# First order perturbation

## Homework Statement

I required to make a perturbation expansion in ε of the function:

## Homework Equations

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

## 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:

## Answers and Replies

MathematicalPhysicist
Gold Member
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.