How do I find the Taylor series for a function with multiple variables?

In summary, the conversation discusses the task of creating a perturbation expansion in epsilon (ε) for the function A(X,y,z). The attempt at a solution includes the terms A0(X,z), ∂/∂XA0(X,z)sin(w,y), and a remainder term. However, there is difficulty in finding the term A1. The question of whether a Taylor series is desired for this function is also raised.
  • #1
Felesinho
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0

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
 
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  • #2
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.
 

FAQ: How do I find the Taylor series for a function with multiple variables?

What is first order perturbation?

First order perturbation is a method used in quantum mechanics to approximate the energy levels and wave functions of a system when a small perturbation is applied. It involves calculating the first order correction to the energy and wave function using perturbation theory.

What is perturbation theory?

Perturbation theory is a mathematical method used to approximate solutions to a problem by treating a small change or perturbation as a known quantity. In quantum mechanics, it is used to calculate the changes in energy levels and wave functions of a system when a perturbation is applied.

When is first order perturbation used?

First order perturbation is used when a system is subjected to a small perturbation that can be treated as a known quantity. It is particularly useful in quantum mechanics to calculate the effects of a perturbation on the energy levels and wave functions of a system.

What are the limitations of first order perturbation?

First order perturbation has limitations when the perturbation is not small enough to be treated as a known quantity. In such cases, higher order perturbation methods may be necessary. Additionally, it may not accurately predict the behavior of a system when the perturbation significantly changes the system's dynamics.

Can first order perturbation be used for any system?

No, first order perturbation is only applicable to systems that can be modeled using quantum mechanics and when a small perturbation can be treated as a known quantity. It is not applicable to classical systems or systems that cannot be described using quantum mechanics.

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