Perturbation Theory

TL;DR

This paper explains the fundamental concepts and mathematical foundations of perturbation theory, emphasizing its conceptual basis and methodological insights through illustrative examples.

Contribution

It provides a clear conceptual explanation of perturbation theory and foundational mathematical notions, which is not common in typical summaries of perturbation methods.

Findings

Clarifies key mathematical notions like limit, continuity, and convergence.

Highlights conceptual insights of perturbation theory.

Provides illustrative examples to underline methodological points.

Abstract

This article aims to explain essential elements of perturbation theory and their conceptual underpinnings. It is not meant as a summary of popular perturbation methods, though some illustrative examples are given to underline the main methodological insights and concerns. We also give brief explications of the mathematical notions of limit, continuity, differentiability, convergence, and divergence, which provide the necessary foundation.