An Introduction to Partial Differential Equations

by Michael Renardy, Robert C. Rogers

Partial differential equations are fundamental to the modeling of natural phenomena. The desire to understand the solutions of these equations has always had a prominent place in the efforts of mathematicians and has inspired such diverse fields as complex function theory, functional analysis, and algebraic topology. This book, meant for a beginning graduate audience, provides a thorough introduction to partial differential equations.

Genres: Mathematics

448 pages, Paperback

First published May 1, 1993

Reviews

[Tomáš Ševček · Rating 5 out of 5]

An interesting book on PDEs, which covers way more than the usual introductory textbook on the subject. The book starts with a recap of the basic ODE concepts and an introduction of the three arguably best-known PDEs (Laplace's, heat and wave). More advanced topics are covered later, such as conservation laws and shocks, maximum principles, distribution theory, transform methods and Green's functions, weak solutions and variational and semigroup methods. The main text also covers some of the basic concepts from functional analysis, so even people with little exposure to this branch of analysis can follow the text. This is in contrast with Evans, where functional analysis is relegated to the appendix, and a deeper prior understanding thereof is assumed. While Evans covers more topics, R&R introduces the theory of distributions and its applications to PDEs (the omission of which is, in my opinion, a gaping hole in Evans). Moreover, more concepts from semigroups, shocks, and characteristics (mostly about classifying PDEs) appear in R&R than in Evans as well. Sometimes, certain concepts are introduced in a different way from Evans, which might pose some issues (for instance, some of the signs in the second-order elliptic operator are swapped, which results in the maximum principles being formulated with opposite inequalities from Evans). All in all, I recommend the book to any pure or applied mathematician who does not feel quite ready to tackle Evans, but still has solid foundations in analysis.

[Cody A · Rating 5 out of 5]

The best introduction to the analysis of PDEs out there. This book and its bibliography have been a guiding light in my research for years.