Symmetries of Ordinary Differential Equations: A Short Introduction

TL;DR

This paper provides an accessible, self-contained introduction to symmetry methods for solving ordinary differential equations, focusing on autonomous first-order ODEs without complex technical prerequisites.

Contribution

It offers a simplified, practical overview of symmetry techniques tailored for non-specialists, emphasizing autonomous first-order ODEs and avoiding advanced mathematical tools.

Findings

Introduces symmetry methods for ODEs in an accessible manner

Focuses on autonomous first-order ODEs, broadening applicability

Provides practical guidance without complex technical prerequisites

Abstract

These lecture notes provide an introduction to the theory and application of symmetry methods for ordinary differential equations, building on minimal prerequisites. Their primary purpose is to enable a quick and self-contained approach for non-specialists; they are not intended to replace any of the monographs on this topic. The content of the notes lies "transversal" to most standard texts, since we put emphasis on autonomous ODEs of first order, which often play a relatively minor role. Moreover, we avoid the technical build-up involving jet spaces and prolongations of group actions.