Beginning Partial Differential Equations / Edition 2

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Overview

Beginning Partial Differential Equations, Second Edition provides a comprehensive introduction to partial differential equations (PDEs) with a special focus on the significance of characteristics, solutions by Fourier series, integrals and transforms, properties and physical interpretations of solutions, and a transition to the modern function space approach to PDEs. With its breadth of coverage, this new edition continues to present a broad introduction to the field, while also addressing more specialized topics and applications.

Maintaining the hallmarks of the previous edition, the book begins with first-order linear and quasi-linear PDEs and the role of characteristics in the existence and uniqueness of solutions. Canonical forms are discussed for the linear second-order equation, along with the Cauchy problem, existence and uniqueness of solutions, and characteristics as carriers of discontinuities in solutions. Fourier series, integrals, and transforms are followed by their rigorous application to wave and difficusion equations as well as to Dirichlet and Neumann problems. In addition, solutions are viewed through physical interpretations of PDEs. The book concludes with a transition to more advanced topics, including the proof of an existence theorem for the Dirichlet problem and an introduction to distributions.

Additional features of the Second Edition include solutions by both general eigenfunction expansions and numerical methods. Explicit solutions of Burger's equation, the telegraph equation (with an asymptotic analysis of the solution), and Poisson's equation are provided. A historical sketch of the field of PDEs and an extensive section with solutions toselected problems are also included.

Beginning Partial Differential Equations, Second Edition is an excellent book for advanced undergraduate- and beginning graduate-level courses in mathematics, science, and engineering.

About the Author:
Peter V. O'Neil, PhD, is Professor Emeritus in the Department of Mathematics at The University of Alabama at Birmingham. He is a member of the American Mathematical Society, the Society for Industrial and Applied Mathematics, and the American Association for the Advancement of Science

"...provides the background needed to pursue more abstract aspects of the subject...includes introductory level theory, techniques, and examples...a sound elementary introduction to PDE."

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Editorial Reviews

UMAP Journal
It is a good book. It is a tract written by a pure mathematician for a fairly advanced audience. If you teach at Podunk U. and you think you are going to use this text to teach junior engineering students. . .then you had better think again: Read the book first.
Zentralblatt Math
The book gives an easy manipulative treatment of the subject with applications rather than a rigorous and systematic theory.... It can be used as a text book at a senior undergraduate and / or first-year graduate level course in mathematics, science and engineering.
The UMAP Journal
It is a good book. It is a tract written by a pure mathematician for a fairly advanced audience. If you teach at Podunk U. and you think you are going to use this text to teach junior engineering students. . .then you had better think again: Read the book first.
Zentralblatt Math
The book gives an easy manipulative treatment of the subject with applications rather than a rigorous and systematic theory.... It can be used as a text book at a senior undergraduate and / or first-year graduate level course in mathematics, science and engineering.
From the Publisher
"It is a good book. It is a tract written by a pure mathematician for a fairly advanced audience. If you teach at Podunk U. and you think you are going to use this text to teach junior engineering students. . .then you had better think again: Read the book first." (The UMAP Journal Vol. 21, No. 2 Summer 2000)

The book gives an easy manipulative treatment of the subject with applications rather than a rigorous and systematic theory.... It can be used as a text book at a senior undergraduate and / or first-year graduate level course in mathematics, science and engineering. (Zentralblatt Math, Volume 938, No 13, 2000)

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Product Details

Meet the Author

PETER V. O'NEIL, PHD, is Professor Emeritus in the Department of Mathematics at the University of Alabama at Birmingham. He has over forty years of experience in teaching and writing and is the recipient of the Lester R. Ford Award from the Mathematical Association of America. Dr. O'Neil is also a member of the American Mathematical Society, the Mathematical Association of America, the Society for Industrial and Applied Mathematics, and the American Association for the Advancement of Science.

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Table of Contents

Preface
1 First Order Partial Differential Equations 1
2 Linear Second Order Partial Differential Equations 29
3 Elements of Fourier Analysis 88
4 The Wave Equation 158
5 The Heat Equation 267
6 Dirichlet and Neumann Problems 337
7 Conclusion 451
Index 497
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