Div, Grad, Curl, and All That: An Informal Text on Vector Calculus (Fourth Edition) 4th Edition

by H. M. Schey (Author)

94 customer reviews

ISBN-13: 978-0393925166

ISBN-10: 9780393925166

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This new fourth edition of the acclaimed and bestselling Div, Grad, Curl, and All That has been carefully revised and now includes updated notations and seven new example exercises.

Since the publication of the First Edition over thirty years ago, Div, Grad, Curl, and All That has been widely renowned for its clear and concise coverage of vector calculus, helping science and engineering students gain a thorough understanding of gradient, curl, and Laplacian operators without required knowledge of advanced mathematics.

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About the Author

H. M. Schey is Professor of Mathematics and Statistics at the Rochester Institute of Technology.

Product details

Paperback: 176 pages
Publisher: W. W. Norton & Company; 4th edition (December 1, 2004)
Language: English
ISBN-10: 9780393925166
ISBN-13: 978-0393925166
ASIN: 0393925161
Product Dimensions: 6.2 x 0.6 x 9.3 inches
Shipping Weight: 1.6 ounces (View shipping rates and policies)
Average Customer Review: 94 customer reviews
Amazon Best Sellers Rank: #39,870 in Books (See Top 100 in Books)
- #4 in Books > Science & Math > Mathematics > Applied > Vector Analysis
- #83 in Books > Textbooks > Science & Mathematics > Mathematics > Calculus
- #104 in Books > Science & Math > Mathematics > Pure Mathematics > Calculus

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Excellent Review of Vector Calculus

May 20, 2011

Format: PaperbackVerified Purchase

This book covers some of the most fundamental topics of vector calculus in a very clear manner. The presentation is lucid, the exercises are thought provoking, and the proofs are a good mix between intuitive and rigorous. I mainly bought this book because I wanted to "redeem" myself and obtain a better understanding of multivariable calculus after taking the course last semester, especially with surface integrals, Stokes Theorem, and the Divergence Theorem. I need to stress that this is best used as a refresher of vector calculus (if you had a good prof), or an avenue for deeper understanding (if you had a bad prof, like me). It is not supposed to be an outright introduction. In fact the authors warn us that:

"To begin with, you should, of course, be fluent in elementary calculus. Beyond that you should know how to work with functions of several variables, partial derivatives, and multiple (double and triple) integrals. Finally you must know something about vectors."

So, you need to know a little bit about multivariable calculus to be successful with self-studying this book. Oh, and this edition, I've heard, is a major change from the first edition in terms of notation, but not a whole lot different from the third and fourth editions, so save some money and get this one. You won't regret it.

11 people found this helpful

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Herbert L Calhoun

Lives up to the Hype

May 6, 2009

Format: PaperbackVerified Purchase

This book lives up to its hype as well as its well-earned reputation as the "definitive review text" on "all this stuff." It also lives fully up to Einstein's edict that: "An explanation should be simple, but no simpler than necessary." It is maximally intuitive and heuristic: both good things in learning difficult subjects.

Electrostatics, which has the concept of a "field" as a central structural element, as is the case with so much of both physics and higher mathematics, seems the perfect vehicle to make more concrete most of the key ideas of vector calculus. Although for mathematicians, it takes a while for applied thinking to take root, and electrostatics has its own subtleties (Coulumb's and Gauss' Laws rendered into functional form for instance), once one gets the basic logic of the ideas down, further elaboration of other key concepts becomes almost repetitive (but a careful) extensions of them.

Thus the progression from "div" to "grad" was gentle enough, basically little more than a review of Vector Analysis. However, with the introduction of the line integral and the curl, things began to get a bit trickier. The functional nature added an important new level of abstraction. The reader's understanding of functions must "kick in." The excellent examples and diagrams involving "basis vectors," both regular and normal, early on, saved the day in the end for me. It gave me a strong conceptual framework to fall back on, in a section where some of the concepts were more counterintuitive and abstract than usual, and more so than in the earlier sections.

On a first reading, I kind of "intuited" (rather than actually "worked through") the result of many of the examples (where partial derivatives, change of coordinate systems, and tangent vectors played a central role) checking the answers in the back of the book to confirm my understanding. The well selection of problems and their gradual increase in difficulty -- as well as having most of the examples based on "unit vectors" centered on the origin made it possible to "intuit" or work out in ones head, rather than actually work out with pencil and paper, many of the examples.

Most of the time I was right on the mark. However, in a second reading, I plan to carefully work through as many of the problems as I can now that I know the "lay of the land." In this regard, I am ashamed to admit that it helped greatly too, that I have a used version of the book in which the previous owner worked through many of the examples in pencil as annotations in the margins. Normally I abhor such mutilation of books, however, this time it proved to be very helpful and a valuable check on my own thinking.

Still, even with all this, for those unfamiliar with the basics concepts of vector calculus, the book is not going to be a "walk over."

Five Stars.

2 people found this helpful

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Intuitive explanation to vector calculus, but it is not ...

June 12, 2017

Format: PaperbackVerified Purchase

Intuitive explanation to vector calculus, but it is not for explaining electrostatics. Also, it should be read with another vector calculus book.

2 people found this helpful

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An Excellent Overview of Vector Calculus

April 1, 2003

Format: PaperbackVerified Purchase

I first checked this book out of a library, and was so pleased I decided to buy it. I am enrolled in a graduate level fluid mechanics class after being out of school for a few years and I needed to brush up on my vector calculus. This book was great for that job. It explains the concepts of divergence, gradient, curl, directional derivatives, line integrals, surface integrals, Stoke's Theorem, and Divergence Theorem with good mathematical rigor and notation, yet also with the "words between the lines" that most math texts leave out. In other words, accompanying each equation you will find a sentence or even a paragraph describing what exactly took place between steps.

Additionally, the author makes a point to describe the concepts behind the jargon and equations. When you took vector calculus the first time (if you ever did), could you explain in words what a "curl" is, or a "divergence"? This book attempts to do so, and does so fairly well (as well as one could given that these concepts don't have the easiest translation into words).

Furthermore, the author even has a sense of humor and made me laugh a few times. When was the last time you laughed out loud at a math book?

Finally, this book also includes applications to physics such as electrostatics (the recurring thematic problem of the book is Gauss's Law), fluid dynamics, and work.

Not only was it a great refresher, I wanted to own this clear and simple book as a reference.

24 people found this helpful

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