The Peano-Baker series
Classical Analysis and ODEs
2025-07-22 v3
Abstract
This note reviews the Peano-Baker series and its use to solve the general linear system of ODEs. The account is elementary and self-contained, and is meant as a pedagogic introduction to this approach, which is well known but usually treated as a folklore result or as a purely formal tool. Here, a simple convergence result is given, and two examples illustrate that the series can be used explicitly as well.
Cite
@article{arxiv.1011.1775,
title = {The Peano-Baker series},
author = {Michael Baake and Ulrike Schlaegel},
journal= {arXiv preprint arXiv:1011.1775},
year = {2025}
}
Comments
6 pages; instructional in nature, with (some) historical references; some minor improvements, and some cosmetic updates