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

This is an introduction to Vector Calculus motivated by an easy way to calculate electric field. The author leads you through the math in an uncomplicated manner and clearly explains the motivation and physical interpretations behind the various vector calculus tools. Highly recommend.

Someone recommended I get this book as a way to refresh many topics within physics and I was happy with the way it does it. At times it missed steps and was a little confusing but for the most part it helped out.

This is a wonderful overview of vector calculus, presented in a very easy-to-read, sometimes humorous manner. I can't speak for other disciplines, but as a mechanical engineer I found this book to be amazingly easy to understand and a very helpful review of vector calculus. My multivariate calculus professor was an outer space theoretical mathematician who couldn't explain physically what "flux" is, let alone the higher concepts of divergence, gradient, and curl, so working my way through this book made a lot of fundamental concepts click for me.Schey takes his time explaining all the concepts of vector calculus, in the context of Maxwell's equations, without the formality/rigorousness in "proper" math texts- even the definitions and proofs of the main theorems are explained from a physical standpoint. Indeed, Schey remarks that "rigorous" is just a synonym for "useless". The emphasis is on learning the concepts intuitively and physically, rather than just memorizing formulas. I think this would be a wonderful supplement (for engineers) to a traditional calculus course- but not really that great for learning the material for the first time. I very highly recommend this book as a refresher, especially if you are a graduate student and you are just expected to know everything about vector calculus like the back of your hand.

Very hard concepts when I took Engineering Electromagnetics in college. Now I actually understand divergence, gradient, and curl vectors.

Great book for my Electromagnetic Fields course. This book goes into great detail to ensure the reader fully grasps the materials presented using great examples from Electrostatics.

The title of the book "an informal text on vector calculus" makes you believe that somehow you are going to understand what vector calculus is all about, maybe an instructor didnt explain everything to you in a way that "got into you" and you hope this book will do just that in a less rigourous way.I am an engineering student and I already took an electromagnetic theory course at school and I thought this book would clear some concepts on vector calculus. However it did just the opposite, it over complicated what I already knew.The book is very strange in a way that some times the author tries to excesively dumb down his explanations for you, and other times he will go to the other extreme making no sense to the reader, flashing equations out of the blue, giving no explanations as to how he got certain results, etc... For example he will start by giving a very easy going explanation, something any reader could follow, he will continue his explanation by solving an example, but at somepoint during the development of his example it seems that he forgot all about the reader and got carried away doing his own thing. At times I have to stare at a single page for minutes trying to figure out the 5 or 6 steps he skipped.On the foreword the author tells you what you need to know in order to understand his book, concluding with "an hours time with any reasonable text on the subject should provide you with anything you need to know to follow this text". I strongly disagree with the previous statement, you need a solid background in multivariable calculus and electromagnetism, in fact you need a solid background in vector calculus which is the subject you are trying to learn with this book in the first place!In my opinion if you are trying to learn vector calculus for an electromagnetics course, you are much better off dumping this book and reading Dan Fleisch's "A students guide to Maxwell equations" which covers vector calculus applied to electromagnetics in such a beautiful way. However if your goal is to learn vector calculus for a different subject, I would say that given the amount of previous knowledge on multivariable, vector calculus and electromagnetism you need to know in order to read this book, you are much better with a standard vector calculus book.As one of the reviewers wrote, this book can make a lot of sense reading it back after years of study, but if you are still not a master on the field, then it will just make things worse, like it did it to me...

If you're looking for a book to aid with understanding the fundamentals of multivariable or vector calculus, this is a must.

I took a multivariable calculus course in college and found myself having to revisit the material several years later. I was a theoretical computer science student in graduate school, and am no stranger to mathematical rigor. I found this book exceptionally useful for developing an intuitive understanding of what these operators do (as the title suggests) and equations such as the Laplace and Poisson equation (although I feel like an understanding of complex analysis and the calculus of variations goes a very long way in truly understanding what it means to obey these equations). The development of electro/magnetostatics and the (static) Maxwell's equations on the side is a great added bonus (plus, I believe a lot of these tools were developed for this particular application) - also, it's nice to see real world examples of the concepts.I don't fully agree with the other reviewers that say this is a good book for engineers - a more rigorous treatment should be mandatory for anyone in science or engineering (note: I'm currently doing electrical engineering graduate work). For people learning the material for the first time - this would a fantastic add-on for a more rigorous treatment from another book. It also makes for an excellent review for people who need to brush up (like I did) on vector calculus. The figures in particular are simple, yet very effective in explaining the concepts. Either way, it's a must have for any applied scientists/engineers/math teacher's shelf.

This book is all about intuition rather than rigor.Pros:1) Intuition: Non-rigorous derivations that are so intuitive that it will be easy for everyone to reproduce them and actually really understand the basic ideas behind them.2) Applications to Electromagnetism.3) Figures: A lot of figures mean that you better understand what the author says.4) Quick read due to its small size.Cons:1) Not enough examples: Although the author has justified the existence of the 4th edition largely due to the insertion of more examples, I still think that they are not enough. And the reason is that most of them are trivial. At many occasions I have found that non-trivial exercises give small details that can largely enforce one's intuition and understanding. These kind of examples are simply not here. Maybe they are left as exercises, but it wouldn't hurt if some where examples.2) Author's stubbornness to preserve the small size of the book: While the small size makes for a quick and easy read, it certainly would not hurt if the next edition was bumped up to 200 pages. A lot of meaningful things could be added as there are a lot of topics that beg for this kind of basic yet highly intuitive and pictorial exposition.3) Applications ONLY to electromagnetism: Many students build their basic intuition about field lines on fluids, so it would be very reasonable to have some examples/applications to fluid dynamics. As a second point, I will say that applications to other subjects would have been a pleasant and welcome change from the many applications to electromagnetism.Conclusion:I give it a 4-star rating because while it has many very good points that differentiate it from other books on Vector Calculus, it also has some restrictions. These restrictions are just enough to justify a 4-star rating, although I would gladly give it an easy 5-star rating if it had just a bit more examples.

Sometimes to get to grips with more complex ideas its good to start with a basic understanding, founded around practical ideas, and to learn the underlying abstractions later. The title of the book was really attractive, and sounded like it would sort out these concepts for me straight away. I like mathematical rigor, but was attracted to a volume with less rigor to start with.For me I found that the book came in at too abstract an angle. I later found that I gained a more profound understanding of the concept by reading the book "A Student's guide to Vectors and Tensors" by Daniel Fleisch. It made grad div and curl seem more intuitive to me.

This book is a very useful companion to a course in vector calculus and would certainly be an asset to anyone looking to study electromagnetism. The reason I wouldn't rate higher is because "informal" suggests that the topics can be covered with relatively little mathematical rigour, this is not really possible for a topic such as vector calculus and an understanding of geometric calculus is a major advantage. However, I highly recommend the book for anyone currently taking a course in multivariable calculus as it serves as a welcome alternatives to detailed texts on the subject. The author deserves praise for keeping the presentation of material to the point, but this is subject that on first presentation deserves significant visual association with the subject matter to appreciate geometric interpretations and this book is not designed to fill this role. A great companion but not suitable to learn the subject on its own.

I cant believe this book only has 3 stars at the minute. This book has been around for ages and many people have learnt from it a subject that somehow is prohibitively difficult when learnt from standard textbooks. Come on guys, this is a very cheap book and I would definitely buy this book and any other as good as this if there was any other and if I wanted to learn electromagnetism properly. Particualrly I went through all the exercises and I found them very nice. Some challenging and in the end, it was a very nice experience. Go straight to standard textbooks and I guarantee you wont have half teh fun you can have with this book. They might actually put you off!By the way, I cant believe you can cover this subject in less pages and learn as much as you can from this book. Of course I can simply write down Maxwell's equations and call it a one page book with all covered but you are lying to yourself if you think you will learn this topic in just a few pages. This book is an introdcution and I find it a through one that has exactly the number of pages and questions required for an undergraduate physicist.On a more scientific note, you need to be good at integratinga and differentiating both one and several variables fucntions. Then youc an read this quite comfortably. I would also encourage knowing quite a bit about solving and the meaning of differential equations. After all, the wave (differential) equation is Maxwell's greatest achievement here. the author says you dont need to know much, but if you want to understand the end result I encourage learning them. Besides, who as a scientist wouldnt need differential equations?By the way, have you noticed that many books you read on anything requiring vector calculus recommend this? It must mean something!

Poorly written, barely anything is explained. Worst of all and the reason for writing this review: The solutions to the problems are not included in the massive £30 asking price, you actually have to buy another book. Straight in the bin.