How to compute a Fourier series: an example

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.

[gergerger]

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.

[productions]

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!

[RossJenk]

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!

[MadeyeMoody]

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

[arialamoosai]

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

[RossJenk]

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!

[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!

[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.

[mikey]

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

[martafajlhauer]

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.

[LLL]

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.

[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!

[ManuelMendez]

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

[Arnabactor]

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

[MDMAx]

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

Science bless technology advanced 21.st century.

[davidfof]

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

[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🎉

[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.

[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).

[DrChrisTisdell]

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