About this ebook
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.
This book is intended for researchers engaged in applied mathematics and is structured so it can be used in a one-semester advanced undergraduate or graduate course. Necessary course prerequisites are a knowledge of differential equations (analytical and numerical methods), linear algebra, and complex variables.
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About the author
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.
He is on the faculty in RIT’s mathematical modeling PhD program and are affiliate members of RIT’s Center for Computational Relativity and Gravitation and has authored numerous peer-reviewed publications that utilize power series methods to obtain analytical solutions to problems arising in diverse areas of mathematical physics.
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.
He is on the faculty in RIT’s mathematical modeling PhD program and are affiliate members of RIT’s Center for Computational Relativity and Gravitation and has authored numerous peer-reviewed publications that utilize power series methods to obtain analytical solutions to problems arising in diverse areas of mathematical physics.
