DescriptionThis new edition features the latest tools for modeling, characterizing, and solving partial differential equations
The Third Edition of this classic text offers a comprehensive guide to modeling, characterizing, and solving partial differential equations (PDEs). The author provides all the theory and tools necessary to solve problems via exact, approximate, and numerical methods. The Third Edition retains all the hallmarks of its previous editions, including an emphasis on practical applications, clear writing style and logical organization, and extensive use of real-world examples.
Among the new and revised material, the book features:
* A new section at the end of each original chapter, exhibiting the use of specially constructed Maple procedures that solve PDEs via many of the methods presented in the chapters. The results can be evaluated numerically or displayed graphically.
* Two new chapters that present finite difference and finite element methods for the solution of PDEs. Newly constructed Maple procedures are provided and used to carry out each of these methods. All the numerical results can be displayed graphically.
* A related FTP site that includes all the Maple code used in the text.
* New exercises in each chapter, and answers to many of the exercises are provided via the FTP site. A supplementary Instructor's Solutions Manual is available.
The book begins with a demonstration of how the three basic types of equations-parabolic, hyperbolic, and elliptic-can be derived from random walk models. It then covers an exceptionally broad range of topics, including questions of stability, analysis of singularities, transform methods, Green's functions, and perturbation and asymptotic treatments. Approximation methods for simplifying complicated problems and solutions are described, and linear and nonlinear problems not easily solved by standard methods are examined in depth. Examples from the fields of engineering and physical sciences are used liberally throughout the text to help illustrate how theory and techniques are applied to actual problems.
With its extensive use of examples and exercises, this text is recommended for advanced undergraduates and graduate students in engineering, science, and applied mathematics, as well as professionals in any of these fields. It is possible to use the text, as in the past, without use of the new Maple material.
1. Random Walks and Partial Differential Equations.
2. First Order Partial Differential Equations.
3. Classification of Equations and Characteristics.
4. Initial and Boundary Value Problems in Bounded Regions.
5. Integral Transforms.
6. Integral Relations.
7. Green's Functions.
8. variational and Other Methods.
9. Regular Perturbation Methods.
10. Asymptotic Methods.
11. Finite Difference Methods.
12. Finite Element Methods in Two Dimensions.
- Two new chapters are presented to reflect direct numerical methods for the solution of numerical methods via Maple 8.
- New sections are provided at the end of each chapter dealing with the solution of PDEs and are tied in with the newly created Maple procedures.
- A related FTP site includes all of the Maple procedures (codes) used within the text.
- Coverage of random walk problems, discontinuous and singular solutions, and perturbation and asymptotic methods is provided.
- Over 800 practice exercises and solutions, many of which are fully worked out, are included. Selected solutions are provided on the FTP site. (A supplementary Instructor's Solutions Manual is available upon request.)
- Covers the fields of engineering and the physical sciences via numerous up-to-date examples.