Fourier Series: Complex Version! Part 1

There is another version of Fourier Series: the complex form! In part 1, we look at the general form of the complex Fourier Series and then find an equation to calculate the coefficients of this version.

NOTE: @ about 3:00, the cosine(nx) formula has an extra i on the bottom of the fraction. it should be: cos(nx) = (e^(inx) + e^(-inx))/2

Questions about this or other math topics?? Leave a comment and let's tackle it together!

Derivation of Euler's Formula:

Links to the sine and cosine Fourier Series:

[tai-t]

Oh my god! I have been spending a full day trying to clarify so many things about this. Thank you so much for this video! Was exactly what I was looking for.

[aymanadel]

You are so funny. I like this way of teaching. Break a leg!

[umamaheswar]

I was lacking in this topic but today all the doubts were clarified. I wish my institution professors were this good

[williamauditore]

Just love everything about you plus the content

[peterg]

Beautiful video and beautiful person! very helpful!

[huangjinalexliu]

Thanks for making these lectures they are great. I wonder why is it that we can assume, if for example, C5 is larger than C8 and with C8 being very small in comparison, we could ignore Cn larger than C8? Is it not possible that C103 is larger than C5?

[rmw]

Brilliant video - thanks for making and posting. I'm new to this so I don't understand how the bounds of integration changed from -ve infinity and +ve inf. to -pi tp pi once you multiplied the integral by the complex conjugate. Sorry to be thick!

[haseebahmed]

Ok so that was the average value of the function what if we find the solution of general equation with - infinity to + infinity?

[philcooper]

Question I was watching a video from blackpenredpen, dealing with this problem, in the video , he uses eulers identities, with just a 2 in the denominator for sine, could you please clarify whether this is correct or not. Thank you.

[mnada]

Hi, when it's better to use one form over the other ?

[josephmotsamai]

Hi beautiful!! You are good in what you are doing!! Love you!!!

[Ayat-Men-AlQuran]

I think you made a mistake in cosine equation of Eurler's formula take a look in your vedio an check it

[zersund]

2:51 You got the cos(nx) formula wrong, if cos(nx) is meant to be a real function. This shines out of the board as a matter of fact, hurting the viewer's eyes.