomorrow and this is what's been keeping me awake until you appeared on my search results. I wish you the best as well🎉

[@ManuelMendez1]

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

[@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

[@BlakLotus]

I had no idea what my book was saying. You just saved my butt. Thanks a bundle!

[@alreadytakenindeed]

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

[@WaqasKhan411]

Thanks Dr. Chris for uploading such an informative video

[@MigLMariano]

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

[@allinengineering8168]

I saw your video 5 years ago in my undergraduate degree now I am watching again in masters degree you are wonderful both lessons going well

[@TheAnatomias2]

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

[@chevon1920]

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

[@ragnarlothbrok4090]

Sir you are best lectirer you deserve more recognition!

[@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!

[@DrChrisTisdell]

Hi Steve D'Alembert's solution is used to solve PDEs with ONLY initial condtions. Separation of variables is used when there are both initial and boundary conditions. It's important to understand which method to use when. With D'Alembert's solution, you assume that the solution is of the form $u(x,t) = \phi(x + ct) + \psi(x - ct)$ and then you want to determine the functions $\phi$ and $\psi$ from the given initial conditions. Hope this helps!

[@DrChrisTisdell]

My pleasure! My current mantra is: free videos + free ebooks = better education. I'm glad I could help.

[@niftyusername]

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

[@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?

[@MDMAx]

On behalf of all the undergraduate viewers I THANK YOU for your videos. Science bless technology advanced 21.st century.

[@Saila36]

This is exactly what I was looking for. THNX :)

[@danykelvin7720]

This is Really awesome! Just what i have been looking for... Thank you Sir!

[@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

[@mexico442]

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

[@saadamiens]

You are the best teacher on youtube

[@Lownayto]

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

[@DrChrisTisdell]

That's it DMan - you got it!! Just in case you forget, if you follow my "is my integrand even or odd?" method (in the vid) then you can't go wrong!

[@nablarnermk8844]

Never lose trust in a 14 year old calculus video! Best video on this topic by far

[@Jonorocks999]

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

[@chuckjls]

Nice video, Dr. Tisdell. I am looking for material that explains the derivation of the double Fourier series. Do you have any suggestions?

[@DxBoi]

thanks heaps Dr Chris! i see now what u were talking about...and thanks so much for all these awesome vids! i feel they're the best way to get started on a topic. cheers!

[@aluminous0]

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

[@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.

[@sukd2669]

This is really helpful. Well done.

[@kingrobin12]

Man this is AWESOME!! You saved my exam!

[@06suyash]

sir u are the best i couldnt understand what is this bt after ur video i can finally clear my exam

[@DxBoi]

cheers mate. thanks for explaining it in that other way. helped out a lot.

[@khaaaled2007]

Thanks :) I'll watch all of them tonight , exams are just around the corner thanks again

[@DrChrisTisdell]

Look in my playlist "Fourier series"

[@chekwubeugwu4015]

Dr please what do I do to know this Fourier series. I have given it so much time but it seems not to sink in my memory

[@colloupdated]

@@chekwubeugwu4015 u have to believe in ur mind and ur ability to learn,as well as practice 💯 ...u will be gud

[@dansdendanable]

Nice lecture! Well explained. Thanks

[@DrChrisTisdell]

Hi Fartx: the $f(x)$ is usually a given function (given initial temperature). If $f$ is not specified then you can't do anything more than just write down the integral form for the $b_k$ as you have done above. Good luck!

[@DrChrisTisdell]

Always happy to help.

[@ozzyfromspace]

Bonus for having a ‘Stralian accent 😊🥳🎊🙌🏽 Awesome video Dr. Chris! Greetings from the US

[@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.

[@brandonphan1437]

exactly what i was looking for.. thanks!

[@confidencedavid8890]

Most simplified..I've seen so far🙌

[@jeremymandela5400]

THANKS A LOT Dr Chris Tisdell. Finally I get a full understanding on the whole thing. God bless you in your carrier.

[@zayed9902]

Wow😮, you upload this video before i start kindergarten and now i watch it for my first year in engineering college

[@DrChrisTisdell]

Glad to know they are useful to you. Thanks.

[@bearded-cat]

thanks a lot! I wish we had such lecturers in my uni

[@srijandhakal3277]

Watching from Nepal sir🇳🇵 ,really helpful for bachelor degree.

[@studiowomi7723]

we are greatful for provisions of your reference.from proff.Wanyoyi and Abbas from Kenya.

[@theprodigalduck]

Great video. Didn't know the even*odd functions integral trick, I just always had to integrate

[@fransiscocauchy309]

Very helpful video thanks alot for the Fourier transformation.

[@houssamzitouni2406]

Amazing Lecture !! Thank you !

[@sisip123]

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

[@rcomid]

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

[@JamesTuchel]

Great stuff Dr. Chris! Thanks a ton.

[@jaijeffcom]

Fabulous. Enjoyed that a lot. Very clear.

[@mominator_]

Thankyou man i really cant thank you enough this was so helpful

[@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.

[@DrChrisTisdell]

Thanks! Hope you find the free ebook of some use also!

[@madgary187]

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

[@fartx211]

Hey Chris, you know how in the end of the Heat Equation questions, when trying to figure out the that last constant Bk by using the condition that u(x,0)=f(x), resulting in a Fourier sine series. We use those formulae that were in the Fourier series topic. But this requires us to to integrate f(x)sin(n*Pi*x/L). How can we do that if we dont know what f(x) is? Or is it there somewhere and i cant see it? I mean, for some reason, the working suggests f(x) is even, but how do we know that?

[@MsBourne47]

awesome lesson man

[@nabilnader566]

you are lifesaver dr chris .... could u do more video about Fourier series

[@TheBeartha]

oh.... thanks... this helped me . Was struggling with fourier series

[@NYMT19]

Thank you so much Dr. Tisdell

[@banytoshbot]

Awesome explanation :D thanks alot Mr Tisdell!

[@kiwalabyemarkjoel7324]

your lecture is the best

[@BinarySecond]

Such a hero! Many thanks Dr Tisdell

[@simrannahar8262]

this was super helpful sir thank you so much

[@annmarryp.k.1283]

Thank you, sir🙏it was really helpful

[@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.