Fourier Series

[Dave]

I think it can be any periodic function (since you can alter sine/cosine to give you any period).

[NSX]

We've gone through the theory of Fourier Theory in Physics III, but the Math comes in Calc III....next year...

 

[Dave]

I'm sure you'll have fun doing that

[bloodhound]

We've gone through the theory of Fourier Theory in Physics III' date=' but the Math comes in Calc III....next year...

 

[/quote']

 

how could they teach u , theory of fourier theory in physics module and not in maths?

[NSX]

how could they teach u , theory of fourier theory in physics module and not in maths?

 

Why not?

We just went over what Fourier Series are, and their applications.

[Dave]

how could they teach u , theory of fourier theory in physics module and not in maths?

 

It's not exactly the most complicated principle: it basically says that a periodic function can be represented by multiples of sines and cosines.

[fourier jr]

WOW Fourier series in highschool! I'm in BC & I don't think anybody does Fourier series in highschools here. That's crazy. Well, if you want to learn about Fourier series look no further than Antoni Zygmund's epic 800-page "Trigonometric Series" (hehe just jokin')

 

edit: a Fourier Series doesn't have to be an infinite series, nor does it have to be sines or cosines. My analysis text (by Pfaffenberger & Johnsonbaugh, Apostol's also uses this as a definition) says Let X = {x_1, x_2, .... } be a countable orthonormal set in an inner product space V and let x be in V. The infinite series sum( (x.x_n)*x_n, n=0..infinity ) is called the Fourier series (relative to X). The coefficient x.x_n (x inner-product with x_n) is called the Fourier coefficient of x. Maybe it would be better to just say that any periodics function can be represented as a sum of sines & cosines....

[NSX]

WOW Fourier series in highschool! I'm in BC & I don't think anybody does Fourier series in highschools here. That's crazy. Well, if you want to learn about Fourier series look no further than Antoni Zygmund's epic 800-page "Trigonometric Series" (hehe just jokin')

 

hehe

I made this thread when I was still in High School [i was researching for a project dealing with spectroscopy or something]. Sources I looked at kept mentioning "Fourier Analysis, Fourier Series" and such. I read up on some of it, and it was way over my head at the time [only knowing how to sum finite arithmetic & geometric series at the time ].

 

Speaking of which, I'd like to give a shoutout to my fellow Canuck, Fourier JR!

hehe

But yeah ... I think Canada's cirricula is relatively level throughout the country [unless you're taking AP or IB courses, or @ UTS ].

 

It's a really neat tool though [the Fourier Analysis]. I look forward to learning more about it.

 

[Z-space]

hehe

It's a really neat tool though [the Fourier Analysis]. I look forward to learning more about it.

 

Indeed. I use it a lot on an applied level for analysis of periodic functions in biological systems. It's sweet fun.

[Dave]

a Fourier Series doesn't have to be an infinite series, nor does it have to be sines or cosines.

 

Sorry, I've not done fourier series yet

 

Being in the first year of my degree, I've hardly learnt anything new yet. We're still on bloody first principles of differentiation and damned Taylor Series in analysis, which is starting to get on my nerves quite considerably.

[fourier jr]

That's ok I think engineers & physicists would say infinite series of sines & cosines because that's how they learned it & that's how it's done in science. I did it that way too in a 'calculus-for-physics-students' course, but then I learned the more general way in a real math course this year. I don't think it's as well known.

[Dave]

Here's the page from MathWorld (which is like a shrine to Mathematics ):

 

http://mathworld.wolfram.com/FourierSeries.html

[AntiMagicMan]

Fourier series can be used to solve certain differential equations where the solution is a superposistion of an infinite number of sine or cosines.

 

The heat equation is one example of a differential equation in which you use Fourier series to solve it.