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Div, Grad, Curl, and All That: An Informal Text on Vector Calculus, Fourth Edition
Download PDF Div, Grad, Curl, and All That: An Informal Text on Vector Calculus, Fourth Edition
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- Sales Rank: #10898366 in Books
- Published on: 2005
- Binding: Paperback
Most helpful customer reviews
130 of 138 people found the following review helpful.
Not as super as some make it to be. Buy the cheaper older edition.
By Kris
I picked this book up, based on the reviews that said it would explain vector calculus to "engineers". I probably read the book 3 times, but I never felt I really _understood_ the material. A few years later, I think I do understand the material; looking at the book, many of the things I read seem obvious now. I feel this is where most of the reviewers were coming from...
The book is great if you already know the material, and just need a nice, unifying refresher. It is not that great for learning it the first time, since there is very little application of the material, and for me that is what motivates me to understand something. Morse & Feshbach is much more rigorous and dense, but that is where it first "clicked" for me. Also, I think this book is supposed to be in tandem with a more standard Calculus reference. Between two books one might have a better time at figuring things out.
There are a few very good figures in the book that have helped me understand some key concepts (the flowchart relating the different operators and their associated assumptions), but the lack of rigor and general long-windedness of the book could actually be considered a fault, rather than a benefit "for engineers".
Also, buy the cheapest edition of this book you can find. They are all basically the same (only the problems and very minor wording change between editions). Don't think you need to get the latest edition, get a cheaper earlier edition.
53 of 56 people found the following review helpful.
Great way to learn your basics!
By D. Huang
I had three years of higher-level calculus between my BS and MS in mechanical engineering, and none of these classes have explained the concepts in this book with such clarity and accessibility. The sample problems at the end of each chapter cement the concepts just learned. For me, they were just challenging enough to test and hone my skills, but not so crazy that I felt like I was stroking some intellectual ego instead of learning practical concepts.
I highly recommend it to people of similar backgrounds as myself--people with already decent math backgrounds, but who need to hone their vector calculus skills to enter the world of physics, electrical engineering, fluid mechanics, continuum mechanics, or anything else along those lines (lines! Hah! Pun!). I feel like this book was written just for me! Are there really that many of us?
One tip on this book--get serious with it, and you will really cement your skills. Do the problems, for real--work them out with pencil and paper; don't just skim them while you watch TV. They are, as I've said, challenging enough to be rewarding, but none are the type that would send you sobbing to your prof in office hours. Suck it up, fix yourself a nice cup of tea, get your dog to sit with you, and go for it! It's well worth the effort.
1 of 1 people found the following review helpful.
Lives up to the Hype
By Herbert L Calhoun
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.
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