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Title: Div, Grad, Curl, and All That: An Informal Text on Vector Calculus by Harry M. Schey ISBN: 0-393-96997-5 Publisher: W.W. Norton & Company Pub. Date: August, 1997 Format: Paperback Volumes: 1 List Price(USD): $17.95 |
Average Customer Rating: 4.75 (20 reviews)
Rating: 5
Summary: Excellent Introduction to Vector Calculus
Comment: This book teaches the main topics in vector calculus with an emphasis on its applications to electrostatics. As its subtitle suggests, the presentation is rather informal, but I enjoy Schey's conversational style.
The proofs are by no means rigorous, but the proof sketches are detailed enough to convey the main ideas. Schey takes great care to motivate the equations and to provide some geometric intuition for what they mean. To illustrate the geometric ideas, the book includes a liberal dose of excellent figures.
As is true with most math books, however, you really have to do the problems to get the most out of it. Some of the problems are not only challenging, but are designed with incremental sub-parts to teach new results. The book also includes solutions for many problems. Be warned however: writing out the complete solutions to all the problems (as I have done) takes a large amount of time and fills more pages than the book itself!
Rating: 5
Summary: Clear, well-integrated introduction to vector calculus
Comment: This text provides a systematic introduction to vector calculus in a very readable, informal format. Key concepts like divergence, curl, gradient, line integrals, surface integrals, Divergence Theorem, and Stokes Theorem are introduced in the context of investigating solutions to electrostatics problems without requiring the reader to be especially familiar with physics. I particularly enjoyed the humor that is woven into the text. ("Thus, the anguish of remembering the form of curl F in Cartesian coordinates can be replaced by the pain of remembering how to expand a three-by-three determinant.") I would highly recommend this concise book to students of physics, engineering, and mathematics. It is particularly suitable for self-instruction.
Rating: 5
Summary: A must for engineering and science students.
Comment: If you are an undergraduate engineering or science major, then you need to get a copy of this old classic and become good friends with it. If you are a graduate student or a professional in some branch of engineering or science, and you have not already read this book, then sneak out and get a copy before anybody finds out. (You can pretend that you really knew this stuff all along.) Seriously, this book should be considered Math 101 for scientists and engineers. You simply cannot get by without knowing the basics of vector calculus, curvilinear coordinates, Gauss' law, Stokes' theorem, and of course, the protagonists Divergence, Gradient, and Curl, known to their friends as Div, Grad, and Curl.
This is about as tame a book on vector calculus as you could ever hope to meet, which is part of the reason it's been so popular for so long. It's very easy to read (as far as math texts go), it has many simple but effective illustrations, it has ample exercises (most of which have solutions in the back), and it avoids excessive formalism, instead focusing on the nuts-and-bolts of vector calculus as it most commonly arises in electrostatics, for example.
Math majors will not be so enamored of this book, simply because of its heuristic approach (hence the word "informal" in the subtitle) and its close ties with applications, which it uses as motivation. Moreover, Schey does not develop differential forms or exterior calculus, which logically subsume and extend the material in this book (at the expense of far greater abstraction, which the majority of engineering and science students will prefer to avoid or at least delay). Instructors, if you teach electrostatics or fluid dynamics, you may wish to consider having this as a supplementary text for your students. It's such a clear and helpful little book your students will really appreciate it. (But, you already knew that.)
Bottom line for engineering and science students: You need to know this material, and it simply won't get any easier than this. Don't wait for the audio edition!
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Title: Geometrical Vectors (Chicago Lectures in Physics) by Gabriel Weinreich ISBN: 0226890481 Publisher: University of Chicago Press Pub. Date: July, 1998 List Price(USD): $17.50 |
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Title: Schaum's Outline of Vector Analysis by Murray R. Spiegel ISBN: 007060228X Publisher: McGraw-Hill Trade Pub. Date: 01 June, 1968 List Price(USD): $16.95 |
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Title: Partial Differential Equations for Scientists and Engineers by Stanley J. Farlow ISBN: 048667620X Publisher: Dover Pubns Pub. Date: 01 September, 1993 List Price(USD): $14.95 |
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Title: Introduction to Electrodynamics (3rd Edition) by David J. Griffiths ISBN: 013805326X Publisher: Prentice Hall Pub. Date: 30 December, 1998 List Price(USD): $108.00 |
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Title: Electricity and Magnetism, Vol. II by Edward M. Purcell ISBN: 0070049084 Publisher: McGraw-Hill Science/Engineering/Math Pub. Date: 01 August, 1984 List Price(USD): $103.44 |
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