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This book is the first of its kind to provide a systematic methodology and guide for solving nonlinear ordinary differential equations (ODEs) via power series that arise in problems of mathematical physics. Tools are provided to eliminate the need for the laborious calculations that involve manipulation of infinite power series, allowing one to obtain all terms recursively. The authors also provide a structured methodology to overcome convergence barriers that naturally arise. In doing so, the authors demonstrate that the power series solution technique for ODEs can be both accessible and useful. The book is structured such that its content may be taught in a single semester course. Necessary course prerequisites are a knowledge of differential equations (analytical and numerical methods), linear algebra, and complex variables. The presentation style throughout the book reflects the authors’ teaching philosophy--that mathematics is learned by doing. Most of this book is composed of idea-driven examples and physically-motivated problems that have been encountered in the authors’ research; proofs are only provided when it is anticipated that readers may need to generate their own custom-fit theorem or definition for problems they are likely to encounter in practice. To meet the end-use envisioned by applied mathematicians for a given problem, the book demonstrates that power series solutions can complement numerical methods as a powerful and versatile mathematical approach.
Cover Art by Renee Marie McLean