An Introduction to Partial Differential Equations

This textbook is an introduction to the methods needed to solve partial differential equations (PDEs). Readers are introduced to PDEs that come from a variety of fields in engineering and the natural sciences. The chapters include the following topics: First Order PDEs, Second Order PDEs, Fourier Series, Separation of Variables, the Fourier Transform, and higher dimensional problems. Readers are guided through these chapters where techniques for solving first and second order PDEs are introduced. Each chapter ends with series of exercises to facilitate learning as well as illustrate the material presented in each chapter.

Introduces methods and techniques for solving first and second order PDEs Presents the main four PDEs (advection equation, diffusion equation, Laplace's equation, wave equation) Contains numerous exercises throughout to facilitate learning

Autorentext

Daniel Arrigo earned his PhD 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 Professor of Mathematics. He has published over 30 journal articles and three books. 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 America's Award for Distinguished Teaching of College or University Mathematics and in 2019 the University of Central Arkansas's Teaching Excellence Award.

Zusammenfassung

"This book offers a bit more relaxed approach but still provides a solid introduction. ... This is a plain but appealing text that would work well in courses for mathematics majors as well as science and engineering majors. It introduces the relevant subjects simply and clearly. Carefully chosen exercises come in each chapter with solutions in an appendix. This is one book that would work reliably for self-study." (Bill Satzer, MAA Reviews, November 21, 2023)

Inhalt
Introduction.- First Order PDEs.- Second Order Linear PDEs.- Fourier Series.- Separation of Variables.- Fourier Transform.