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This book is described in its preface as a second course in differential equations, but it would be more accurate to call it a course in elementary differential equations from an advanced standpoint. The prerequisites are modest: a good grasp of calculus and some knowledge of matrices and eigenvalues. The present work is a slightly-corrected 1975 reprint of the 1964 work published by Holt, Rinehart and Winston.
The book covers all the familiar solution methods for ordinary differential equations, but whenever possible works in the language of matrices and handles systems of equations rather than single equations. Much of the book takes a qualitative perspective, showing how to infer the behavior of solutions directly from the equations without finding an explicit solution. It is slanted to the theoretical side, and although it uses several equations from mathematical physics as examples, it does not explore the physical model or the consequences of the solution. It also omits any numerical work. The book has a large number of exercises, most of which are to solve particular equations but many of which ask for proofs.
Allen Stenger is a math hobbyist and retired software developer. He is webmaster and newsletter editor for the MAA Southwestern Section and is an editor of the Missouri Journal of Mathematical Sciences. His mathematical interests are number theory and classical analysis. He volunteers in his spare time at MathNerds.org, a math help site that fosters inquiry learning.