Differential Equations: Practice Problems, Methods, and Solutions

The author presents a collection of problems and solutions of many kinds of ordinary differential equations (ODEs). Problems that have explicit solutions are the focus. The text is divided into pairs of chapters. The first of the pair consists of a sequence of problems for a particular class of equations with multiple-choices for solutions. The second of each pair has solutions for each problem from the first part. Each problem is solved in detail, and occasionally multiple solution methods are described. Every problem is assigned a difficulty level (easy, normal or hard), and a calculation amount (small, medium or large).

 

The topics include solutions of first- and second-order differential equations, series solutions, and the use of Laplace transform methods. Both problems and solutions are presented very clearly. The large format of the book, together with its generous spacing, means that each page has a good deal of text with plenty of additional room for notes. Problems involving Laplace transform methods are by far the most numerous. Relatively few problems and solutions using series methods are included.

 

The preface implicitly suggests that the book is intended to support first and second-year undergraduates in engineering courses. The author also notes that a main reference for the book is a collection of problems from graduate entrance exams for electrical engineering programs at some universities.

 

While ordinary solution methods of first and second-order ODEs are included in many current textbooks, problems and solutions using series solutions and Lagrange transform methods are not usually treated in such detail. These may be of less interest to students in mathematics but are probably of more value to engineering students. Mathematics courses now tend to emphasize explicit solutions much less than they once did in favor of qualitative analysis of solutions and dynamical system methods.  As a consequence this book is more likely to be of interest for courses directed at engineering students.

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Bill Satzer (bsatzer@gmail.com), now retired from 3M Company, spent most of his career as a mathematician working in industry on a variety of applications. He did his PhD work in dynamical systems and celestial mechanics.