• Support PF! Buy your school textbooks, materials and every day products via PF Here!

Taylor expansion

  • Thread starter Niles
  • Start date
1,868
0
1. The problem statement, all variables and given/known data
Hi

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

Best,
Niles.
 

Dick

Science Advisor
Homework Helper
26,252
615
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.
 
1,868
0
Thanks!

Best,
Niles.
 

Dick

Science Advisor
Homework Helper
26,252
615
1,868
0
Ah, I see. Thanks for clarifying.

Best,
Niles.
 

Physics Forums Values

We Value Quality
• Topics based on mainstream science
• Proper English grammar and spelling
We Value Civility
• Positive and compassionate attitudes
• Patience while debating
We Value Productivity
• Disciplined to remain on-topic
• Recognition of own weaknesses
• Solo and co-op problem solving
Top