Fourier Analysis 4: Example of Fourier Series on [-L, L]

[andr00123]

This is 3 semesters from where I'm at now!

I just started cal

[LANN98]

int x at 3 is 3x. 3x/6 when x is 3 is 3(3)/6 which is 9/6 which is 3/2, not 3/4.

could you please explain what a and b is?

[nateroll4life]

@LANN98, int of x is 1/2*x^2, the const outside the int is 1/6, therefore 1/6 * 1/2*x^2 = x^2/12, sub in 3 for x and the result is 9 /12 or 3/4 :)

[sai1120]

u speaking too fast Mr lee..

[Muckincontemplation]

hey are u malaysian? you sound like one

[Formslip]

how did you change cos(npi-1) to [(-1)^n-1]?

thats the only part that lost me

[jh00ny]

@Formslip cos(n*pi)=(-1)^n is an identity, look at integer mutliples of pi on the graph of cos(x)

[Harryhicy]

@Formslip because cos(pi) = (-1). And, raising it to n-1 is simillar to having the pi multiplied by n-1.

Try drawing the simple cosine graph from 0 to 5pi, and youll notice that it is 1 at even values of pi, and -1 at odd values of pi. Hence the substitution.

[zibray]

@Formslip I had the same confusion and went over my notes from class...he made a mistake with the brackets he means cos(npi) -1 not cos(npi -1)

[hifhif123]

Awesome!!!!!

[BOOPACHECO]

Probly the best teacher of Fourier seris on the internet!! Thnx

[shrusteddy]

Thank you so much! This video was very helpful!

[Popcornchicken101]

thank you!!! =)

[pooz0r]

was having trouble doing finding a way to do the integration but the lesson helped alot...thanks!

[calltheworld555]

oo shit..shud be an= 1/3 integral from -3 to 3 of f(x) TIMES cos(npix/3) dx...not an= 1/(2x3) integral from -3 to 3 of f(x) TIMES cos(npix/3) dx

[outlawkelb]

i was thinking about the same thing, my textbook has 2/T aswell,

[lithe333]

how come cos(nPi - 1) = [(-1)^n -  1]

=S

[regginscanjump]

I'm pretty sure he made a mistake but he corrected it when he wrote the whole Fourier series.

It's supposed to be (cos(nPi) - 1). he just didn't put a few brackets in there is my guess

[Lu1stron]

Hahahaha What do u see? the answers? hahaha Nice DonyLee :D

[surfax100]

well done. however, the equation we are trying to fourierize is not a function there. But everything else is correct.

[andyvalencia]

YOOOOOOOOOOOOOOOOOOOO THATS a Cool way of integration by parts. I mean, its the same as always, but it looks nicer, LOLZ

[4txx]

slight typo in final expression of An

great vid

[illusion422]

Excellent. I've never seen Fourier Series before your lessons sequel. Very interesting, keep up the good work!