# First order perturbation

1. Jul 22, 2013

### Felesinho

1. The problem statement, all variables and given/known data
I required to make a perturbation expansion in ε of the function:
2. Relevant equations

A(X,y,z)=A(x-εsin(wy),y,z).
X=x-εsin(wy)

3. The attempt at a solution
Solution:
A(X,y,z)=A0(X,z)+ε[A1(X,z)+∂/∂XA0(X,z)]sin(wy)+o(ε^2)
I get the terms A0(X,z) and ∂/∂XA0(X,z)sin(w,y) with the derivative with respect to ε . But I could not get A1.
Thanks

Last edited: Jul 22, 2013
2. Jul 28, 2013

### MathematicalPhysicist

Can you elaborate on this?

Do you want to find a Taylor series for this function?

In that case you've got the formula for Taylor series in more than one variables.