How to Compute a FOURIER SERIES // Formulas & Full Example

How do you actually compute a Fourier Series? In this video I walk through all the big formulas needed to compute the coefficients in a Fourier Series. First we see three integrals that will really make everything easier, integrals of products of sin and cos terms of different frequencies. Then we will use these to compute out formulas for the coefficients of the in and cos terms. Next we see a full example computing everything, and finally see the formulas for the general situation.

0:00 Big Idea of Fourier Series
1:08 3 Important Integrals
2:33 The formulas for the coefficients
6:40 Full Example
11:06 General Case

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[jlpsinde]

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

[thegil-martingetaway]

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

[bebarshossny]

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

[samyakhp]

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 🙏🏼.

[littleKingSolomon]

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.

[mrinalkantidebnath]

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.

[anweshpanda]

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

[sunsun]

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

[youngdd]

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

[crazygury]

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

[MrLee-cypw]

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!

[bismis]

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

[HassanKhan-csho]

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

[HuaijinSun-iksg]

Fascinating video! I understand it completely

[Vladzag]

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

[inquisitiverakib]

1 of the best explaination.
Unfortunately underrated video.

[unlucky-]

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

[matthewdevis]

Professor, you are a national treasure. I love you

[wuyqrbt]

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

[michaelzumpano]

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