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Ordinary Differential Equations

Morris Tenenbaum and Harry Pollard
Dover Publications
Publication Date: 
Number of Pages: 
[Reviewed by
Megan Sawyer
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Although an older text, Ordinary Differential Equations contains appropriate material for the modern student, at least from an analytical perspective. This text balances proofs with applications, and heavily self-references throughout examples and subsequent chapters. Applications, although not among the most current trends, still have validity and can be visualized by students. Topics range from technical methods of solving DEs analytically to linearization and an introduction to numerical methods.

The organization of the text is fairly reasonable. Lessons are punctuated with examples and a few proofs, but not an overwhelming amount. The scaffolding of the text has tended to work well for this reviewer’s students. Problems are presented in a straightforward fashion, and few steps are left out on the initial problem. A typical example has a smattering of text accompanying the problem to verbalize what is happening mathematically. There are limited illustrations, and to that extent, nothing flashy in the text. This puts the focus on the differential equations themselves, relying on the reader to pursue modern technology for visualization of the behavior of the ODEs.

The number and degree of difficulty for problems are suitable for undergraduates. Exercises are arranged at the end of the lessons and nicely reflect material in that lesson. The difficulty of the problems increases with both the depth of the material (later lessons have significantly deeper-thinking questions) and the level of application to tangible examples. I would caution instructors, however, to give the problems more than a cursory glance before assigning them, as some exercises (especially in later chapters) rely on subtle integration techniques and trigonometric identities.

Although the text touches upon numerical methods, this book more suited to teaching about solving particular forms of differential equations than it is about setting up general strategies. For an analytical course on ODEs, however, this text is more than sufficient, and for some students enjoyable.

Megan Sawyer is an assistant professor of mathematics at Southern New Hampshire University in Manchester, NH. 

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