Complex Fourier Series (fourier series engineering mathematics)

We will derive the coefficients formula for the complex Fourier series.

@blackpenredpen

[blackpenredpen]

At 8:15, n should go from negative inf to postive inf. Sorry I missed the negative sign.

[iabervon]

Complex is better; you don't need to remember which coefficients have a 1/π and which have 1/2π. It also just works if f is a complex-valued function, and you just don't get all conjugate pairs.

[amritas]

His positivity and enthusiasm is contagious! I find myself smiling while he explains everything clearly and simply. Love him.❤

[jesroe]

why is the conjugate a+ib ignored and simply merged into the equation as if it is a-ib????

[EnglishNijisanji]

I’m Japanese, university’s 2nd grade, majoring in physics.

[nimmira]

you deserve a 1M subscriber by the end of the year, not just 400K.

[angelmendez-rivera]

With this formula, the Fourier series for e^x in the interval (-π, π) is more obvious, since the coefficient sequence is easier to calculate. One has that the integrand is e^[(1 - im)x] which is anti-differentiated to [(1 + im)/(1 + m^2)]e^[(1 - im)x]. Evaluate this at the boundaries and subtract to get [(1 + im)/(1 + m^2)][(e^π - e^(-π))][(-1)^m]. The real and imaginary parts gives you the cosine and sine coefficients of the real Fourier series, respectively. Yet this is neater and easier to obtain.

You should make a video on the Fourier transform and its inverse. It would complete this series, and it also relates to the Laplace transform as well, which you have covered in this channel already.

[ozzyfromspace]

It's January 1st, 2020 and, yes, we met his goal of 400k subs (he has 409k today) ☺️ I'm very happy for you bro!

[quantised]

I'm sorry if this is a dumb question but at 12:29 where did the summation of Cn go?

[ccuuttww]

any non EE students are watching this video?

[moskthinks]

Who came to the unlisted vid from the link in the Lil Integral's description? : )

[bumpyturtle]

For anyone wondering, if you were to evaluate the integral at 10:39, it would evaluate to 2sin(pi(n-m))/(n-m). This is defined for all values of n and m except where n = m. For every other value, n-m becomes a whole number, and sin(any whole number*pi) = 0.

[andreapaps]

Watching all these maths videos to relax is making me want to return to university :D ... So much better than Netflix <3 <3 <3

[rybaplcaki]

Now Fourier transform derived from Fourier series pls

[igoreccard]

try to find three numbers a b c such that all three are prime and satisfy the equation a² + b² = c²
please, someone help
I'm having problems with this, although I'm pretty sure there are numbers like this
save my soul ;-;

[rogerkearns]

For forty years I've been wondering whether there is any natural number for which, if it is written down in English, all of its letters occur in alphabetical order.

[harryjohnson]

I was trying to find this derivation for ages after my university lecturers seemed to ignore it. Thanks, you absolutely nailed it!

[tickettomathsisland]

Wow, here comes heavenly sent lecturer. Thank you very much

[jfposada]

You, sir, are amazing. Besides the mastery of complex math and the Fourier transform, I cannot get over your mastery of the black and red pens! Fantastic video!

[farshadshamsyahoo]

I have a question on Fourier transform ( FT). Why in FT, the sign of the parameter of the exponential function is negative ( exp(-i2\pi nk/N))? Why don't we use the positive sign in FT and negative sing in the inverse one? Is it just by definition, or there is a mathematical reason for that?