Elements of Partial Differential Equations
There are plenty of books devoted to partial differential equations and a novice can find many textbooks among them. But these generally have hundreds of pages, e.g. one of the most popular (the Evans PDEs) contains nearly 700 pages. It is surprising that it is still possible to write a readable book in which all of the important basic facts together with their motivation and physical relevance can be found in much fewer pages. This book is such a text, comprising only 245 pages. Evidently, something has had to be omitted. The reader will not be introduced to Sobolev spaces or weak solutions, the classification of equations is rather brief and the Cauchy-Kovalewski theorem is missing. All equations are linear (with a few exceptions in the exercises) and all solutions are classical. On the other hand, the propagation of singularities and the conservation of energy for the three dimensional wave equation are included.
Even though the arrangement of the book mainly follows three basic types of equations (wave, diffusion and Laplace), their common features such as energy estimates, the maximum principle and Fourier's method and integral transforms are explained in one place for all the equations. The text is sufficiently rigorous, with a majority of the theorems being proved. The student will certainly find the illustrative pictures useful (66 figures in all). The book contains 250 exercises demonstrating the main goal of this book, namely to introduce students of mathematics, physics and engineering to partial differential equations as one of the main tools of mathematical modelling. It can be highly recommended for this purpose.