<< 1 >>
Rating: 
Summary: difficult
Review: As a graduate student in engineering, I found this book to be somewhat difficult to understand. That in itself isn't a major problem, but I have just found other books which present the material in a much clearer fashion. Part of the problem is Evans' fascination with non-linear equations to the point of muddling even simple formulations.
Rating: 
Summary: Excellent
Review: Evans succeded in writing a text on partial differential equations which can serve a broad spectrum of users: from pure mathematicians interested in hard theorems about the properties of solutions to various types of PDEs to sophisticated practitioners interested in solving specific problems leading to PDEs. The book covers in sufficient detail and great clarity the basic types of PDEs including modern topics such as optimal control, Hamilton-Jacobi equations, and viscosity solutions. Emphasis is pretty evenly distributed between general qualitative properties of solutions, and techniques for explicit construction of solutions in representative cases.
Rating:
Summary: Best textbook for a modern one-year course in PDE available.
Review: I have taught a one-year course in PDE based on Evans' book and found it extremely cogent and stimulating both for myself and for the students. The treatment is up-to-date, with a definite nonlinear flavor. Beyond that, the exercises are very good, and the treatment is sufficiently detailed to make class preparation fairly fast. It does demand mathematical dexterity and maturity of the students right from the start, though.
Rating: 
Summary: Dense, but quite good
Review: This book is a mathematician's book and not an engineer's--it hasn't a bit of material on approximating solutions of PDEs (which subject could fill several volumes by itself), and devotes a great deal of space to proving existence, regularity, and other properties of solutions to non-linear PDEs. The exposition is extremely compressed (many moderately difficult proofs are reduced to a paragraph or two). It is also very much a graduate course (as the title indicates). Undergraduate students are advised to stay away unless they have excellent teachers, or are very good, or both.
Rating:
Summary: PDE making sense
Review: This is a textbook for a first-year graduate course in PDE (for mathematics students). You should take courses in analysis (on the level of Rudin) and measure theory before you expect to understand everything in this book. This is by far the best book on PDE. The text is extremely clear, and most of the rather technical proofs are prefaced with "heuristic" calculations to help the reader understand what is going on. The chapter on the calculus of variations is the best exposition I have found of the subject, and Evans completely dispenses with the awful "delta" notation which never made any sense. The text doesn't make much use of the Fourier transform and doesn't even mention distributions, and this gives his book a definite nonlinear flavor (which is a good thing). This should become the standard introduction to PDE on the graduate level.
Rating:
Summary: This will become the standard text in PDE
Review: This is a very well written textbook for graduate-level students as well as an excellent reference for researchers. The outlook of the author, a leader in his field, is non-linear and very broad and includes maechanics and geometry. Any department library needs this book.
<< 1 >>
| 
