Beginning Partial Differential Equations 2/e (絕)
- 20本以上，享 8.5折
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- 一般書籍
- ISBN：9780470133903
- 作者：Peter V. O'Neil
- 版次：2
- 年份：2008
- 出版商：John Wiley
- 頁數/規格：477頁/精裝單色
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Description
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 diffusion 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 to selected problems are also included.
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 diffusion 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 to selected problems are also included.
Features
New to This Edition
- Solutions to selected problems are included at the end of the book and experimental, computer-based exercises are designed to develop students inquiries.
- A separate Student Solutions Manual is availableDiscussion of first order equations and the method of characteristics for quasi-linear first order PDEs; canonical forms of second order PDEs; characteristics and the Cauchy problem; a proof of the Cauchy-Kowalevski theorem for linear systems and connections between the mathematics and physical interpretations of PDEs.
New to This Edition
- Sections on numerical approximation of solutions in Chapter 4 (The Wave Equation) and Chapter 5 (The Heat Equation) are new to the second edition.
- A new chapter has been added that features selected applications and additional techniques, including solutions in series of orthogonal functions, convection/diffusion, shocks, shallow waves, as well as solitons and asymptotic solutions.
- A second new chapter has been added and provides an introduction to the advanced theory of partial differential equations, including distributions, Hilbert spaces, Sobolev spaces, and weak solutions.
Table of Contents
1. First Order Equations.
2. Linear Second Order Equations.
3. Elements of Fourier Analysis.
4. The Wave Equation.
5. The Heat Equation.
6. Dirichlet and Neumann Problems.
7. Existence Theorems.
8. Additional Topics.
9. End Materials.
1. First Order Equations.
2. Linear Second Order Equations.
3. Elements of Fourier Analysis.
4. The Wave Equation.
5. The Heat Equation.
6. Dirichlet and Neumann Problems.
7. Existence Theorems.
8. Additional Topics.
9. End Materials.
Peter V. O'Neil, PhD, is Professor Emeritus in the Department of Mathematics at The University of Alabama at Birmingham. Dr. O'Neil has over forty years of academic experience and is the recipient of the Lester R. Ford Award from the Mathematical Association of America. 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.
