Analytical Techniques for Solving Nonlinear Partial Differential Equations

Daniel J. Arrigo

jun 2022 · Springer Nature

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This is an introduction to methods for solving nonlinear partial differential equations (NLPDEs). After the introduction of several PDEs drawn from science and engineering, the reader is introduced to techniques used to obtain exact solutions of NPDEs. The chapters include the following topics: Compatibility, Differential Substitutions, Point and Contact Transformations, First Integrals, and Functional Separability. The reader is guided through these chapters and is provided with several detailed examples. Each chapter ends with a series of exercises illustrating the material presented in each chapter.

The book can be used as a textbook for a second course in PDEs (typically found in both science and engineering programs) and has been used at the University of Central Arkansas for more than ten years.

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Daniel J. Arrigo earned his Ph.D. from the Georgia Institute of Technology in 1991. He has been on staff in the Department of Mathematics at the University of Central Arkansas since 1999 and is currently a professor of mathematics. He has published over 30 journal articles and one book. His research interests include the construction of exact solutions of PDEs; symmetry analysis of nonlinear PDEs; and solutions to physically important equations, such as nonlinear heat equations and governing equations modeling of granular materials and nonlinear elasticity. In 2008, Dr. Arrigo received the Oklahoma-Arkansas Section of the Mathematical Association of Americas Award for Distinguished Teaching of College or University Mathematics.