Fourier Analysis 3: Fourier Series of function on [-L, L]

Using a simple substitution, we extend the definition of a Fourier Series of a function, this time integrable from -L to L.

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[Formslip]

at like 5:04 i think you meant to say make a substitution with cos(nt) not cos(xt) otherwise with what youve defined there would be an x^2 up in there

[bunty939]

Thanks Mr.Lee :)

[Wilewee]

Dont listen to ppl who want you to slow down. You have a good energy and very well structured lectures here and I want to thank you for powering through these math subjects for us who need it.

[minaamq]

i was just wondering if there is the difference between the fourier series of

F(x) = x ; where -pi<x<pi

and

F(x) = x ; where 0<x<2pi

[thing1thingtwo]

awesome!



[hsoonali]

why u are too fast ..clam down ...explain properly ...step by step ..show some details ..convince ur viewers ...any way nice lecturing ...but please next time show us something good in Fourier series with nice quiet explanation ..thanks anyway

[zimbabelka]

There is no mistake there -- it is a simple application of change of variable theorem. However, I do agree that the variable declaration of t in the very beginning (i.e. sudden change to a function g(t)) is very sketchy. But this is all pedantic stuff, and we need not worry about it.

[OHFUFI]

umm, doing the (dt/dx) thing, changes the variable that we are integrating with respect to. When we change the limits of the integral, we are not actually changing the number "value" you could say, we are changing it's value with respect to a certain function. example, x=2*t. therefore t=1 means that x=2. but as long as the integral is integrated with respect to right variable, you will get the same answer.

[dannylee86]

not bad....but the variable declaration in the beginning is a bit sudden (during t=piX/L).