Vector Calculus [Hardcover]

Jerrold E. Marsden (Author), Anthony J. Tromba (Author)

Book Description

ISBN-10: 0716724324 | ISBN-13: 978-0716724322 | Publication Date: April 1996 | Edition: 4th

This acclaimed course in the calculus of functions of several variables and vector analysis is aimed mainly at second-year undergraduates. Marsden and Tromba provide a concrete, student-oriented text that fosters computational skills and intuitive understanding. The Fourth Edition maintains the balance between theory, applications, optional materials and historical notes present in earlier editions, but has been refined throughout. "This is a superbly produced book, whose clear and orderly presentation and informative diagrams immediately invite closer study ...The best way to evaluate a textbook is to teach from it, and it is clear from the companion study guide by Pao and Soon that it has passed this test." The Mathematical Gazette Supplements: Student Guide/Instructor's Manual

Editorial Reviews

About the Author

JEROME E. MARSDEN teaches at the California Institute of Technology, Pasadena - ANTHONY J. TROMBA teaches at the University of California, Santa Cruz --This text refers to an alternate Hardcover edition.

Product Details

• Hardcover: 704 pages
• Publisher: W H Freeman & Co (Sd); 4th edition (April 1996)
• Language: English
• ISBN-10: 0716724324
• ISBN-13: 978-0716724322
• Product Dimensions: 9.6 x 7.6 x 1.4 inches
• Shipping Weight: 2.8 pounds
• Average Customer Review: 2.5 out of 5 stars  See all reviews (61 customer reviews)
• Amazon Best Sellers Rank: #501,952 in Books (See Top 100 in Books)

Customer Reviews

Most Helpful Customer Reviews

32 of 35 people found the following review helpful:

4.0 out of 5 stars A Fair Review, a Text Not For Everyone, January 26, 2010

By 

Jonathon DiTroia "Jonny" (Baltimore, MD) - See all my reviews
(REAL NAME)   

Amazon Verified Purchase

This review is from: Vector Calculus (Hardcover)

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.

(2) You have to think of this text as all or nothing. If you don't use it, fine; if you do, YOU MUST rely on the text throughout the entire course, i.e. read everything (except perhaps for the historical information)... this is critical because by reading all the chapters and sections, you'll find that you'll begin to develop an ability to read the text efficiently, i.e. your math-reading skills will increase dramatically. If instead, you choose to rely on your class notes and turn to this book when you need clarification, you won't find it simply because you won't understand what you're reading.

(3) This is obvious: work all example problems as you read the text. I've found the examples to be easier than those in the exercises (other reviewers have made this observation as well), but with some help from your TA (or novel thinking on your part), you should never feel lost in attempting to solve these problems (given that you've invested the time to really understand those examples).

(4) If you have experience in Linear Algebra, you're in a much stronger position to succeed with the text. Even though Marsden introduces the topics you'll need, obviously, the experience can only help you.

(5) In difference to the common opinion, Calculus III is actually an easy course--only right up until the end (chapters 7 & 8), does the material become much more difficult. Unfortunately, in my opinion, the most poorly written chapters in the text are chapters 7 and 8. So, a word of advice: if you find yourself coasting throughout the course, be aware that the material gets harder--and be prepared for that dramatic change in difficulty. Though Marsden 'gets the job done' in explaining the material, for all students, I'd recommend thinking about a supplement text for these 2 chapters (or very good class notes; one learns chapters 7 & 8 by working through example problem after example problem).

(6) Buy (or better yet go to your college's library and find) the student solutions manual! Assign yourself problems to practice before tests; as with all quantitative and physical science courses, one learns by solving problems, bottom line.

In summary, Marsden is a good text; its simple for the trained math reader (by that, I don't mean only professors!), but very very difficult to inexperienced students. It's not light reading, and it's going to challenge you; but for those that put in the time, you'll find that the book is very logical and well-organized in its presentation of the material.

28 of 32 people found the following review helpful:

2.0 out of 5 stars Not a good intro., March 26, 2004

By 

"durathae" (Los Angeles, CA United States) - See all my reviews

This review is from: Vector Calculus (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.

28 of 33 people found the following review helpful:

1.0 out of 5 stars Inadequate for all purposes, October 7, 2007

By 

An unimpressed student (Milwaukee, WI USA) - See all my reviews

This review is from: Vector Calculus (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. The exercises are useless for developing one's understanding; as other reviewers correctly noted, they frequently involve only a brief calculus setup followed by needlessly contorted algebraic operations, and students are likely to second-guess themselves when they arrive at (correct) answers that are so complicated they look wrong.

Part of the problem is that Marsden and Tromba's text is far shorter than the bulky book makes it appear. The margins, type, and spacing are outrageously generous; many pages are devoted to cute but unnecessary and often irrelevant history essays; and the pictures and figures (whose colors are badly aligned) take up huge amounts of space on the page. There is a vast amount of wasted space that could have been occupied by proofs, examples, motivation for the development of the subject, etc. It's just not worth the price of a textbook to have something with so little useful material.