Partial Differential Equations of Applied Mathematics
(Sprache: Englisch)
This book is a comprehensive guide to modeling, characterizing, and solving partial differential equations, presenting some numerical methods for the solution of PDEs. The introduction of computer codes (Maple) to implement the solution of PDEs via direct numerical methods enhances this new edition.
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This book is a comprehensive guide to modeling, characterizing, and solving partial differential equations, presenting some numerical methods for the solution of PDEs. The introduction of computer codes (Maple) to implement the solution of PDEs via direct numerical methods enhances this new edition.
Klappentext zu „Partial Differential Equations of Applied Mathematics “
This new edition features the latest tools for modeling, characterizing, and solving partial differential equationsThe 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
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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.
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.
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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 continues in a less statistical vein to cover an exceptionally broad range of topics, including stabilities, singularities, transform methods, the use of Green's functions, and perturbation and asymptotic treatments. The idea of the book is to present some numerical methods for the solution of PDEs, not simply in the abstract and accompanied by some elementary manually generated solutions. Rather, this book allows for the analysis and numerical solution of some tougher problems. The introduction of computer codes (Maple) to implement the solution of PDEs via direct numerical methods, such as finite difference and finite element methods, enhance this new edition. However, it is possible to use the text as in the past without making use of the new Maple material.
Inhaltsverzeichnis zu „Partial Differential Equations of Applied Mathematics “
Preface1. 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
Bibliography
Index
Autoren-Porträt von Erich Zauderer
ERICH ZAUDERER, PhD, is Professor of Mathematics in the Department of Mathematics at Polytechnic University. Prior to joining the faculty of Polytechnic University, he was a Senior Weizmann Fellow at the Weizmann Institute of Science. His research interests include applied mathematics and nonlinear wave propagation, as well as perturbation and asymptotic solutions of partial differential equations.
Bibliographische Angaben
- Autor: Erich Zauderer
- 2006, 3. Aufl., 976 Seiten, Maße: 24,2 cm, Gebunden, Englisch
- Verlag: Wiley & Sons
- ISBN-10: 0471690732
- ISBN-13: 9780471690733
Sprache:
Englisch
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