Introduction to Partial Differential Equations with Applications (Mark A. Pinsky)

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  • 594 BOOK REVIEWS

    communicate with designers who seemed to have a different conception of geometry.But clearly they were able to construct geometric entities of considerable sophistication.This discrepancy of mutual understanding is caused by the existence of two differentapproaches to the understanding of spatial forms: the mathematical (analytic) one andthe engineering (constructive) one.

    This book helps bridge the gap between these two approaches. The author startswith an introduction to descriptive geometry and proceeds to cover analytic geometryextensively. He then treats polyhedral structures--these being essential geometric enti-ties for engineers but also of interest for CAD mathematics. Another part is dedicatedto curve and surface design, again with a detailed treatment of schemes not commonlyknown to a person in CAD development. A final chapter is dedicated to computergraphicsit is treated as an application of the previously developed methods foranalytic geometry. Here one misses some discussion of modem available hardware.

    One criticism: This review being written in the US, it appears that the book isslightly too British; the description of British industry examples prevail, even to theextent of suppressing other important developments--e.g, the British aircraft systemNMG is described at some length, whereas the concept of Gordon surfaces (developedin the US) is not even mentioned.

    I recommend this book to CAD mathematicians who lack the engineering (con-structive) view of CAD, and vice versa to engineers or designers who need to under-stand more about the mathematics underlying their work.

    GERALD FARINUniversity of Utah

    Introduction to Partial Differential Equations with Applications. By MARK A. PINSKY.McGraw-Hill Book Company, New York, 1984. x + 326 pp. No price given. ISBN0-07-050117-3.This book gives an elementary introduction to partial differential equations which.

    should be accessible to university students of mathematics, science, and engineering atthe senior level and to some juniors. It is carefully written and well thought out. Realattention is paid to mathematical details and yet the book does not become toopedantic or "dense". The author states that this book evolved from a course given atNorthwestern University and from my reading of this material I suspect the course hasbeen very successful. As is to be expected, the book emphasizes separation of variablesand integral transform techniques. There is also material on partial differential equa-tions of several spatial variables which are amenable to these techniques. The bookcloses with a very brief introduction to numerical methods, which means in this casefinite difference approximations. I think it would be useful in subsequent editions topoint out here that the Fourier-type representations do in fact yield excellent numericalresults, and problems illustrating that should be given. Evaluating special functions and"messy" integrals numerically is no longer the problem it once was. There is the dangerboth in this book and in other books on this subject as well that students will comeaway with the feeling that the explicit, analytical solutions are mainly of theoreticalinterest and numbers have to be obtained using numerical techniques such as finitedifferences.

    In summary, this is a nice book which will be popular with both instructors andstudents. It is not too advanced and speaks directly to the audience for which it isintended.

    RONALD B. GUENTHEROregon State University

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