Most Helpful Customer Reviews
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36 of 44 people found the following review helpful:
1.0 out of 5 stars
Difficult to learn multivariable/vector calc from this book, September 13, 2004
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.
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16 of 19 people found the following review helpful:
1.0 out of 5 stars
Inadequate for all purposes, October 7, 2007
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.
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15 of 18 people found the following review helpful:
2.0 out of 5 stars
Not a good intro., March 26, 2004
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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