Partial Differential Equations: Sources and Solutions (Dover Books on Mathematics) by Arthur David Snider (PDF)

Description

Newly updated by the author, this text explores the solution of partial differential equations by separating variables, rather than by conducting qualitative theoretical analyses of their properties. These qualitative features–uniqueness, existence, elegance of composition, and convergence modes–are substantiated by physical reasoning, rather than rigorous arguments. Geared toward applied mathematicians, physicists, engineers, and others seeking explicit solutions, the book offers heuristic justifications for each construction.The first three chapters review the necessary tools for understanding the separation of variables technique: basics of ordinary differential equations, Frobenius-series construction and properties of Bessel functions, and Fourier analysis. Subsequent chapters explore the exposition of the algorithmic nature of the separation of variables process, based on a sequence of steps that infallibly leads to the solution expansion, regardless of the nature of the boundary conditions.

User’s Reviews

Reviews from Amazon users which were colected at the time this book was published on the website:

⭐Honestly, I don’t understand why the reviews of this text are so harsh. Several reviewers have lamented about the non-standard notation, but by the time anyone is using this text they should have already had an introduction to ordinary differential equations (ODEs). Furthermore, I don’t see what is so “non-standard” about the author’s notation. Is it because he often uses prime notation instead of the Leibniz notation commonly used in introductory differential equations texts? I can’t help but think that most of the negative reviews of this book are from students who never actually read it, and merely tried to solve the problems they had been assigned by their professors.The author spends the first three chapters building up the tools necessary for the student to approach partial differential equations (PDEs). In chapter 1 he goes through a brief review of ODEs, teaches the student about changing variables, introduces them to delta functions, Green’s functions, and generalized functions/distributions. Chapter 2 is focused on series solutions to ODEs, which is a technique not normally covered in most introductory classes. He goes about this in a fairly standard way, by first reviewing Taylor series and their associated polynomials, followed by the Frobenius method and Bessel functions. Personally, I felt that his treatment of the Gamma function was wonderfully succinct and straight-forward! Chapter 3 focuses on Fourier methods, where he covers the very important concepts of Fourier series, the Fourier transform, and the Laplace transform.Beginning with chapter 4, the author begins his exclusive coverage of PDEs. In this first chapter, he covers the PDEs so common to physics and engineering. This also serves as a gentle introduction to the common types of second-order PDEs. Specifically, the wave equation (hyperbolic), the heat equation (parabolic), and Laplace’s equation (elliptic). The author also covers the calculus of variations and the Schrodinger equation in this chapter. Chapter 5 gives a short overview of the separation of variables technique. Chapter 6 covers eigenfunction expansions, focused largely on Sturm-Liouville techniques. In chapter 7 the author then shows how to apply eigenfunctions to each of the classes of PDEs introduced in chapter 4. Chapter 8 provides excellent coverage of Green’s functions, while chapter 9 covers perturbation methods.Personally, I feel that this book provides an excellent introduction to PDEs for the serious student of applied math, physics, and/or engineering; provided that they have already had an introduction to ODEs. Perhaps the text is not ideal for self-study, given that answers to the problems are not provided in the back of the book. However, the problems are straight-forward enough that the reader should be able to work out when they have arrived at the desired solution. If nothing else, given the excellent coverage, the many tables, and how inexpensive it is, this book should serve as an excellent companion to anyone studying PDEs.

⭐The introduction of the text addresses Differential Equations, Fourier Series, Fourier Transforms and Laplace Transforms. This is not the book to choose to learn the aforementioned subject matter. The author has clearly put great effort into developing this text and has some good tables and reference information. However, there are many other texts that are much better teaching the fundamentals, concepts and solution methodologies of the topics covered in this text, in my opinion. I did buy the text but would not do so again. This is the only poor review I have given to a Dover Book.

⭐A very well written book and a nice reference for a PDE’s course for applied mathematicians and engineers

⭐Cheap and nice book. Good explanations, few topics in the book are treated without prior explanation. Good exercise level.

⭐good, as advertised

⭐Excellent service and product exactly as described.

⭐The notation for this book is awful. Completely different from three other math books that I have used before. It doesn’t adequately explain its own examples, even for the 1 chapter review on ODEs confused me as to what they were trying to accomplish. I gave up on it shortly after that. Even browsing wikipedia is more useful than this book.Cons: Hard to understand; doesn’t seem to use standard notation from what I’ve read.Pros: Cheap. Seems to have a lot of material?

⭐Excellent book, Highly recommended. Thanks

⭐El libro es excelente para un primer curso en ecuaciones diferenciales en derivadas parciales.El paquete llegó casi deshecho. Se recomienda empaquetar con mayor cuidado, en particular cuando los libros son grandes como es este caso.Very bad

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