Rating: 
Summary: My wife thinks I am crazy but I love this book!
Review: As a graduate student in Electrical Engineering, I needed a book to help me review vector calculus. After much searching, I bought this book. It was worth every penny.Unlike any other book on math I have read...this author IS FUNNY. Granted, it is not funny every sentence but I found myself laughing at points in this book; looking up to notice only quizzical looks from my wife. I admit humor in a math book is a rare thing. But the humor is just an element of the author's easy-to-comprehend style. This book takes a very difficult topic and makes it approachable. A great book for students of vector calculus who need a new approach to understand the material.
Rating:
Summary: Excellent book, but not as a stand-alone text
Review: As an undergraduate, I've already taken a course in multivariable calculus, and I found this text to be a quick and accessible review (you can read it in one sitting). That being said, I'm not sure if I would have gotten much out of it if I hadn't already had exposure to the subject. In addition to single-variable calculus, the book assumes knowledge of double and triple integration, which I didn't learn until I took a course in multivariable calculus. If you really want to learn the subject, but can't take a course in it for whatever reason, I'd recommend actually spending the $100 or so it takes to buy a textbook, and working through it on your own. I used "Vector Calculus" by Marsden and Tromba, which was adequate for my purposes. If you're not good at translating mathematical jargon into everyday language, you'll find "Div, Grad, and Curl" to be a useful supplement. I had better insight into the physical meaning of the del operator after reading it.
Rating: 
Summary: An Excellent Overview of Vector Calculus
Review: 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 text?? 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 this a great refresher, I wanted to own it as a reference. When I inevitably forget again what "del cross F" means, I can look it up in this clear and simple book.
Rating:
Summary: An Excellent Overview of Vector Calculus
Review: 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 text?? 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 this a great refresher, I wanted to own it as a reference. When I inevitably forget again what "del cross F" means, I can look it up in this clear and simple book.
Rating: 
Summary: Friendly but vacuous
Review: I recently began an intensive review of electromagnetic theory, having used it very little in my career as a circuit designer having graduated with an EE degree twenty-two years ago. Since a knowledge of vector analysis is essential to understanding the physical interpretation of Maxwell's equations, I needed a way to quickly review the relevant information about vector analysis to prepare for this journey. The book turned out to be perfect for that task. The author assumes that the reader already knows what a vector is, and how the fundamental vector operations such as dot product and cross product are computed. He begins by introducing the motivating example of the need to calculate the electric field in a region. This example serves as the unifying thread of the book, keeping the reader focused on a concrete goal and providing motivation for the discussion. The ideas of vector analysis are introduced step-by-step as pieces of the puzzle needed to calculate the field. On the way, he uses many illustrations which greatly help to clarify the physical interpretation of the various vector operations. Despite the apparent appeal to intuition that this technique represents, there is actually substantial mathematical rigor in his approach to many of the topics discussed. He does a number of proofs of various theorems, such as the divergence theorem. These proofs might not be as rigorous as a mathematician would like, but his technique avoids the often distracting detail present in a more formal mathematical approach. The understanding of vector analysis concepts acquired by reading the book prevents the engineer studying field theory from being overwhelmed by what might otherwise appear to be meaningless mathematical abstraction. Any EE student who is about to study EM theory but has not yet had a class specifically dedicated to vector analysis would benefit greatly by reading this book. It's also excellent for people like myself who need an intensive review of the subject after having been away from it for many years. I know it will save me many hours that would have otherwise been spent either trying to understand some topic insufficiently discussed in the field theory texts, or trying to sift out the relevant material that's discussed in excruciating detail in a more formal mathematical text.
Rating:
Summary: What to expect
Review: I thought this book was an excellent introduction to the subject of Vector Calculus without drowning the reader with overbearing mathematical formalisms. This book gives the reader a friendly taste of an interesting mathematical concept. This book was an interesting and educational read. You must get your feet wet before learning how to swim.
Rating:
Summary: A must for engineering and science students.
Review: 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!
Rating:
Summary: A must for engineering and science students.
Review: 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!
Rating:
Summary: Vector calculus presented from an applied approach
Review: If you've taken (or are in the process of taking) vector calculus (whether an intro in multivariable calculus or as a class itself) this book is indispensible for support. It's best feature is the fact that physics and engineering students can benefit from it's applied viewpoint, specifically on electric charge, potential. etc. The title of the book is established quite well in that this book is a relatively light read and that the reader will be able to comprehend vector calculus with an understanding of why scientists use vector calc in the first place. Overall, an excellent read with the answers to selected exercises placed in the back allow the reader to monitor learning.
Rating:
Summary: For an informal test it's good
Review: This book is good for learning concepts but bad for actually learning how to do Vector Calculus problems.
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