Elements of partial differential equations (Q2454141)

The second edition (for the first edition see [the authors, Elements of partial differential equations. Berlin: Walter de Gruyter (2007; Zbl 1170.35001)]) of this textbook provides an elementary introduction to principles of PDEs. The changes and improvements from the first edition stem from the teaching experience of the authors. The material is structured into 13 chapters. Chapter 1 is devoted to conservation and constitutive laws. Chapter 2 deals with the classification of PDEs, to the various notions of solutions and to the concept of initial and boundary conditions for PDEs. In Chapter 3 the authors are concerned with first order linear PDEs. Chapters 4--10 present an elementary exposition to wave, diffusion and Laplace/Poisson equation. Chapters 11--13 extend such exposition to the case of higher dimensions. For the sake of clarity, the authors restrict themselves to dimension \(d\leq 3\) with respect to the space variable. Each chapter is complemented with with many thououghly worked examples, illustrations and carefully selected exercises. Basic calculus and linear ODE theory are the only prerequisite materials for this book. The textbook is a highly recommended source for students in pure/applied mathematics, engineers or scientists at the upper undergraduate level.