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Book review

Author(s) Bleecker, David
Csordas, George
Title Basic Partial Differential Equations
Publisher Van Nostrand Reinhold
Year of publication 1992
Reviewed by Paul Blaga

I know from my own experience of student that the ocurse of partial differential equations (PDE's) has the reputation of being very complicated and hard to understand. By reading this book, I found out that it's not quite so, if it is teached with sufficient pedagogical care. The main "secret" of the authors is to inverse the "natural" order of presentation of the material, so that the reader is first accustomed with each subject by means of many worked examples and only then the subject is treated in all its generality. This little trick allowed them to write a textbook of PDE's accessible to any undergraduate student with no more than a year and a half of calculus. There is no need for him to know not even ordinary differential equations, or linear algebra, so I can say that the book is, to a large extent, self-contained. On the other hand, they succeeded in making accessible some topics generally recognized as "advanced" (e.g. maximum principle, the uniform convergence of Fourier series, PDE's on manifolds a.o.).

The first six chapters of the book are traditionally in contents (first order PDE's, heat equation, Fourier series and Sturm-Liouville theory, wave equation, Laplace equation). The last three chapters are, somehow, more special, being devoted, in order, to Fourier transforms, numerical solutions and PDE's on higher dimensions (including spherical harmonics, Laplace series, special functions, PDE's on manifolds). There are, also, six appendix.

The matter is very well sructured, each section being followed by a summary of the main results and a list of exercises, of different difficulties, ranging from routine to challenging. That is unusual, but enjoyable, is the great number of worked examples (about 280, most of them related to practical applications). The book ends with a comprehensive list of references, an index of notations and an index of notions.

The book is highly recommended to all those which have necessary knowledges of calculus and wish to learn about PDE's and their applications. The students and their teachers could hardly find a better introductory course to be used as a basic textbook.