Rating: 
Summary: The Perfect Book for Vector Calculus
Review: After you've learned calculus from a book like Stewart's, this is the definite next step. It includes lots of proofs for most of the theorems. I love the way the textbook is organized. And all the explanations are incredibly clear. The choice of notation makes all the formulas a lot clearer than in other books. Although I am not as big a fan of math as I am of physics, I must say that I really enjoyed reading this book a lot, and believe you will too. This book seriously makes advanced calculus incredibly fun!
Rating: 
Summary: A good reference for vector calculus.
Review: As a student studying mathematics, this book has proved to be a valuable aid. The explainations are good, and the practice questions have been worthile for revising for exams. Although it is expensive, it will be useful throughout my course - so it is worthwhile.
Rating: 
Summary: A good book for a quick reference
Review: First of all. I have mostle used the second part of this book, that is, double, triple, line and surface integration. I have read some pages of the first part but not much. I will focus on the title. This boos is good as a quick reference for some information. Have you forgotten Stokes Therome? No problem, you will find it fast. Don't know how to parametrize an helicoid? Well, look in page number ... Examples are good and information is somewhat ordered in a good way, except maybe some things about vector fields. In the bad side. This book is not rigorous. It focus a lot with "graphics" demonstrations, which renders it quite bad in a strictly theoretical point of view. Some of the examples should have been somewhat more clear. More tome should be spent in a more formal tratment of parametrization of curves and surfaces.Conclution: buy it if you just need it for some practical thing. That is, if you need this book just to have some ideas of how to do vectorial calculus wihtout caring much for justification, go for it. Otherwise, drop it. Maybe Calculus from Apostol is a better choice for a rigorous treatment of the subject.
Rating: 
Summary: Relatively weak as a standard textbook on vector calculus
Review: I am well aware of the usefulness of these reviews in determining the applicability of a book for self-study; so let me address this quickly. This has got to be the worst vector calculus book available if you're looking to study the subject on your own!!! This book is frustrating and dry; please consider other self-study options! Unfortunately, most people who use this text are required to for a class, and for whatever reason, this book has become somewhat of a standard at many universities. I used this book a while back in a Vector Calculus class at UT Austin, and I was largely disappointed by its contents. First of all, the author of the book is dry and completely uninspiring. That's not to say that people read calculus books like novels, but the author presents the material from a strictly technical and theoretical perspective. Further adding to its blandness, the author (or the publisher) has opted for the cost-effective choice of using no color in the book. The graphs and figures are confused and lacking - often difficult to understand. Now, the obvious rebuttal to my accusations will come from purists (hardcore math majors). I am, myself, a math (and physics) major, and though I am not saying that this text is completely inaccessible, I have to say that the author wrote this book wholly without imagination or sincerity. There is no emphasis on vector calculus' usefulness to applied mathematical sciences or other areas of math (if I do recall, though, a bit is addressed in association with integral theorems). The only reason I give this book two stars is that the later parts of the book offer a peak at more advanced topics in geometry. Last, and perhaps most inexcusable, the book requires an errata as a full supplement (I'm not exaggerating). This book is littered with errors, and not just grammatical typos! I suffered a couple of times on assignments due to incorrect formulas in the book. For example, the edition of the book I used gave the incorrect formula for the second derivative test! Now come on, they're actually charging people for this!!!
Rating:
Summary: Relatively weak as a standard textbook on vector calculus
Review: I am well aware of the usefulness of these reviews in determining the applicability of a book for self-study; so let me address this quickly. This has got to be the worst vector calculus book available if you're looking to study the subject on your own!!! This book is frustrating and dry; please consider other self-study options! Unfortunately, most people who use this text are required to for a class, and for whatever reason, this book has become somewhat of a standard at many universities. I used this book a while back in a Vector Calculus class at UT Austin, and I was largely disappointed by its contents. First of all, the author of the book is dry and completely uninspiring. That's not to say that people read calculus books like novels, but the author presents the material from a strictly technical and theoretical perspective. Further adding to its blandness, the author (or the publisher) has opted for the cost-effective choice of using no color in the book. The graphs and figures are confused and lacking - often difficult to understand. Now, the obvious rebuttal to my accusations will come from purists (hardcore math majors). I am, myself, a math (and physics) major, and though I am not saying that this text is completely inaccessible, I have to say that the author wrote this book wholly without imagination or sincerity. There is no emphasis on vector calculus' usefulness to applied mathematical sciences or other areas of math (if I do recall, though, a bit is addressed in association with integral theorems). The only reason I give this book two stars is that the later parts of the book offer a peak at more advanced topics in geometry. Last, and perhaps most inexcusable, the book requires an errata as a full supplement (I'm not exaggerating). This book is littered with errors, and not just grammatical typos! I suffered a couple of times on assignments due to incorrect formulas in the book. For example, the edition of the book I used gave the incorrect formula for the second derivative test! Now come on, they're actually charging people for this!!!
Rating:
Summary: An Average Book, Too many mistakes
Review: I had this book as my text book when I took a graduate-level vector calculus course in Purdue. Basically this book gives a pretty good explaination on the subject of vector calculus, however its shortcoming is that it contains many errors and typos which scattered throughout the text and the problem sets. A fourth edition book should not contain that many mistakes. For example in the application section one of the Maxwell's equations is incorrectly termed. div(D) = p but in the book it is written div(E) = p. Note D=eE where e is the permittivity, so, it should be div(E)=p/e (assuming a simple medium, ie isotropic, linear and homogenous). What leaves me a really deep impression throughout my vector calculus classes was that the professor kept shaking his head while telling us what corrections needed to be made for a particular section or/and problem(s). In view of the price of this book and its quality, I won't recommend it.
Rating: 
Summary: Difficult to learn multivariable/vector calc from this book
Review: I have had several other math courses prior to and concurrent with the one in which I used Marsden and Tromba's Vector Calculus, including some of the toughest 400-level undergrad math courses at Cornell. I have done well in all of them and have understood the textbooks just fine. In my single-variable calculus courses, I got rare perfect scores on some of the exams. In high school, I ranked #8 in Maryland in the statewide math competition. Furthermore, reading comprehension is one of my greatest strengths. On standardized tests such as the GRE and SAT, I always get a perfect or near-perfect score on the reading comprehension questions. When I used Marsden and Tromba's Vector Calculus in my multivariable calculus class, I read the chapters both before and after the corresponding lectures. I spent many hours over each one, trying to understand it and working through those examples that were given. In spite of all of this, I found most of Marsden and Tromba's Vector Calculus extremely difficult to understand. (Chapter 1 was the biggest exception--it was easy.) I consider this especially problematic in a multivariable calculus course because I think it is very difficult to learn the material by lecture.
Essentially, for most of the material in Marsden and Tromba's Vector Calculus, I did not understand it until after I had learned the material by doggedly slogging through problems without the benefit of prior understanding. (By the way, many of the problems from Marsden and Tromba's Vector Calculus, at least the problems we were assigned by our professors, were far too difficult. A lot of these problems required tricks or unnecessarily difficult steps, rather than just having us practice the material we were supposed to be learning. And yet I don't think the professors were just assigning us the harder questions from the book.)
I can understand why faculty members like this book. They understand the material already. They look at this book and they see the material presented succinctly and in a way that resembles, more than the ways in most textbooks, the way that academic mathematicians do math. The problem with this way is that it is is extremely difficult for a person to understand when learning the material for the first time. Understanding the material is necessary for becoming proficient in math. Without that, a high-level presentation style is of little use. With this book, the self-described "aristocrat of multivariable calculus textbooks," I believe that a student sees a high-level presentation style, but has a hard time building understanding.
For one section, late in the course, I picked up another text instead (an old edition of Adams, which was the only multivariable calc book left at a used booksale I went to). Even though the notation in Adams was different from what I'd been seeing so far in the semester, I understood the material quickly and learned it better.
If you are a faculty member, I urge you to select, or push for the selection of, another textbook. If you are a student assigned this book, I suggest that you might consider the following:
- Use another multivariable calculus textbook in conjunction with it. Perhaps there is some multivariable calc book that is designed to be an auxiliary text, as the Schaum's Guides are.
- Print out this review and/or others of the same book from Amazon and show them to your professor, either to ask for advice on avoiding an experience like mine or to raise their awareness about how this book may be for students.
Rating:
Summary: mathematical beauty at its best
Review: I love this textbook and highly recommend it to any math major. The book is fairly technical, but the explanations are brilliant. And the authors really do try to give the student an intuitive understanding of what the underlying concepts mean (e.g. the explanation of the curl operator). Like any technical text, don't expect to read it like a novel. Applications are of periphery importance in the text (if it doesn't have "Applications" in the title, don't expect applications!)
Rating:
Summary: The BEST book on undergraduate vector calculus
Review: I taught myself vector calculus from this book. It is clear, concise, and fabulously well written. Though it doubtlessly makes an valuable reference, you will enjoy just reading it from cover to cover. Really a treat, worth the price.
Rating:
Summary: A nice book using a modern view of vector calculus
Review: I used this book when I was an undergraduate. At the time, I found the lack of practical problems and motivation frustrating and difficult to read. I did not have an apprieciation for the beauty of the presentation. Now that I have a Ph.D. and am a professor in Mechanical Engineering working in the area of Computational Mechanics, I find myself pulling this book off my shelf often to review fundamental vector concepts, especially in Chapters 6 and 7 on integrals over paths and surfaces and Green's, Stokes', Gauss', theorems from a modern and clean derivation. I would highly recommend this book to graduate students but do not recommend the book for undergraduate students.
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