Primer on PDEs

From the book reviews: "This book, presented at the advanced undergraduate or first year graduate level, takes a very interesting mixed approach to partial differential equations, shining a modern light on a classic subject. In addition to the usual analytic solution methods, the presentation includes both numerical approaches and mathematical techniques for proving rigorous existence and regularity results. ... Each chapter concludes with an informative set of exercises, and solutions to many of them are provided at the end of the book." (Peter Bernard Weichman, Mathematical Reviews, May, 2014) "The present text is suitable for a two semester introduction to partial differential equations. ... The text is well-written and can be particularly recommended for students who are interested in the interplay between modeling, theory, and numerics." (G. Teschl, Monatshefte fur Mathematik, 2013) "Part I (Chapters 2-6) of this book ... is entitled Differential models. ... Part II (Chapters 7-9) is entitled Functional analysis techniques for differential problems and it is devoted to Hilbert space methods for the variational formulation and the analysis of linear boundary and initial-boundary value problems. ... at the end of each chapter the authors include a brief account of numerical methods, with a discussion of some particular case study. ... recommend this book to students in engineering, applied mathematics and physics." (Vicentiu D. Radulescu, zbMATH, Vol. 1270, 2013)

• Introduction.- Scalar Conservation Laws.- Diffusion.- The Laplace Equation.- Reaction-diffusion models.- Waves and vibrations.- Elements of Functional Analysis.- Variational formulation of elliptic problems.- Weak formulation of evolution problems.- Solutions.- Fourier Series.- Notes on ordinary differential equations.- Finite difference approximation of time dependent problems.- Identities and Formulas.