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

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.

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.

Recently an acquaintance of mine asked me for help on passing her advanced calculus course. I was delighted to hear that Schey's book was one of her references. Because the book was not the main text (nor could it ever be in my opinion), she had not been reading it, so I urged her to do so. After a couple of hours of reading she was back on track.

As many reviewers relay, the book is a great companion book to vector calculus. If a reader hasn't at all with vector calculus the reader will not benefit much from the book. However readers with even the faintest acquaintance to the subject matter and having difficulties understanding will appreciate it enormously. For it is exactly such audience the book addresses (the title of the book also alludes to this fact -- how would one know what "div grad curl and all that" mean without hearing those terms from elsewhere?). The book serves as a nice step back from the usually hurried vector calculus courses. It allows you to revisit the very fundamentals (for e.g. defining div, grad, and curl via limits instead of from differential operators), and relates the topics in a highly readable manner.

As mentioned earlier, the book by itself cannot be a text on its own, primarily due to its limited scope of coverage. For instance there are no mentioning of exterior forms, or neither inverse nor implicit function theorems. Many advanced students will not need this book either. However if you find yourself uncertain in recalling how to compute surface integrals, or you are having difficulties understanding Stoke's theorem and/or Gauss' divergence theorem, this is a good place to build your foundations.

Simply put, this book provides the best explanation of the gradient, the divergence, and the curl in any book I've seen. It really should be a required reference/text for every physics and engineering program in the country. All the mathematics is here, but the author also lucidly explains in words and diagrams the physical meaning of these three operations. Many students learn how to manipulate these operations, but they often have trouble understanding exactly what they mean. This book is easy to read (how many textbooks can you say that about?) and there are lots of problems to illustrate key points after each chapter. The author uses the mathematical formalism to solve some basic problems in electrostatics to provide real-world examples. After working through this book, you'll not only be able to calculate the curl of a vector function, you'll know exactly what it means.

This book does it all. Without being overly verbose, it explains div, grad, and curl in concepts clearer and maybe even more precise than you would see in some upper level vector analysis classes. The integral definitions for grad and curl are given and well-justified. Homework problems and a number of examples from E&M give practice and application. It's an easy read, relatively cheap, and I think it's great supplementary material for any math or physics student.