Taylor expansion

1. Apr 5, 2012

Niles

1. The problem statement, all variables and given/known data
Hi

Say I want to Taylor-expand
$$f(\omega + m\sin(\Omega t))$$
where ω and Ω are frequencies, m is some constant and t denotes time. Then I would get
$$f(\omega + m\sin(\Omega t)) = f(\omega) + (m\sin(\Omega t)\frac{dI}{d\omega} + \ldots$$
Is it necessary to make any assumptions on the sizes of m and Ω in order to make the above expansion?

Best,
Niles.

2. Apr 5, 2012

Dick

If you are Taylor expanding in the quantity you are adding to ω and I means f(ω) that's fine. If you are going to truncate the expansion there and wondering if it's a accurate expansion that's going to depend on the size of the quantity you are adding to ω and the behaviour of f''(ω). You'll want to look at Taylor series remainder terms if you are concerned about how good it is.

3. Apr 6, 2012

Niles

Thanks!

Best,
Niles.

4. Apr 15, 2012

Niles

5. Apr 15, 2012

Dick

Sure it is. It's 'around' ω. I say the expansion is 'in' msin(Ωt) because that's the thing that appears in all the powers. Just terminology.

6. Apr 15, 2012

Niles

Ah, I see. Thanks for clarifying.

Best,
Niles.