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Vector Calculus Fifth Edition Edition

49 customer reviews
ISBN-13: 978-0716749929
ISBN-10: 0716749920
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Editorial Reviews

About the Author

JERROLD E. MARSDEN teaches at the California Institute of Technology, Pasadena ANTHONY J. TROMBA teaches at the University of California, Santa Cruz


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Product Details

  • Hardcover: 704 pages
  • Publisher: W. H. Freeman; Fifth Edition edition (August 1, 2003)
  • Language: English
  • ISBN-10: 0716749920
  • ISBN-13: 978-0716749929
  • Product Dimensions: 7.5 x 1.4 x 9.2 inches
  • Shipping Weight: 2.8 pounds
  • Average Customer Review: 2.6 out of 5 stars  See all reviews (49 customer reviews)
  • Amazon Best Sellers Rank: #241,053 in Books (See Top 100 in Books)

Customer Reviews

Most Helpful Customer Reviews

69 of 74 people found the following review helpful By Jonathon DiTroia on January 26, 2010
Format: Hardcover Verified Purchase
Having read some of the reviews written here, I feel compelled to write some brief comments on Marsden's text. If you're the kind of math student who has always learned through repetition of techniques presented by a teacher or professor in non-mathematical language (I'd say this is the majority of non-math major undergraduates), this textbook is a bad choice. Marsden's approach is relatively simple, providing ample explanations that are concise and clear for any individual well-adjusted to "reading Math"... by that, I mean a student who is fluent in mathematical notations and in comprehending proofs. For example, test yourself (here's an actual quotation from the text, taken from the discussion on limits and continuity):

Definition, Open Sets: "Let U be a subset of R^n, we call U an open set for every point x in U there exists some r > 0 such that D(x) is contained within U." [in that sense, we might imagine the open set U to be the open disk or ball of radius r and center x denoted by D(x)]

Now, this is a simple concept; but if you find yourself struggling to understand this definition in a superficial way, you might have some problems with Marsden's text. This is the kind of language that is used throughout the text--its rather bourgeois when compared to other multivariable calculus texts (another reviewer makes the comment that Marsden's text is the self-proclaimed 'aristocrat' of Calculus III texts--I find such a comment quite fitting). If you are one of those struggling individuals that nevertheless decides to use this text, here's some advice:

(1) First, read the introductory section on prerequisites and notation--put some time into understanding how to read math and believe me, it will pay off in a big way.
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36 of 40 people found the following review helpful By A Customer on March 26, 2004
Format: Hardcover
While some of my peers deem "Vector Calculus" to be a fine integration of theory and practice, I'd have to COMPLETELY disagree. From a teaching stand point, it is one of the worst texts out there (at least for a first course). At my university, some of the instructors have tried to use it as the text for the second half of a four quarter calculus sequence. This attempt has met with terrible failure, in my opinion. Most of my students (math majors and engineering students) found the book difficult and perplexing with few examples that pertained to the material they were required to learn. Luckily, the professor for my course was very good at conveying the ideas present without alluding to the text; nevertheless, I spent countless hours in discussion helping my students understand material that most standard texts would have clearly elucidated for them. In fact, at numerous points, the text becomes so involved with its own pedagogy that it neglects to delinate between important, must-know theorems and simply interesting facts.
In addition, only the very first exercises in a given section are useful for most students. A number of the later questions become interesting problems in some upper div. class, but have no bearing on the course at hand. Quite a few of them are not difficult but require "tricks" which often discourage the students by giving them the impression that they don't get the material simply because they couldn't come up with the solutions to these extraneous questions.
I would strongly recommend Stewart's text (for those of you on the West Coast) and Salas and Hille's text (for those of you in the Southwest).
Prehaps, Marsden's text would be o.k. for a more advanced course on vector calc. or as a go-between supplement for a more rigorous text.
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35 of 40 people found the following review helpful By An unimpressed student on October 7, 2007
Format: Hardcover
This book's target audience is a little unclear. Ostensibly, this is a somewhat more rigorous treatment of multivariable calculus than a typical second-year sequence, but in fact this book is absolutely deficient as an analytical text. There are very few proofs in the book--the proofs of most theorems are relegated to an "internet supplement"--and the ones that are included are at far too low a level and fail to do what the theorems of a good text ought to do: gradually and methodically develop the topic. In some cases, such as the implicit function theorem, the statement of the theorem is just plain convoluted, apparently because the authors attempted to strike some kind of balance between being mathematically correct and working within the comfort zone of students coming out of low-level math courses.

Furthermore, nothing in the book is taught at an appropriate level of generality. For example, many "proofs" involve low-level calculations of dot products when it would be far more elegant, not to mention mathematically preferable, to use the general properties of inner product spaces instead. Many theorems and formulas are stated only for cases in which the domain is in two or three dimensions rather than working in n-dimensional vector spaces, and the complex field is essentially absent from the entire work.

So, since the book is not an analytical treatment, is it useful as a "standard" multivariable text? No. It's extremely difficult to learn the material for the first time from this book because there are numerous unexplained leaps, and examples are scarce.
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