I used this book for an introductory differential equations course. With the help of this book, I was completely prepared for everything the professor threw at us and more.
Some of the problems are simple and should help to reinforce the basic concepts learned from another book. Learn the fundamentals from some other book (or even a professor), and refine your thought processes using this one. There are some basic explanations of concepts and problem types, but most of the space is devoted to problems and solutions, as you may have guessed. If I had trouble with a problem from another book, I could almost always find a similar one in the REA book. A few problems are extremely difficult or involved, but the book leads you through every step of every problem. I was blown away by the depth of a few problems, but following the reasoning in this book really helped me to develop a better "feel" for the subject.
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This is an excellent supplement to any Differential Equations class. It starts out with easy and straight forward problems and progressively gets to the more advanced problems. All steps are worked out in an easy to understand way. Most importantly this book shows the algebraic steps in obtaining solutions, which is ussually where students have trouble. This book is a must have for any science major.
If you are studying DEs, get this book! It beats the usual text books that only contain solutions to selected problems, namely the ones that the professor does not assign or examine you on. This book is comprehensive and contains stratagies for attacking the various problems you will encounter in undergraduate DE courses. It even contains problems and solutions to Partial Differential Equations, Fourier Series and Boundary Value Problems, not just ODEs!
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