An introduction to partial differential equations /

Renardy and Rogers provide the necessary background and thoroughly develop the tools needed for advanced studies in partial differential equations. Their book is well written for beginning graduate students and researchers in applied mathematics and mathematical physics who intend to use partial differential equations as an everyday tool. Readers with a background in advanced calculus and complex analysis will feel comfortable with the material presented here. Most chapters are self-contained, and many of the background materials are presented in a novel way, with examples, problems, references, and sometimes hilarious remarks that make the book very readable. The book begins with an introduction in which is discussed a group of questions that arise in various partial differential equations. The text continues with characteristics, conservation laws and shocks, maximum principles, and the theory of distributions. An introduction to function spaces and operator theory is made before the discussion of linear and nonlinear elliptic equations, energy methods for evolution problems, and semigroup methods for partial differential equations. Highly recommended. Graduate through faculty. D. E. Bentil; University of Massachusetts at Amherst