Saturday 24 September 2011

[A935.Ebook] Get Free Ebook Partial Differential Equations (AMS Chelsea Publishing), by Paul R. Garabedian

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Partial Differential Equations (AMS Chelsea Publishing), by Paul R. Garabedian

Partial Differential Equations (AMS Chelsea Publishing), by Paul R. Garabedian



Partial Differential Equations (AMS Chelsea Publishing), by Paul R. Garabedian

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Partial Differential Equations (AMS Chelsea Publishing), by Paul R. Garabedian

This book is a gem. It fills the gap between the standard introductory material on PDEs that an undergraduate is likely to encounter after a good ODE course (separation of variables, the basics of the second-order equations from mathematical physics) and the advanced methods (such as Sobolev spaces and fixed point theorems) that one finds in modern books.Although this is not designed as a textbook for applied mathematics, the approach is strongly informed by applications. For instance, there are many existence and uniqueness results, but they are usually approached via very concrete techniques. The text contains the standard topics that one expects in an intermediate PDE course: the Dirichlet and Neumann problems, Cauchy's problem, characteristics, the fundamental solution, PDEs in the complex domain, plus a chapter on finite differences, on nonlinear fluid mechanics, and another on integral equations. It is an excellent text for advanced undergraduates or beginning graduate students in mathematics or neighboring fields, such as engineering and physics, where PDEs play a central role.

  • Sales Rank: #510183 in Books
  • Published on: 1998-06
  • Original language: English
  • Dimensions: 9.50" h x 6.50" w x 1.50" l, 2.40 pounds
  • Binding: Hardcover
  • 672 pages

Most helpful customer reviews

4 of 5 people found the following review helpful.
Exceptionally Written Advanced Presentation
By G. A. Schoenagel
A well-written text concentrating on material beyond separation of variables or fourier techniques.
Prerequisites are modest (i.e., elementary solution methods for PDE's, ODE's and Complex Variables--say, Weinberger.).
The author touches upon: geometrical optics, Hamilton-Jacobi theory, Lorentz Transformations of Special Relativity.
Excellent chapters expound Integral Equations, Eigenvalue problems, Hyperbolic Equations, Fluid Dynamics,
and PDE's in the complex domain. Verbose and explanatory herein replace terse and succinct.
Nonlinear PDE's of Fluid Dynamics, as the author writes "..serves as an important
guide in the investigation of partial differential equations."
Paraphrasing from the preface: " ...Central theme is existence and uniqueness theorems,
written for engineers and physicists, as well as for mathematicians."
Many of the problems at Chapter's End are physical in nature (straightforward) serving to augment the theoretical exposition.
For many a reason, the problems are stimulating without seeming burdensome. "Discuss equations for the spherically
symmetric motion of a gas,that is, for radial flow depending only on time and the distance from the origin" (Page 518).
The exposition is very clear, a fine text and reference.

0 of 0 people found the following review helpful.
Nice overview of theory and applications
By Paul A. Bonyak
The first chapter of this long used text presents a proof of the Cauchy-Kowalewski Theorem. This essentially establishes the existence of an analytical solution by assuming a multivariable Taylor expansion solution, plugging it in the partial differential equation and then finding conditions on the coefficients which ensure convergence (majorants)-pretty much an application of the comparison test similar to that seen in the Weirstrass M-test. Almost trivial but most books relegate it to a reference.
Engineers and physicists would find his frequent use of the method of characteristics valuable. The method is dependent on the bilinear form which classifies the equation and thence also determines a natural geometry. Singular curves are determined usually by constructing a determinant wherein the partial derivatives are treated as the variables like x,y,z and their coefficicients are the elements in the determinant. Some of these coefficients will be the infinitesimals-dx, dy, etc.- from their parameter (usually time) derivatives in the system of partial differential equations. You equate the determinant to zero and using Cramer's rule you get systems of ordinary differential equations. An easy example is streamlines-infinitesimal vector must be parallel to the flow field vector at an arbitrary given point-vector cross or determinant is zero, giving the differential equations of the streamlines. Actual solutions are found using compatibility equations which are usually also singular but ensure physical constraints. As you might infer, the author freely uses physical examples throughout the text. This may appear cluttered to the purist or as one reviewer claimed "beating around the bush" but these ideas arose from these examples.

0 of 0 people found the following review helpful.
Needs more!(for a book of its level)
By Hari Rau-Murthy
I bought this for a class that changed the book on the first day. What I found is that Pierre Germain's notes online are far more succint and lucid, and do not beat around the bush. Important and elementary theorems such as Sobolev Embedding theorem, Rellich Kondrakov compactness, Morrey's inequality, any techniques for establishing well posedness(local or global), lax milgram, direct method of calculus of variations(for anything other than dirichlet's principle), mountain pass lemma, etc are simply not presented. Baisically this book is okay if you want to learn a bit about connections with complex variables and on integral equations.

This book attempts to present Hamilton Jacobi Bellman equations and its a shame that he does not go into the theory of viscosity solutions. Even for the simplest optimization problems, such as a minimum time problem, you will run into trouble if you only want to consider classical solutions.

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