- Tapa blanda: 262 páginas
- Editor: Dover Publications Inc. (26 de diciembre de 2008)
- Colección: Dover Books on Mathematics
- Idioma: Inglés
- ISBN-10: 0486469190
- ISBN-13: 978-0486469195
- Valoración media de los clientes: Sé el primero en opinar sobre este producto
- Clasificación en los más vendidos de Amazon: nº744.686 en Libros en idiomas extranjeros (Ver el Top 100 en Libros en idiomas extranjeros)
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Partial Differential Equations (Dover Books on Mathematics) (Inglés) Tapa blanda – 26 dic 2008
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Reseña del editor
This three-part treatment focuses on elliptic and evolution equations. Largely self-contained, this volume concludes with a series of independent topics related to the methods and results of preceding sections and introduces advanced topics for further study. Geared toward graduate and postgraduate students, it also constitutes a valuable reference for professionals. 1969 edition.
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Contents are as follows:
2. Differential Geometry
3. First-order Equations
5. Equations of Higher Order
6. The Laplace Equation
7. The Diffusion Equation
8. The Wave Equation
9. The Vector Helmholtz Equation
"This text is designed as a one-term course for senior and graduate students. A knowledge of partial differential equations is obviously necessary for advanced work, not only in mathematics but also in physics, and today even in engineering. various instructional methods have been used to meet this need. At present, however, there is a complete lack of agreement on coverage, on order of presentation, and on degree of mathematical sophistication required of the student. Available textbooks range from those specializing in existence proofs to those dealing exclusively with practical applications.
In writing the present text, we have tried to steer a middle course which will not be objectionable to the \epsilon- mathematician but will also cover the best procedure on solving the equations of physics.
The first two chapters are introductory. Teaching experience seems to indicate that, no matter how extensive his previous training, the average student has some difficulty with partial derivatives and with differential geometry. Accordingly, we have devoted the first two chapters to a review of these subjects. The fortunate instructor with an unusually well-prepared class may omit Chapters 1 and 2 or assign them as outside reading.
The basic chapters are 3 and 5, the former dealing with the very satisfactory general theory of first-order partial differential equations, the latter with the less complete theory of higher-order partial differential equations. Since the first-order theory is the stepping stone to the second order, we have explained it in unusual detail and have included a chapter (Chapter 4) on applications of first order equations.
The second-order equations are, of course, vastly more important than the first-order. We have therefore devoted Chapters 6,7,8, and 9 to a detailed consideration of the most important second-order partial differential equations of mathematical physics. Plenty worked examples are included in the text, and problems are given at the end of each chapter.
With such a vast subject as partial differential equations, covering active developments over a span of three centuries, any introductory work like the present one must be marked principally by omissions. No two writers will select the same topics or treat them in the same way, since there is no established criterion on what is important or what the student is supposed to gain from the study. In the latter chapters, we have unified the subject by concentrating on separation of variables as the most useful method of solution, neglecting other methods such as the variational approach, the use of integral eqautions, and the Laplace transform. We have found that the treatment given here is highly teachable. We hope that others will find it equally efficacious...," - The Authors
Also, I might note that I have found the authors other books well written and useful also:
Foundations of Electrodynamics (Dover Books on Electrical Engineering)
Field theory for engineers,
Field Theory Handbook: Including Coordinate Systems, Differential Equations and Their Solutions
and although I haven't read it yet
Theory of Holors: A Generalization of Tensors
Three other books that are strong on the method of characteristics are
Partial Differential Equations: Theory and Technique
Elements of Partial Differential Equations (Dover Books on Mathematics)
Partial Differential Equations (AMS Chelsea Publishing)