Vector Calculus (3rd Edition) | 
 enlarge | Author: Susan J. Colley
Publisher: Prentice Hall
Category: Book
List Price: $133.20
Buy New: $80.26
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Rating:  17 reviews
Sales Rank: 132060
Media: Hardcover
Edition: 3
Pages: 576
Number Of Items: 1
Shipping Weight (lbs): 2.8
Dimensions (in): 10.1 x 8.2 x 1.2
ISBN: 0131858742
Dewey Decimal Number: 515.63
EAN: 9780131858749
Publication Date: March 26, 2005
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Condition: FAST SHIPMENT. Brand-new book.Excellent condition. Hardcover.Same edition as Amazon listed. Phone # required for P.O.Box.Tks.
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Product Description
For sophomore-level courses in Multivariable Calculus. This text uses the language and notation of vectors and matrices to clarify issues in multivariable calculus. Accessible to anyone with a good background in single-variable calculus, it presents more linear algebra than usually found in a multivariable calculus book. Colley balances this with very clear and expansive exposition, many figures, and numerous, wide-ranging exercises. Instructors will appreciate Colley's writing style, mathematical precision, level of rigor, and full selection of topics treated.
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| Customer Reviews: Read 12 more reviews...
 The best introduction to Vector Calculus ever written March 1, 2002
R. Prabhaharan (Singapore / Malaysia)
21 out of 21 found this review helpful
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.
Perfect text for year-long course in vector calulus October 8, 1999
David P. Lang, Ph.D.(Math), Ph.D.(Phil) (Worcester, MA)
19 out of 21 found this review helpful
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.
A solid, thorough treatment of multivariable calculus. September 10, 1999
17 out of 19 found this review helpful
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.
A book to inspire a math career September 30, 1999
11 out of 12 found this review helpful
This undergraduate text treats its readers as mathematicians. The organization is terrific, the examples are great, and the treatment of material includes explanation and proof, unlike this text's counterparts. It is fortunate to have a clear and insightful treatment of multivariate calculus at the undergraduate level, to inspire more to seriously consider a math career. I think this book has promise of growing the number of math majors around the country.
a very profound and majestic treatment August 6, 2001
11 out of 12 found this review helpful
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.
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