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4.5
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.
