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" Well, like many other books, this book does not give you the slightest idea what ODEs and PDEs really are (try John's book as an introduction to PDEs), they are far more intellectually challenging and deep that most students can imagine. One reader wrote: "This book makes ODEs and PDEs look much more difficult than they really are. Really interesting and challenging problems can be found sometimes but authors clearly understand that too many of those would hurt the sale numbers. There are very few examples that really require Mathematica and they are mentioned clearly. Those, who need Mathematica for solving integrals - you'd better retake your Calculus course. If anything, many of the exercises are too easy. Poor mathematical background makes many readers believe that the exercises are hard, the answers are put in weird form (meaning the reader has problems with middle school algebra), etc. It was interesting to me to read most of the negative reviews here. "Proof" in Boyce-DiPrima is a dirty word but so is in any other mainstream text on Diff. You either have to write a book like this, or a real one, like Arnold's book, but that would be a book for a few only. I can hardly blame the authors for this - they, and the publisher, just want to sell more books, and they have therefore to follow the general trend.
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The examples take too much space and have too many details. The book suffers from too many examples and pictures. However, I believe that this is the best compromise of a "recipe book" and a book that really tries to encourage understanding of the subject. Eqns, namely those that can be solved in closed form and like most of those books avoids, but not completely, the qualitative study of the subject. Like most books on this subject it emphasizes on solving relatively small classes of Diff. It is mainly oriented to engineers but a math major could benefit from it as well. This is the best mainstream book on (ordinary) Diff.
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