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Description
This book is an introduction to methods for solving partial differential equations (PDEs). After the introduction of the main four PDEs that could be considered the cornerstone of Applied Mathematics, the reader is introduced to a variety of PDEs that come from a variety of fields in the Natural Sciences and Engineering and is a springboard into this wonderful subject. The chapters include the following topics: First-order PDEs, Second-order PDEs, Fourier Series, Separation of Variables, and the Fourier Transform.The reader is guided through these chapters where techniques for solving first- and second-order PDEs are introduced. Each chapter ends with a series of exercises illustrating the material presented in each chapter.
The book can be used as a textbook for any introductory course in PDEs typically found in both science and engineering programs and has been used at the University of Central Arkansas for over ten years.
Preface.- Acknowledgments.- Introduction.- First-Order PDEs.- Second-Order Linear PDEs.- Fourier Series.- Separation of Variables.- Fourier Transform.- Solutions.- Author's Biography . 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.
