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Rating: 
Summary: Little confusing
Review: I have been using this book for a course in Vector Cal. this
semester. I have to say that the large price tag was a big turn
off to start, but I can get past that if the book is worth it. So far I am not impressed with this book. The examples are poor and the methods taught are a little confusing at best. Some have
found this book to be great in the way that the material is explained but I had some serious issues with the way the material was presented. I ended up buying several other books on vector calculus and using internet sites from other universities to supplement this book. As a stand alone this book has some serious issues. Try to avoid it if you can.
Rating: 
Summary: Perfect text for year-long course in vector calulus
Review: I have examined a number of textbooks in multi-variable calculus, and I conclude that this is the best of the recent breed. The theory is well-motivated by discussion and illustrative examples, yet presented as rigorously as possible at this level. The applications (especially to physics) are outstanding, the text examples illuminating, and the exercises both doable and beneficial for enhancing comprehension through sufficient practice. The negative comments that this highly competent and well-structured book has received are entirely unfair, failing to render a realistic assessment of its real value. I wonder whether they are referring to the same obviously proficent author and the same publication (which I read nearly cover-to-cover). The only drawback is that the great amount of material cannot (by the author's own admission) be covered in one semester; it would require an entire academic year to do adequate justice to all the essential topics.
Rating:
Summary: Perfect text for year-long course in vector calulus
Review: I have examined a number of textbooks in multi-variable calculus, and I conclude that this is the best of the recent breed. The theory is well-motivated by discussion and illustrative examples, yet presented as rigorously as possible at this level. The applications (especially to physics) are outstanding, the text examples illuminating, and the exercises both doable and beneficial for enhancing comprehension through sufficient practice. The negative comments that this highly competent and well-structured book has received are entirely unfair, failing to render a realistic assessment of its real value. I wonder whether they are referring to the same obviously proficent author and the same publication (which I read nearly cover-to-cover). The only drawback is that the great amount of material cannot (by the author's own admission) be covered in one semester; it would require an entire academic year to do adequate justice to all the essential topics.
Rating:
Summary: wonderful book
Review: I love this book. Unlike most math majors who get through life by memorizing formulas in a relatively brainless activity, this book actually explains why/how things work. If you take the time to go through this book step by step, examples and all, you will get a beautiful understanding of multivariable calculus. I enjoyed both geometry and single variable calculus a lot, and multivariable calculus is a nice combo of those two.
Rating:
Summary: A solid, thorough treatment of multivariable calculus.
Review: I used Susan Colley's Vector Calculus when I took multivariable calculus in the spring of '99. The book is very well written and I would definitely recommend it to anyone, but most especially to those who have a strong interest in the subject and aren't just fulfilling a requirement. Here is why--When the reader is presented with an mathematical idea, it is nice to know where that idea comes from, and to be given whatever explanations or proofs are needed. An example of where Colley does this is in the chapter on the chain rule in several variables. This is a difficult chapter and Colley does an excellent job of explaining the underlying concepts (with lots of visual aids) where a less thorough author might have simply offered formulas and methods to solve a few specific types of problems. Also, Colley introduces vector notation which, although at first unfamiliar, ultimately leads to a better understanding of the relationships between functions of different numbers of variables. For example, instead of the notation f(x,y,z,w,...) we have f(x->) (the arrow indicates that x is a vector). This notation, as well as the extensive use of matrices is very helpful and eliminates much confusion. The visuals are simple and easy to understand, and the problems are appropriately designed, with plenty of very simple exercises for dealing with basic calculations, as well as very challenging and thought-provoking problems which require plenty of thought and help develop good mathematical intuition and visualization. Overall this is a very good book, and it appears to me that the other reviews on this page come from neither a good knowledge of the book nor multivariable calculus.
Rating:
Summary: a very profound and majestic treatment
Review: Of all the math texts I have ever read, this is the first one which really seems infused with great enthusiasm for the subject as well as with humor. It is the textbook that one would use if one didn't want to just memorize techniques and formulas with little understanding, but wanted to have as deep and as beautiful (not to mention fun) appreciation of the subject as possible without being dragged down in minutiae. The people who criticized it were probably frustrated by the book because it really tries to bring the reader into the almost magical world of multivariable calculus so she or he may marvel at it. But to do so takes a great deal of effort, so people who just wanted to know how and not why would certainly prefer a different text. Being a Oberlin student myself, as the critics were, I understand that in the midst of all their other classes and being confronted for the first time with real math (multivariable is definitely a step up in difficulty from ordinary calculus) they could be frustrated by such an approach. But, I'm not an even a math minor and I was so happy to be able to use this text and not your standard blah-blah, humorless, lifeless,and arcane math text. Bottom line: if you want to understand come here; if you want to just do seek another text.
Rating:
Summary: Awesome
Review: Professor Colley's book excels in all the areas one would look for including abundant examples, fine graphics, excellent graded problems, clear writing, good organization and so on. It stands out particularly for the author's sensitive presentation which not only presents the material in a clear, logical form but in such a way as to anticipate the questions of the reader. The use of geometric intuition is especially effective. Not being a great talent at mathematics, I found that this book clarified many ideas that I had not understood before. How the negative critics came up with their ideas is a mystery.
Rating:
Summary: Awesome
Review: Professor Colley's book excels in all the areas one would look for including abundant examples, fine graphics, excellent graded problems, clear writing, good organization and so on. It stands out particularly for the author's sensitive presentation which not only presents the material in a clear, logical form but in such a way as to anticipate the questions of the reader. The use of geometric intuition is especially effective. Not being a great talent at mathematics, I found that this book clarified many ideas that I had not understood before. How the negative critics came up with their ideas is a mystery.
Rating: 
Summary: A very poor mathematics text indeed
Review: The author has written a carefully thought out introduction to the subject whose only assumptions are that you know the most rudimentary coordinate geometry and single variable calculus. From this all the classical subjects in vector calculus are built up using geometric ideas to motivate the definitions of the concepts. Typically the first course in vector calculus tries to get to Stokes Theorem and so on as quickly as possible without explaining what motivated these ideas. Much of the technical apparatus in vector calculus was used in modelling fluid dynamic flows in the nineteenth century, this is where the idea of "vector field" came from. As far as I know, this is the first vector calculus book I've read that defines a vector field, and next to it shows a picture of water flowing out of an upturned cup, with velocity vectors pointing in all directions. Just one picture captures the essence of the definition and immediately renders concrete something very abstract. There are many other examples in the book where a picture is shown of an abstract concept, making the definitions and theorems intuitive.
However, this book is not just pretty pictures, the calculus is built up in a rigorous manner (as far as a first introduction to the subject goes) and by the end of the book you are well placed to read your first book on manifolds and differential geometry. The book is not cheap, but if you think about it in terms of if you wanted to replicate this book you'd need at least 3 other standard textbooks, then its reasonable. Even advanced mathematicians would be surprised how much they could learn by looking at some of the pictures ! This book would be ideal as an appetiser before a main course of graduate differential geometry.
Rating:
Summary: DO NOT BUY THIS TEXTBOOK!
Review: This is most likely the most miserable math textbook I have ever had the misfortune to read. I showed it to my Mom (who has a Master's Degree in Math) thinking perhaps I was simply really stupid and she agreed that this textbook is abysmal. For example, the proofs often go into great detail concerning the arithmetic of the proof, but then the author fails to state clearly by what principle she jumps from one step of the proof to another. The great bonding session for the 13 members of my class has been comiserating over the poor quality of the textbook and trading tips about better Multivariable/Vector Calculus texts to buy in order to elucidate the material presented in Colley. Perhaps math professors find this book wonderful, but if the point of the text is to teach Multivariable Calculus to less than math-genius students (who are nevertheless somewhat adept at math) the text completely fails. If you have to get this text for your class because your teacher doesn't care whether his students actually learn the material, get an accompanying text to help. I have been using my brother's Multivariable text (by Larson, Hostetler, and Edwards) and another person in my class highly recommended Stewart's treatment of Multivariable Calculus.
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