Question

Can someone help me make sense of Fourier series? I know it is a way to rewrite a function in sin or cos

Answer 1

i know fourier series have something to do with basics of integral transforms

Answer 2

I was looking at the proof the Prof did , couldn't make sense of it.

Answer 3

Learning Diffiq myself; it was fine until I got to fourier series

Answer 4

http://www.youtube.com/watch?v=fzXnww4om80&feature=related

looks like something i could watch :)

Answer 5

Ok first off, the fourier series is an orthonormal projection of a function onto a basis of sines and cosines.

Answer 6

Are you familiar with this from linear algebra?

Answer 7

I haven't taken linear algebra

Answer 8

Oh. Then it won't make much sense. Sorry. Usually they have you take it before diff-eqs

Answer 9

It'll make more sense when you take linear algebra.

Answer 10

In my school diffiq is requirement for linear algebra

Answer 11

The reason you do it is because it turns a function that is hard to solve into one that is just a sum of sines and cosines which are easy to integrate.

Answer 12

any function or just periodic ones?

Answer 13

differential equations>linear algebra

Answer 14

Any function can be projected.

Answer 15

i hated differential equations i don't think we got far enough to talk about fourier

Answer 16

but we did talk about a little in partial differential equations

Answer 17

all the other stuffs before fourier was so easy

Answer 18

it was more of a engineering class
she only cared if we could apply the fourier thingy
not know how to prove how it works

Answer 19

lol , engineering class: proof? it works that's the proof

Answer 20

lol

Answer 21

Well in linear algebra you will learn how to find projections of functions onto orthogonal bases. And it turns out that sine and cosine functions are orthogonal. So you can use them as a basis for a vector space you can then project other functions into.

Answer 22

And it's handy for differential equations because if you transform the function into a sum of sines and cosines it's easier to solve them.

Answer 23

because they say trignometric?

Answer 24

Or integrate them rather. In the same way that with laplace transforms you're projecting the function into a 'frequency' space.

Answer 25

is laplace tranform even more involved?

Answer 26

These are all linear transformations of the functions.

Answer 27

No, laplace is usually perceived to be easier. But that's mostly cause you do it by tables usually.

Answer 28

I think I should just forget the proof for now, and just learn how to do it

Answer 29

Yeah. I suggest coming back to it after you've taken linear algebra. It will make more sense.

Answer 30

I took diff-eq's before LA, though it was recommended to do it the other way around, and it wasn't until I finished linear algebra that I finally understood fourier from the semester before.

Answer 31

in my school diffiq is like 200 level while linear algebra is 300 level

Answer 32

Odd. My school has 2 different Linear algebra classes, one is introductory, and the other is for upper division.