Power Series Solutions to Nonlinear Ordinary Differential Equations

This book is the first to offer a systematic methodology for solving nonlinear ordinary differential equations via power series, specifically those arising in mathematical physics. It provides tools to eliminate the tedious manipulation of infinite series, enabling recursive computation of all terms. The authors also present a structured approach to overcoming convergence issues inherent to such methods, demonstrating that power series solutions can be both accessible and practical. The authors’ teaching philosophy—that mathematics is best learned by doing—is reflected throughout, with the text largely composed of idea-driven examples and physically motivated problems from their own research. Proofs are included only when necessary for readers to construct custom theorems or definitions relevant to real-world applications. Ultimately, the book shows that power series methods can effectively complement numerical techniques, offering applied mathematicians a powerful and versatile toolset.

Nathaniel S. Barlow is an associate professor in the School of Mathematics and Statistics at Rochester Institute of Technology (RIT), where he has been a faculty member since 2014. A recipient of teaching awards at both RIT and Clarkson University, he has been coordinator of the Computational Mathematics and Applied Mathematics undergraduate programs at RIT since 2022. In addition to the topics of this book, his research interests are in fluid mechanics with a focus on algebraic wave instabilities and the modeling of thin liquid sheets.

Steven J. Weinstein is a professor at Rochester Institute of Technology (RIT) in the chemical engineering department, which he founded and chaired until 2023. Prior to joining RIT in 2007, he worked for 18 years in manufacturing research and development at Eastman Kodak Company. At Kodak, he focused on the mathematical and experimental underpinnings of coating engineering science, including, among many topical areas, thin film flows, wave stability, and die manifold design. His teaching and research span interfacial fluid mechanics, experimental and theoretical coating applications, flow instabilities, and asymptotic methods.