This original Dover publication boasts a title suggesting that it is a blueprint for mathematical modeling. On cracking open the text I expected to find out what gamut of problems are approached and at what level the mathematics is. I was disappointed to find contents more like that REA's Problem Solvers series: bluntly stated problems immediately following by a complete solution. There is no discussion of notation, theory, or building up a model from a real world situation.
What it lacks in REA’s emphatic redundancy, this collection makes up in breadth. Engineering and physics are the focus of the presented problems. Topics covered include vector algebra, kinematics, fluid dynamics, electricity, magnetism, Fourier series, Laplace transforms, wave motion, heat conduction, tensor analysis, relativity, quantum theory, and more. The result is a survey of the main tools of applied mathematics in what is a potpourri of examples that is illustrative although not educational. Rather than an enlightening text, this book is more appropriate for students seeking an adjunct to existing texts or educators that need a question bank.
The cover promises that the book "bridges the gap between lectures and practical applications, offering students of mathematics, engineering, and physics the chance to practice solving problems from a wide variety of fields." I think anyone expecting exactly what that implies will be disappointed. I do not see this work as useful to anyone that has not already grasped the relevant lectures or has other tools to do so. If the idea is to practice solving problems, then this work would have multiple problems of each type and solutions would be separated from the problems.
The general principles laid out at the end of the preface are sage advice, but curiously are not followed by the author. It is indeed very good advice to “introduce a good notation” when solving applied mathematical problems, yet this work assumes the reader already knows and appreciates the presented notation, which is taken as established and without need of explanation. It is of course key to “try to understand what you want to prove” but here the breathless pace does not allow for context nor gives the reader a chance to make any inference. Finally, it is a surprise to see so many problems from classical mechanics, wave motion, etc. without a single illustration.
Tom Schulte, a teacher of mathematics, enjoys many Dover titles in his home in Waterford, Michigan.