Constanda C. Differential Equations: A Primer for Scientists and Engineers

New York: Springer Science+Business Media, 2013. — 272 p. — ISBN: 978-1-4614-7296-4Differential Equations for Scientists and Engineers is a book designed with students in mind. It attempts to take a concise, simple, and no-frills approach to differential equations. The approach used in this text is to give students extensive experience in main solution techniques with a lighter emphasis on the physical interpretation of the results. With a more manageable page count than comparable titles, and over 400 exercises that can be solved without a calculating device, this book emphasizes the understanding and practice of essential topics in a succinct fashion. At the end of each worked example, the author provides the Mathematica commands that can be used to check the results and where applicable, to generate graphical representations. It can be used independently by the average student, while those continuing with the subject will develop a fundamental framework with which to pursue more advanced material. This book is designed for undergraduate students with some basic knowledge of precalculus algebra and a first course in calculus.The book should be easy to follow without being excessively verbose. A crisp, concise, and to-the-point style is much preferred to long-winded explanations that tend to obscure the topic and make the reader lose the thread of the argument.
The book should not talk down to the readers. Students feel slighted when they are treated as if they have no basic knowledge of mathematics, and many regard the multicolored, heavily illustrated texts as better suited for inexperienced high schoolers than for second-year university undergraduates.
The book should keep the theory to a minimum. Lengthy and convoluted proofs should be dropped in favor of a wide variety of illustrative examples and practice exercises. The book should not embed computational devices in the instruction process. Although born in the age of the computer, a majority of students candidly admit that they do not learn much from electronic number-crunching.
The book should be ‘slim’. The size and weight of a 500-page volume tend to discourage potential readers and bode ill for its selling price.
In my view, a book that tries to be ‘all things to all men’ often ends up disappointing its intended audience, who might derive greater profit from a less ambitious but more focused text composed with a twist of pragmatism. The textbooks on differential equations currently on the market, while professionally written and very comprehensive, fail, I believe, on at least one of the above criteria; by contrast, this book attempts to comply with the entire set. To what extent it has succeeded is for the end user to decide. All I can say at this stage is that students in my institution and elsewhere, having adopted an earlier draft as prescribed text, declared themselves fully satisfied by it and agreed that every one of the goals on the above wish list had been met. The final version incorporates several additions and changes that answer some of their comments and a number of suggestions received from other colleagues involved in the teaching of the subject.