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Introduction to Differential Equations

Michael E. Taylor
Publication Date: 
Number of Pages: 
Pure and Applied Undergraduate Texts
[Reviewed by
Miklós Bóna
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There are a very large number of introductory differential equations textbooks on the market, and they largely cover the same topics. So the task of the reviewer is to explain how the book under review is different, and what the potential audience is.
The main difference is that the book assumes a higher level of mathematical sophistication from the reader than most competing textbooks. This book proceeds much faster. Second-order differential equations, which are the content of an entire chapter in other books, are discussed in three sections only.  Two sections are devoted to Power Series, and one section is devoted to Laplace transforms, while in the textbook this reviewer uses, a whole chapter is devoted to each.
What is then the rest of the book about? There are four chapters, three of which cover material that is not part of many introductory courses. One is about linear algebra, another one is about linear systems of differential equations, and another one is about nonlinear systems. So if most of your students will take a separate course in linear algebra after their course of differential equations, then this book is probably not for you. There are exercises at the end of each section. They do not come with solutions, or even, numerical answers, but some do come with hints.
As we explained, the book is quite different from most competing textbooks. Whether you want to use it or not depends on whether you think your students can handle its fast pace, and whether its somewhat unusual set of topics matches the needs of your audience.


Miklós Bóna ( is a Professor and Distinguished Teaching Scholar at the University of Florida, and the author and editor of several books. His main research interest is Enumerative Combinatorics.